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A comparison is conducted between measured velocities for the buoyant rise of single bubbles of varying size and composition, in a soda-lime silicate glass melt, with the steady state velocities predicted by the Stokes and Hadamard-Rybczynski formulas. In all cases, the data are noted to fit the Hadamard-Rybczynski expression for steady state rise speed considerably better than the Stokes formula.
The effect of very low speed forced flows on the size and shape of a solid fuel diffusion flame are investigated experimentally. Flows due to natural convection are eliminated by performing the experiment in low gravity. The range of velocities tested is 1.5 cm/s to 6.3 cm/s and the mole fraction of oxygen in the O2/N2 atmosphere ranges from 0.15 to 0.19. The flames did not reach steady state in the 5.2 sec to which the experiment was limited. Despite limited data, trends in the transient flame temperature and, by means of extrapolation, the steady state flame size are deduced. As the flow velocity is reduced, the flames move farther from the fuel surface, and the transient flame temperature is lowered. As the oxygen concentration is reduced the flames move closer to the fuel sample and the transient flame temperature is reduced. With stand off distances up to 8.5 + or - 0.7 mm and thicknesses around 1 or 2 mm, these flames are much weaker than flames observed at normal gravity. Based on the performance of the equipment and several qualitative observations, suggestions for future work are made.
A numerical method for solving the isenthalpic form of the governing equations for compressible viscous and inviscid flows was developed. The method was based on the concept of flux vector splitting in its implicit form. The method was tested on several demanding inviscid and viscous configurations. Two different forms of the implicit operator were investigated. The time marching to steady state was accelerated by the implementation of the multigrid procedure. Its various forms very effectively increased the rate of convergence of the present scheme. High quality steady state results were obtained in most of the test cases; these required only short computational times due to the relative efficiency of the basic method.
This is the user's manual for the TETRA 2 Computer Code, a program developed in the NASA-Lewis Blade Loss Program. TETRA 2 calculates a turbine engine's dynamic structural response from applied stimuli. The calculation options are: (1) transient response; and (2) steady state forced response. Based on the method of modal syntheses, the program allows the use of linear, as well as nonlinear connecting elements. Both transient and steady state options can include: flexible Bladed Disk Module, and Nonlinear Connecting Elements (including deadband, hardening/softening spring). The transient option has the additional capability to calculate response with a squeeze film bearing module. TETRA 2 output is summarized in a plotfile which permits post processing such as FFT or graphical animation with the proper software and computer equipment.
Accurate estimates of the mass, stiffness, and damping characteristics of a structure is necessary for determining the control laws best suited for active control methodologies. There are several modal identification techniques available for determining the frequencies, damping ratios, and mode shapes of a structure. However, modal identification methods in both the frequency and time domains have difficulties for certain circumstances. Frequency domain techniques which utilize the steady-state response from various harmonic inputs often encounter difficulties when the frequencies are closely distributed, the structure exhibits a high degree of damping, or the steady-state condition is hard to establish. Time domain techniques have produced successful results, but lack robustness with respect to measurement noise. In this paper, two identification techniques and an estimation method are combined to form a time-domain technique to accurately identify the mass, stiffness, and damping matrices from noisy measurements.
Experimental data validating advanced engine designs at three thrust levels (5, 15, and 100 lbF) is presented. All of the three engine designs considered employ a Moog bipropellant torque motor valve, platelet injector design, and iridium-lined rhenium combustion chamber. Attention is focused on the performance, robustness, duration, and flexibility characteristics of the engines. It is noted that the 5- and 15-lbF thrust engines can deliver a steady state specific impulse in excess of 310 lbF-sec/lbm at an area ratio of 150:1, while the 150-lbF thrust engines deliver a steady state specific impulse of 320 lbF-sec/lbm at an area ratio of 250:1. The hot-fire test results reveal specific impulse improvements of 15 to 25 sec over conventional fuel film cooled columbium chamber designs while operating at maximum chamber temperatures.
Current status of a steady state, axisymmetric analysis of an experimental 11 inch diameter hybrid rocket motor internal flow field is given. The objective of this effort is to develop a steady state axisymmetric model of the 11 inch hybrid rocket motor which can be used as a design and/or analytical tool. A test hardware description, modeling approach, and future plans are given. The analysis was performed with FDNS implementing several finite rate chemistry sets. A converged solution for a two equation and five species set on a 'fine' grid is shown.
In this paper, the two dimensional(radial and circumferential) transient Navier-Stokes equations are used to solve the hydrodynamic problem in conjunction with the time dependent motion of the journal, and the deformable, spring supported foil. The elastic deformation of the foil and its supports are simulated by a finite element model. The time-dependent Navier-Stokes formulation is used to solve for the interaction between the fluid lubricant, the motion of the journal and the deformable foil boundary. The steady state, the quasi-transient and the full transient dynamic simulation of the foil-fluid journal interaction are examined on a comparative basis. For the steady state simulation, the fluid lubricant pressures are evaluated for a particular journal position, by means of an iterative scheme until convergence is achieved in both the fluid pressures and the corresponding foil deformation. For the quasi-transient case, the transient motion of the journal is calculated using a numerical integration scheme for the velocity and displacement of the journal. The deformation of the foil is evaluated through numerical iteration in feedback mode with the fluid film pressure generated by the journal motion until convergence at every time step is achieved. For the full transient simulation, a parallel real-time integration scheme is used to evaluate simultaneously the new journal position and the new deformed shape of the foil at each time step. The pressure of the fluid lubricant is iterated jointly with the corresponding journal position and the deformed foil geometry until convergence is achieved. A variable time-stepping Newmark-Beta integration procedure is used to evaluate the transient dynamics at each time step of the bearing.
Chorin's method of artificial compressibility is extended to both compressible and incompressible fluids by using physical arguments to define artificial fluid properties that make up a local preconditioning matrix. In particular, perturbation expansions are used to provide appropriate temporal derivatives for the equations of motion at both low speeds and low Reynolds numbers. These limiting forms are then combined into a single function that smoothly merges into the physical time derivatives at high speeds so that the equations are left unchanged at transonic, high Reynolds number conditions. The effectiveness of the resulting preconditioning procedures for the Navier-Stokes equations is demonstrated for a wide speed and Reynolds number ranges by means of stability results and computational solutions. Nevertheless, the preconditioned equations sometimes fail to provide a solution for applications for which the non-preconditioned equations converge. Often this is because the reduced dissipation in the preconditioned equations results in an unsteady solution while the more dissipative non-preconditioned equations result in a steady state. Problems of this type represent a computational challenge; it is important to distinguish between non-convergence of algorithms, and the non-existence of steady state solutions.
Simplified algebraic area specific impedance (ASI) correlations have been developed for solid-state composite battery electrodes made of a single ion conducting electrolyte, conductive additive, and intercalation active material. Two ASI expressions were developed, one for short times ( i.e. , pulsed power operation) and another for the pseudo steady state operation (i.e., sustained discharge for energy estimation). A full electrochemical model based on porous electrode theory was developed to examine the accuracy of the simplified ASI expressions. The simplified expressions agree favorably with full model results over a wide range of parameters (i.e. , electrode thicknesses, electrolyte conductivities, solid-state diffusion coefficients, specific surface areas, etc.) and conditions (i.e. , C-rates, states of charge, and pulse times). Under most conditions, the error between the full model and the correlations is well below 7 %. Higher errors were observed for the pseudo steady state expression at high/ low states of charge where the assumption of uniform reaction distributions loses validity. Here, the short time ASI has higher error at low states of charge due to the nonlinearity of the open circuit voltage equation, which is assumed linear in the formulation of the simplified algebraic expression.
Tritium inventory reduction for fusion power plants is central to the successful adoption of fusion energy. The advent of direct internal recycling in deuterium-tritium fusion fuel cycle design has led to significant reduction in startup tritium inventory estimates for fusion power plants but requires an isotope rebalancing and protium removal (IRPR) system to ensure acceptable isotopic fuel composition. Cryogenic distillation is a potential solution for near-term deployment in an IRPR system due to its demonstrated performance in similar operating regimes. Using protium removal in the fuel cycle as the primary performance metric, this paper presents an optimization methodology for a single-column continuous cryogenic distillation-based IRPR system for a 500 MW fus magnetic fusion device. Distillation column optimization was performed using the CryOgenic Distillation For Isotopic Separation of Hydrogen (CODFISH) code developed at Savannah River National Laboratory. The distillation column design presented maximizes direct recycling of hydrogen isotopes from the fusion chamber exhaust to the fueling system while minimizing IRPR system steady-state tritium inventory. The optimized IRPR distillation column presented achieves direct recycling of 60 % of the hydrogen isotopes in the fusion chamber exhaust with an estimated steady-state system tritium inventory <30 g. In conclusion, the optimized IRPR distillation column operation was then used to estimate the design requirements for a detritation column to treat the IRPR system effluent stream.
A tokamak, a torus-shaped nuclear fusion device, needs an electric current in the plasma to produce magnetic field in the poloidal direction for confining fusion plasmas. Plasma current is conventionally generated by electromagnetic induction. However, for a steady-state fusion reactor, minimizing the inductive current is essential to extend the tokamak operating duration. Several non-inductive current drive schemes have been developed for steady-state operations such as radio-frequency waves and neutral beams. However, commercial reactors require minimal use of these external sources to maximize the fusion gain, Q, the ratio of the fusion power to the external power. Apart from these external current drives, a self-generated current, so-called bootstrap current, was predicted theoretically and demonstrated experimentally. Here, we reveal another self-generated current that can exist in a tokamak and this has not yet been discussed by present theories. We report conclusive experimental evidence of this self-generated current observed in the KSTAR tokamak.
Recently, a method to achieve a “natural hot-ion mode” was suggested by utilizing ion viscous heating in a rotating plasma with a fixed boundary. We explore the steady-state solution to the Braginskii equations and find the parameter regime in which a significant temperature difference between ions and electrons can be sustained in a driven steady state. Here, the threshold for this effect occurs at ρ i ≳ 0.1R. An analytic, leading order low flow solution is obtained, and a numerical, moderate Mach number M ≲ 2 is investigated. The limitation is found to be at moderate Mach numbers.
This paper describes 'type 1' servo techniques applied to explicit model following systems. The advantages of using these are: (1) steady-state decoupling is provided for the controlled state variables as determined by a reference input (the pilot command for example), (2) overall stability of the decoupled adaptive scheme is guaranteed, (3) a zero steady-state error for those state variables incorporating integral feedback, to a constant input reference, and (4) improved transient performance. Example calculations have been performed using a mathematical model for a typical fighter aircraft and a desired performance reference model based on satisfactory aircraft flying qualities. Numerical results are given.
Experimental methods were evaluated for the determination of lifetime and diffusion length in silicon intentionally doped with potentially lifetime-degrading impurities found in metallurgical grade silicon, impurities which may be residual in low-cost silicon intended for use in terrestrial flat-plate arrays. Lifetime measurements were made using a steady-state photoconductivity method. Diffusion length determinations were made using short-circuit current measurements under penetrating illumination. Mutual consistency among all experimental methods was verified, but steady-state photoconductivity was found preferable to photoconductivity decay at short lifetimes and in the presence of traps. The effects of a number of impurities on lifetime in bulk material, and on diffusion length in cells fabricated from this material, were determined. Results are compared with those obtained using different techniques. General agreement was found in terms of the hierarchy of impurities which degrade the lifetime.
Three-dimensional finite element models were generated and transferred into three-dimensional finite difference models to perform transient thermal analyses for the SSME high pressure fuel turbopump's first stage nozzles and rotor blades. STANCOOL was chosen to calculate the heat transfer characteristics (HTCs) around the airfoils, and endwall effects were included at the intersections of the airfoils and platforms for the steady-state boundary conditions. Free and forced convection due to rotation effects were also considered in hollow cores. Transient HTCs were calculated by taking ratios of the steady-state values based on the flow rates and fluid properties calculated at each time slice. Results are presented for both transient plots and three-dimensional color contour isotherm plots; they were also converted into universal files to be used for FEM stress analyses.
It is demonstrated that the steady-state and kinetic characteristics of ECR (electron cyclotron resonance) and RF glow discharge plasmas can be readily monitored by OES (optical emission spectroscopy) in real time during a-Si:H and a-SiC:H film depositions using an OMA detection system. The ECR and RF glow discharge plasmas used for a-Si:H and a-SiC:H film depositions were studied by monitoring the emission of SiH(asterisk), H(asterisk), H(asterisk)2, and CH(asterisk) excited states. The OES of the ECR plasma shows a strong emission at 434 nm from H(asterisk), which is not detectable in the glow discharge plasma. Steady-state OES studies have established preliminary correlations between SiH(asterisk) and CH(asterisk) emission intensities and the film deposition rate. Transient OES spectra of SiH4 and CH4 plasmas have shown different kinetics in SiH(asterisk) and CH(asterisk) emission intensities. Transient studies of the SiH(asterisk) emission intensity have indicated that additional mechanisms for producing the SiH(asterisk) species become evident in hydrogen-diluted silane plasmas.
A thin-layer Navier-Stokes has been developed for solving high Reynolds number, turbulent flows past aircraft components under transonic flow conditions. The computer code has been validated through data comparisons for flow past isolated wings, wing-body configurations, prolate spheroids and wings mounted inside wind-tunnels. The basic code employs an explicit Runge-Kutta time-stepping scheme to obtain steady state solution to the unsteady governing equations. Significant gain in the efficiency of the code has been obtained by implementing a multigrid acceleration technique to achieve steady-state solutions. The improved efficiency of the code has made it feasible to conduct grid-refinement and turbulence model studies in a reasonable amount of computer time. The non-equilibrium turbulence model of Johnson and King has been extended to three-dimensional flows and excellent agreement with pressure data has been obtained for transonic separated flow over a transport type of wing.