Results for “power flow equation” — Page 16

NASA NTRS1985

Cosmic-ray acceleration at stellar wind terminal shocks

Steady-state spherically symmetric analytic solutions of the cosmic-ray transport equations, applicable to the problem of acceleration of cosmic rays at the terminal shock to a stellar wind, are studied. The spectra, graidents, and flow patterns of particles modulated and accelerated by the stellar wind and shock are investigated by means of monoenergetic-source solutions at finite radius, as well as solutions with monoenergetic and power-law galactic spectra. On the basis of calculations given, early-type stars could supply a significant fraction of the 3 x 10 to the 40th ergs/sec required by galactic cosmic rays.

Webb, G. M.↗

NASA NTRS1987

Optimizing the antenna system of a microwave space power station: Implications for the selection of operating power, frequency and antenna size

A design for a space power station that is to transmit power to the surface of a planet via high powered microwaves should commence with the optimum design of the transmitting and receiving antenna combination to be employed. Once one has assured that the desired amount of power has been transferred (which, after all, is the prupose of any power transmission system), one can, from the constraints imposed by such a design, taylor other parameters of the system such as antenna sizes and weights, power density in the planet's atmosphere (e.g., to avoid electrical breakdown), and frequency of operation. It is the purpose of this brief analysis to provide the working equations of such an optimized antenna system, and to give examples of their use. Related problems that should be analyzed in the future will then be discussed and a flow chart of the indicated order of priority presented. The analysis given here differs from previous work on this subject in that the development given will allow analytical expressions to be obtained for the relevant parameters. This is made possible by employing an approximation procedure to be given during the exposition.

Manning, Robert M.↗

NASA NTRS2015

A Model for Jet-Surface Interaction Noise Using Physically Realizable Upstream Turbulence Conditions

This paper is a continuation of previous work in which a generalized Rapid Distortion Theory (RDT) formulation was used to model low-frequency trailing-edge noise. The research was motivated by proposed next-generation aircraft configurations where the exhaust system is tightly integrated with the airframe. Data from recent experiments at NASA on the interaction between high-Reynolds-number subsonic jet flows and an external flat plate showed that the power spectral density (PSD) of the far-field pressure underwent considerable amplification at low frequencies. For example, at the 900 observation angle, the low-frequency noise could be as much as 10dB greater than the jet noise itself. In this paper, we present predictions of the noise generated by the interaction of a rectangular jet with the trailing edge of a semi-infinite flat plate. The calculations are based on a formula for the acoustic spectrum of this noise source derived from an exact formal solution of the linearized Euler equations involving (in this case) one arbitrary convected scalar quantity and a Rayleigh equation Green's function. A low-frequency asymptotic approximation for the Green's function based on a two-dimensional mean flow is used in the calculations along with a physically realizable upstream turbulence spectrum, which includes a finite de-correlation region. Numerical predictions, based on three-dimensional RANS solutions for a range of subsonic acoustic Mach number jets and nozzle aspect ratios are compared with experimental data. Comparisons of the RANS results with flow data are also presented for selected cases. We find that a finite decorrelation region increases the low-frequency algebraic decay (the low frequency "rolloff") of the acoustic spectrum with angular frequency thereby producing much closer agreement with noise data for Strouhal numbers less than 0.1. Secondly, the large-aspectratio theory is able to predict the low-frequency amplification due to the jet-edge interaction reasonably well, even for moderate aspect ratio nozzles. We show also that the noise predictions for smaller aspect ratio jets can be fine-tuned using the appropriate RANS-based mean flow and turbulence properties.

Jet↗

NASA NTRS2015

A Model for Jet-Surface Interaction Noise Using Physically Realizable Upstream Turbulence Conditions

This paper is a continuation of previous work in which a generalized Rapid Distortion Theory (RDT) formulation was used to model low-frequency trailing-edge noise. The research was motivated by proposed next-generation aircraft configurations where the exhaust system is tightly integrated with the airframe. Data from recent experiments at NASA on the interaction between high-Reynolds-number subsonic jet flows and an external flat plate showed that the power spectral density (PSD) of the far-field pressure underwent considerable amplification at low frequencies. For example, at the 900 observation angle, the low-frequency noise could be as much as 10dB greater than the jet noise itself. In this paper, we present predictions of the noise generated by the interaction of a rectangular jet with the trailing edge of a semi-infinite flat plate. The calculations are based on a formula for the acoustic spectrum of this noise source derived from an exact formal solution of the linearized Euler equations involving (in this case) one arbitrary convected scalar quantity and a Rayleigh equation Green's function. A low-frequency asymptotic approximation for the Green's function based on a two-dimensional mean flow is used in the calculations along with a physically realizable upstream turbulence spectrum, which includes a finite de-correlation region. Numerical predictions, based on three-dimensional RANS solutions for a range of subsonic acoustic Mach number jets and nozzle aspect ratios are compared with experimental data. Comparisons of the RANS results with flow data are also presented for selected cases. We find that a finite decorrelation region increases the low-frequency algebraic decay (the low frequency "rolloff") of the acoustic spectrum with angular frequency thereby producing much closer agreement with noise data for Strouhal numbers less than 0.1. Secondly, the large-aspectratio theory is able to predict the low-frequency amplification due to the jet-edge interaction reasonably well, even for moderate aspect ratio nozzles. We show also that the noise predictions for smaller aspect ratio jets can be fine-tuned using the appropriate RANS-based mean flow and turbulence properties.

Aircraft↗

NASA NTRS2016

A Model for Jet-Surface Interaction Noise Using Physically Realizable Upstream Turbulence Conditions

This paper is a continuation of previous work in which a generalized Rapid Distortion Theory (RDT) formulation was used to model low-frequency trailing-edge noise. The research was motivated by proposed next-generation aircraft configurations where the exhaust system is tightly integrated with the airframe. Data from recent experiments at NASA on the interaction between high-Reynolds-number subsonic jet flows and an external flat plate showed that the power spectral density (PSD) of the far-field pressure underwent considerable amplification at low frequencies. For example, at the 90deg observation angle, the low-frequency noise could be as much as 10 dB greater than the jet noise itself. In this paper, we present predictions of the noise generated by the interaction of a rectangular jet with the trailing edge of a semi-infinite flat plate. The calculations are based on a formula for the acoustic spectrum of this noise source derived from an exact formal solution of the linearized Euler equations involving (in this case) one arbitrary convected scalar quantity and a Rayleigh equation Green's function. A low-frequency asymptotic approximation for the Green's function based on a two-dimensional mean flow is used in the calculations along with a physically realizable upstream turbulence spectrum, which includes a finite decorrelation region. Numerical predictions of the sound field, based on three-dimensional RANS solutions to determine the mean flow, turbulent kinetic energy and turbulence length and time scales, for a range of subsonic acoustic Mach number jets and nozzle aspect ratios are compared with experimental data. Comparisons of the RANS results with flow data are also presented for selected cases. We find that a finite decorrelation region in the turbulence spectrum increases the low-frequency algebraic decay (the low frequency "roll-off") of the acoustic spectrum with angular frequency thereby producing much closer agreement with noise data for Strouhal numbers less than 0.1. Secondly, the large-aspect-ratio theory is able to predict the low-frequency amplification due to the jet-edge interaction reasonably well, even for moderate aspect ratio nozzles. We show also that the noise predictions for smaller aspect ratio jets can be fine-tuned using the appropriate RANS-based mean flow and turbulence properties.

Jet↗

NASA NTRS1974

Experimental and analytical sonic nozzle discharge coefficients for Reynolds numbers up to 8 x 10 to the 6th power

Sonic discharge coefficients are presented for two different geometry flow nozzles using nitrogen gas at high pressures where real gas corrections are significant. Throat Reynolds number range extended up to 8 million. Experimentally obtained coefficients for a nozzle with a continuous and finite radius of curvature agreed with those obtained analytically to within 0.2 percent. Experimental coefficients for a long radius ASME nozzle agreed to within 1/4 percent to an empirical equation representing the most probable subsonic discharge coefficient.

Szaniszlo, A. J.↗

NASA NTRS1986

Radiation of sound from an infinite cylindrical elastic shell excited by an internal monopole source

The radiation of sound from an infinite elastic cylindrical shell excited by an internal monopole source is investigated analytically. Coupled equations of motion are used. The modal mobility of the shell wall at the source plane is examined for differing source locations and the behavior is explained in terms of free wave propagation. The radiated pressure and line power from the shell surface is then evaluated for a similar range of source positions and frequencies. A real surface power flow, that circulates backwards and forward between the shell and fluid while propagating axially, but does not contribute to the radiated far field, is uncovered. Finally, the transmission loss of the shell wall is evaluated and found to be between 10 and 35 dB lower than predicted by existing simplified theories. The lower transmission losses predicted by the coupled analysis presented here are shown to be due to excitation of higher order 'shell' type waves at the source plane.

Fuller, C. R.↗

NASA NTRS1988

Turbulence modeling in non-inertial frames of reference

The effect of an arbitrary change of frame on the structure of turbulence models is examined from a fundamental theoretical standpoint. It is proven, as a rigorous consequence of the Navier-Stokes equations, that turbulence models must be form invariant under arbitrary translational accelerations of the reference frame and should only be affected by rotations through the intrinsic mean vorticity. A direct application of the invariance property along with the Taylor-Proudman Theorem, material frame-indifference in the limit of two-dimensional turbulence and Rapid Distortion Theory is shown to yield powerful constraints on the allowable form of turbulence models. Most of the commonly used turbulence models are demonstrated to be in serious violation of these constraints and consequently are inconsistent with the Navier-Stokes equations in non-inertial frames. Alternative models with improved non-inertial properties are developed and some simple applications to rotating turbulent flows are considered.

Speziale, Charles G.↗

NASA NTRS1989

Turbulence modeling in noninertial frames of reference

The effect of an arbitrary change of frame on the structure of turbulence models is examined from a fundamental theoretical standpoint. It is proven, as a rigorous consequence of the Navier-Stokes equations, that turbulence models must be form invariant under arbitrary translational accelerations of the reference frame and should only be affected by rotations through the intrinsic mean vorticity. A direct application of the invariance property along with the Taylor-Proudman Theorem, material frame-indifference in the limit of two-dimensional turbulence and Rapid Distortion Theory is shown to yield powerful constraints on the allowable form of turbulence models. Most of the commonly used turbulence models are demonstrated to be in serious violation of these constraints and consequently are inconsistent with the Navier-Stokes equations in non-inertial frames. Alternative models with improved non-inertial properties are developed and some simple applications to rotating turbulent flows are considered.

Speziale, Charles G.↗

NASA NTRS2005

Forecasting Lightning at Kennedy Space Center/Cape Canaveral Air Force Station, Florida

The Applied Meteorology Unit (AMU) developed a set of statistical forecast equations that provide a probability of lightning occurrence on Kennedy Space Center (KSC) I Cape Canaveral Air Force Station (CCAFS) for the day during the warm season (May September). The 45th Weather Squadron (45 WS) forecasters at CCAFS in Florida include a probability of lightning occurrence in their daily 24-hour and weekly planning forecasts, which are briefed at 1100 UTC (0700 EDT). This information is used for general scheduling of operations at CCAFS and KSC. Forecasters at the Spaceflight Meteorology Group also make thunderstorm forecasts for the KSC/CCAFS area during Shuttle flight operations. Much of the current lightning probability forecast at both groups is based on a subjective analysis of model and observational data. The objective tool currently available is the Neumann-Pfeffer Thunderstorm Index (NPTI, Neumann 1971), developed specifically for the KSCICCAFS area over 30 years ago. However, recent studies have shown that 1-day persistence provides a better forecast than the NPTI, indicating that the NPTI needed to be upgraded or replaced. Because they require a tool that provides a reliable estimate of the daily thunderstorm probability forecast, the 45 WS forecasters requested that the AMU develop a new lightning probability forecast tool using recent data and more sophisticated techniques now possible through more computing power than that available over 30 years ago. The equation development incorporated results from two research projects that investigated causes of lightning occurrence near KSCICCAFS and over the Florida peninsula. One proved that logistic regression outperformed the linear regression method used in NPTI, even when the same predictors were used. The other study found relationships between large scale flow regimes and spatial lightning distributions over Florida. Lightning, probabilities based on these flow regimes were used as candidate predictors in the equation development. Fifteen years (1 989-2003) of warm season data were used to develop the forecast equations. The data sources included a local network of cloud-to-ground lightning sensors called the Cloud-to-Ground Lightning Surveillance System (CGLSS), 1200 UTC Florida synoptic soundings, and the 1000 UTC CCAFS sounding. Data from CGLSS were used to determine lightning occurrence for each day. The 1200 UTC soundings were used to calculate the synoptic-scale flow regimes and the 1000 UTC soundings were used to calculate local stability parameters, which were used as candidate predictors of lightning occurrence. Five logistic regression forecast equations were created through careful selection and elimination of the candidate predictors. The resulting equations contain five to six predictors each. Results from four performance tests indicated that the equations showed an increase in skill over several standard forecasting methods, good reliability, an ability to distinguish between non-lightning and lightning days, and good accuracy measures and skill scores. Given the overall good performance the 45 WS requested that the equations be transitioned to operations and added to the current set of tools used to determine the daily lightning probability of occurrence.

Lambert, Winfred↗

DOE OSTI2023

Hydrologic Connectivity and Patch‐To‐Hillslope Scale Relations in Dryland Ecosystems

Abstract In drylands, runoff during storms redistributes water and nutrients from bare soil areas to vegetated patches, subsidizing vegetation with additional resources. The extent of this redistribution depends on the interplay between surface roughness and permeability; greater permeability in vegetated patches promotes run‐on to vegetation, but greater surface roughness diverts runoff, producing tortuous flow paths that bypass vegetation. Here, this interplay is examined in virtual experiments using the 2D Saint Venant Equations to measure runoff connectivity. Flowpaths are delineated using tracers advected by the flow. Distances between tracer sources and sinks along flowpaths measure hydrologic connectivity at two lengthscales: connectivity to the hillslope outlet and within‐slope source‐sink connectivity. Differences between these connectivity lengthscales indicate how flow may “by‐pass” vegetated patches within hillslopes. At the hillslope scale, a derived power‐law relation between the runoff coefficient and outlet connectivity describes hillslope water losses, providing a foundation for identifying landscapes likely to shed water.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1986

Geostationary microwave imagers detection criteria

Geostationary orbit is investigated as a vantage point from which to sense remotely the surface features of the planet and its atmosphere, with microwave sensors. The geometrical relationships associated with geostationary altitude are developed to produce an efficient search pattern for the detection of emitting media and metal objects. Power transfer equations are derived from the roots of first principles and explain the expected values of the signal-to-clutter ratios for the detection of aircraft, ships, and buoys and for the detection of natural features where they are manifested as cold and warm eddies. The transport of microwave power is described for modeled detection where the direction of power flow is explained by the Zeroth and Second Laws of Thermodynamics. Mathematical expressions are derived that elucidate the detectability of natural emitting media and metal objects. Signal-to-clutter ratio comparisons are drawn among detectable objects that show relative detectability with a thermodynamic sensor and with a short-pulse radar.

Stacey, J. M.↗

NASA NTRS2015

Simulation of VSPT Experimental Cascade Under High and Low Free-Stream Turbulence Conditions

Variable-Speed Power Turbines (VSPT) for rotorcraft applications operate at low Reynolds number and over a wide range in incidence associated with shaft speed change. A comprehensive linear cascade data set obtained includes the effects of Reynolds number, free-stream turbulence and incidence is available and this paper concerns itself with the presentation and numerical simulation of conditions resulting in a selected set of those data. As such, post-dictions of blade pressure loading, total-pressure loss and exit flow angles under conditions of high and low turbulence intensity for a single Reynolds number are presented. Analyses are performed with the three-equation turbulence models of Walters- Leylek and Walters and Cokljat. Transition, loading, total-pressure loss and exit angle variations are presented and comparisons are made with experimental data as available. It is concluded that at the low freestream turbulence conditions the Walters-Cokljat model is better suited to predictions while for high freestream conditions the two models generate similar predications that are generally satisfactory.

turbulence modeling↗

DOE OSTI2022

Unstructured mesh-based multi-physics reactor transient simulation with iMC code

In this study, we present a time-dependent Monte Carlo simulation result about a complex fuel-loaded light water reactor system with thermal-hydraulic feedback using the KAIST iMC code. The intra-pin temperature distribution is calculated based on Monte Carlo-tallied detailed power distribution and the finite element heat transfer method. The temperature effect of fuel, absorber, and coolant are adequately reflected into the dynamic response by the on-the-fly Doppler broadened cross-section correction. For the time-dependent Monte Carlo transport simulation, the predictor-corrector quasi-static Monte Carlo method is used for this study. We tested the coupled analysis framework with a 17-by-17 fuel assembly loaded with the centrally-shielded burnable absorber (CSBA) fuel element. The temperature feedback effect on the material cross-section and the moderator density incurred negative reactivity in response to the external positive reactivity insertion, showing the inherent stability of the reactor system. The pin-wise power and temperature change during the system transient are presented and discussed. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

NASA NTRS2014

Simulation of VSPT Experimental Cascade Under High and Low Free-Stream Turbulence Conditions

Variable-Speed Power Turbines (VSPT) for rotorcraft applications operate at low Reynolds number and over a wide range in incidence associated with shaft speed change. A comprehensive linear cascade data set obtained includes the effects of Reynolds number, free-stream turbulence and incidence is available and this paper concerns itself with the presentation and numerical simulation of conditions resulting in a selected set of those data. As such, post-dictions of blade pressure loading, total-pressure loss and exit flow angles under conditions of high and low turbulence intensity for a single Reynolds number are presented. Analyses are performed with the three-equation turbulence models of Walters-Leylek and Walters and Cokljat. Transition, loading, total-pressure loss and exit angle variations are presented and comparisons are made with experimental data as available. It is concluded that at the low freestream turbulence conditions the Walters-Cokljat model is better suited to predictions while for high freestream conditions the two models generate similar predications that are generally satisfactory.

low pressure trubine↗

NASA NTRS2008

Characterization and Simulation of Thermoacoustic Instability in a Low Emissions Combustor Prototype

Extensive research is being done toward the development of ultra-low-emissions combustors for aircraft gas turbine engines. However, these combustors have an increased susceptibility to thermoacoustic instabilities. This type of instability was recently observed in an advanced, low emissions combustor prototype installed in a NASA Glenn Research Center test stand. The instability produces pressure oscillations that grow with increasing fuel/air ratio, preventing full power operation. The instability behavior makes the combustor a potentially useful test bed for research into active control methods for combustion instability suppression. The instability behavior was characterized by operating the combustor at various pressures, temperatures, and fuel and air flows representative of operation within an aircraft gas turbine engine. Trends in instability behavior vs. operating condition have been identified and documented. A simulation developed at NASA Glenn captures the observed instability behavior. The physics-based simulation includes the relevant physical features of the combustor and test rig, employs a Sectored 1-D approach, includes simplified reaction equations, and provides time-accurate results. A computationally efficient method is used for area transitions, which decreases run times and allows the simulation to be used for parametric studies, including control method investigations. Simulation results show that the simulation exhibits a self-starting, self-sustained combustion instability and also replicates the experimentally observed instability trends vs. operating condition. Future plans are to use the simulation to investigate active control strategies to suppress combustion instabilities and then to experimentally demonstrate active instability suppression with the low emissions combustor prototype, enabling full power, stable operation.

DeLaat, John C.↗

NASA NTRS1993

Pickup protons and water ions at Comet Halley - Comparisons with Giotto observations

The cometary ion pickup process along the sun-comet line at Comet Halley is investigated using a quasi-linear diffusion model including both pitch angle and energy diffusion, adiabatic compression, and convective motion with the solar wind flow. The model results are compared with energetic ion distributions observed by instruments on board the Giotto spacecraft. The observed power spectrum index of magnetic turbulence (gamma) is 2-2.5. The present simulation shows that when gamma was 2, the calculated proton distributions were much more isotropic than the observed ones. The numerical solutions of the quasi-linear diffusion equations show that the isotropization of the pickup ion distribution, particularly at the pickup velocity, is not complete even close to the bow shock. Given the observed turbulence level, quasi-linear theory yields pickup ion energy distributions that agree with the observed ones quite well and easily produces energetic ions with energies up to hundreds of keV.

Ye, G.↗

DOE OSTI2024

A Pseudoreversible Normalizing Flow for Stochastic Dynamical Systems with Various Initial Distributions

Here, we present a pseudoreversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with various initial distributions. The primary objective is to construct an accurate and efficient sampler that can be used as a surrogate model for computationally expensive numerical integration of SDEs, such as those employed in particle simulation. After training, the normalizing flow model can directly generate samples of the SDE’s final state without simulating trajectories. The existing normalizing flow model for SDEs depends on the initial distribution, meaning the model needs to be retrained when the initial distribution changes. The main novelty of our normalizing flow model is that it can learn the conditional distribution of the state, i.e., the distribution of the final state conditional on any initial state, such that the model only needs to be trained once and the trained model can be used to handle various initial distributions. This feature can provide a significant computational saving in studies of how the final state varies with the initial distribution. Additionally, we propose to use a pseudoreversible network architecture to define the normalizing flow model, which has sufficient expressive power and training efficiency for a variety of SDEs in science and engineering, e.g., in particle physics. We provide a rigorous convergence analysis of the pseudoreversible normalizing flow model to the target probability density function in the Kullback–Leibler divergence metric. Numerical experiments are provided to demonstrate the effectiveness of the proposed normalizing flow model.

97 MATHEMATICS AND COMPUTING↗