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NASA NTRS2006

Dynamic Response Testing in an Electrically Heated Reactor Test Facility

Non-nuclear testing can be a valuable tool in development of a space nuclear power or propulsion system. In a non-nuclear test bed, electric heaters are used to simulate the heat from nuclear fuel. Standard testing allows one to fully assess thermal, heat transfer, and stress related attributes of a given system, but fails to demonstrate the dynamic response that would be present in an integrated, fueled reactor system. The integration of thermal hydraulic hardware tests with simulated neutronic response provides a bridge between electrically heated testing and full nuclear testing. By implementing a neutronic response model to simulate the dynamic response that would be expected in a fueled reactor system, one can better understand system integration issues, characterize integrated system response times and response characteristics, and assess potential design improvements at a relatively small fiscal investment. Initial system dynamic response testing was demonstrated on the integrated SAFE-100a heat pipe cooled, electrically heated reactor and heat exchanger hardware, utilizing a one-group solution to the point kinetics equations to simulate the expected neutronic response of the system (Bragg-Sitton, 2005). The current paper applies the same testing methodology to a direct drive gas cooled reactor system, demonstrating the applicability of the testing methodology to any reactor type and demonstrating the variation in system response characteristics in different reactor concepts. In each testing application, core power transients were controlled by a point kinetics model with reactivity feedback based on core average temperature; the neutron generation time and the temperature feedback coefficient are provided as model inputs. Although both system designs utilize a fast spectrum reactor, the method of cooling the reactor differs significantly, leading to a variable system response that can be demonstrated and assessed in a non-nuclear test facility.

Bragg-Sitton, Shannon M.↗

NASA NTRS1974

Approach to the origin of turbulence on the basis of two-point kinetic theory

Equations for the fluctuation correlation in an incompressible shear flow are derived on the basis of kinetic theory, utilizing the two-point distribution function which obeys the BBGKY hierarchy equation truncated with the hypothesis of 'ternary' molecular chaos. The step from the molecular to the hydrodynamic description is accomplished by a moment expansion which is a two-point version of the thirteen-moment method, and which leads to a series of correlation equations, viz., the two-point counterparts of the continuity equation, the Navier-Stokes equation, etc. For almost parallel shearing flows the two-point equation is separable and reduces to two Orr-Sommerfeld equations with different physical implications.

Tsuge, S.↗

NASA NTRS1996

A Burst Mode, Ultrahigh Temperature UF4 Vapor Core Reactor Rankine Cycle Space Power System Concept

Static and dynamic neutronic analyses have been performed on an innovative burst mode (100's of MW output for a few thousand seconds) Ulvahigh Temperature Vapor Core Reactor (UTVR) space nuclear power system. The NVTR employs multiple, neutronically-coupled fissioning cores and operates on a direct, closed Rankine cycle using a disk Magnetohydrodynamic (MHD) generater for energy conversion. The UTVR includes two types of fissioning core regions: (1) the central Ultrahigh Temperature Vapor Core (UTVC) which contains a vapor mixture of highly enriched UF4 fuel and a metal fluoride working fluid and (2) the UF4 boiler column cores located in the BeO moderator/reflector region. The gaseous nature of the fuel the fact that the fuel is circulating, the multiple coupled fissioning cores, and the use of a two phase fissioning fuel lead to unique static and dynamic neutronic characteristics. Static neutronic analysis was conducted using two-dimensional S sub n, transport theory calculations and three-dimensional Monte Carlo transport theory calculations. Circulating-fuel, coupled-core point reactor kinetics equations were used for analyzing the dynamic behavior of the UTVR. In addition to including reactivity feedback phenomena associated with the individual fissioning cores, the effects of core-to-core neutronic and mass flow coupling between the UTVC and the surrounding boiler cores were also included in the dynamic model The dynamic analysis of the UTVR reveals the existence of some very effectlve inherent reactivity feedback effects that are capable of quickly stabilizing this system, within a few seconds, even when large positive reactivity insertions are imposed. If the UTVC vapor fuel density feedback is suppressed, the UTVR is still inherently stable because of the boiler core liquid-fuel volume feedback; in contrast, suppression of the vapor fuel density feedback in 'conventional" gas core cavity reactors causes them to become inherently unstable. Due to the strength of the negative reactivity feedback in the UTVR, it is found that external reactivity insertions alone are inadequate for bringing about significant power level changes during normal reactor operations. Additional methods of reactivity control such as variations in the gaseous fuel mass flow rate, are needed to achieve the desired power level oontrol.

Dugan, E. T.↗

NASA NTRS2007

Reply to "Comment on 'A Self-Consistent Model of the Interacting Ring Current Ions and Electromagnetic Ion Cyclotron Waves, Initial Results: Waves and Precipitation Fluxes' and 'Self-Consistent Model of the Magnetospheric Ring Current and Propagating Electromagnetic Ion Cyclotron Waves: Waves in Multi-Ion Magnetosphere' by Khazanov et al. et al."

It is well-known that the effects of electromagnetic ion cyclotron (EMIC) waves on ring current (RC) ion and radiation belt (RB) electron dynamics strongly depend on such particle/wave characteristics as the phase-space distribution function, frequency, wavenormal angle, wave energy, and the form of wave spectral energy density. The consequence is that accurate modeling of EMIC waves and RC particles requires robust inclusion of the interdependent dynamics of wave growth/damping, wave propagation, and[ particles. Such a self-consistent model is being progressively developed by Khazanov et al. [2002, 2006, 2007]. This model is based on a system of coupled kinetic equations for the RC and EMIC wave power spectral density along with the ray tracing equations. Thome and Home [2007] (hereafter referred to as TH2007) call the Khazanov et al. [2002, 2006] results into question in their Comment. The points in contention can be summarized as follows. TH2007 claim that: (1) "the important damping of waves by thermal heavy ions is completely ignored", and Landau damping during resonant interaction with thermal electrons is not included in our model; (2) EMIC wave damping due to RC O + is not included in our simulation; (3) non-linear processes limiting EMIC wave amplitude are not included in our model; (4) growth of the background fluctuations to a physically significantamplitude"must occur during a single transit of the unstable region" with subsequent damping below bi-ion latitudes,and consequently"the bounce averaged wave kinetic equation employed in the code contains a physically erroneous 'assumption". Our reply will address each of these points as well as other criticisms mentioned in the Comment. TH2007 are focused on two of our papers that are separated by four years. Significant progress in the self-consistent treatment of the RC-EMIC wave system has been achieved during those years. The paper by Khazanov et al. [2006] presents the latest version of our model, and in this Reply we refer mostly to this paper.

Khazanov, G. V.↗

NASA NTRS1982

A numerical method for integrating the kinetic equations of droplet spectra evolution by condensation/evaporation and by coalescence/breakup processes

An extension of the method of moments is developed for the numerical integration of the kinetic equations of droplet spectra evolution by condensation/evaporation and by coalescence/breakup processes. The number density function n sub k (x,t) in each separate droplet packet between droplet mass grid points (x sub k, x sub k+1) is represented by an expansion in orthogonal polynomials with a given weighting function. In this way droplet number concentrations, liquid water contents and other moments in each droplet packet are conserved and the problem of solving the kinetic equations is replaced by one of solving a set of coupled differential equations for the number density function moments. The method is tested against analytic solutions of the corresponding kinetic equations. Numerical results are obtained for different coalescence/breakup and condensation/evaporation kernels and for different initial droplet spectra. Also droplet mass grid intervals, weighting functions, and time steps are varied.

Emukashvily, I. M.↗

NASA NTRS1992

Maxwell's second- and third-order equations of transfer for non-Maxwellian gases

Condensed algebraic forms for Maxwell's second- and third-order equations of transfer are developed for the case of molecules described by either elastic hard spheres, inverse-power potentials, or by Bird's variable hard-sphere model. These hardly reduced, yet exact, equations provide a new point of origin, when using the moment method, in seeking approximate solutions in the kinetic theory of gases for molecular models that are physically more realistic than that provided by the Maxwell model. An important by-product of the analysis when using these second- and third-order relations is that a clear mathematical connection develops between Bird's variable hard-sphere model and that for the inverse-power potential.

Baganoff, D.↗

NASA NTRS2001

Relative effectiveness of kinetic analysis vs single point readings for classifying environmental samples based on community-level physiological profiles (CLPP)

The relative effectiveness of average-well-color-development-normalized single-point absorbance readings (AWCD) vs the kinetic parameters mu(m), lambda, A, and integral (AREA) of the modified Gompertz equation fit to the color development curve resulting from reduction of a redox sensitive dye from microbial respiration of 95 separate sole carbon sources in microplate wells was compared for a dilution series of rhizosphere samples from hydroponically grown wheat and potato ranging in inoculum densities of 1 x 10(4)-4 x 10(6) cells ml-1. Patterns generated with each parameter were analyzed using principal component analysis (PCA) and discriminant function analysis (DFA) to test relative resolving power. Samples of equivalent cell density (undiluted samples) were correctly classified by rhizosphere type for all parameters based on DFA analysis of the first five PC scores. Analysis of undiluted and 1:4 diluted samples resulted in misclassification of at least two of the wheat samples for all parameters except the AWCD normalized (0.50 abs. units) data, and analysis of undiluted, 1:4, and 1:16 diluted samples resulted in misclassification for all parameter types. Ordination of samples along the first principal component (PC) was correlated to inoculum density in analyses performed on all of the kinetic parameters, but no such influence was seen for AWCD-derived results. The carbon sources responsible for classification differed among the variable types with the exception of AREA and A, which were strongly correlated. These results indicate that the use of kinetic parameters for pattern analysis in CLPP may provide some additional information, but only if the influence of inoculum density is carefully considered. c2001 Elsevier Science Ltd. All rights reserved.

NASA Center KSC↗

NASA NTRS1976

A quasi-linear kinetic equation for cosmic rays in the interplanetary medium

A kinetic equation for interplanetary cosmic rays is set up with the aid of weak-plasma-turbulence theory for an idealized radially symmetric model of the interplanetary magnetic field. As a starting point, this treatment invokes the Vlasov equation instead of the traditional Fokker-Planck equation. Quasi-linear theory is applied to obtain a momentum diffusion equation for the heliocentric frame of reference which describes the interaction of cosmic rays with convecting magnetic irregularities in the solar-wind plasma. Under restricted conditions, the well-known equation of solar modulation can be obtained from this kinetic equation.

Luhmann, J. G.↗

NASA NTRS1985

Simulation and modeling of homogeneous, compressed turbulence

Low Reynolds number homogeneous turbulence undergoing low Mach number isotropic and one-dimensional compression was simulated by numerically solving the Navier-Stokes equations. The numerical simulations were performed on a CYBER 205 computer using a 64 x 64 x 64 mesh. A spectral method was used for spatial differencing and the second-order Runge-Kutta method for time advancement. A variety of statistical information was extracted from the computed flow fields. These include three-dimensional energy and dissipation spectra, two-point velocity correlations, one-dimensional energy spectra, turbulent kinetic energy and its dissipation rate, integral length scales, Taylor microscales, and Kolmogorov length scale. Results from the simulated flow fields were used to test one-point closure, two-equation models. A new one-point-closure, three-equation turbulence model which accounts for the effect of compression is proposed. The new model accurately calculates four types of flows (isotropic decay, isotropic compression, one-dimensional compression, and axisymmetric expansion flows) for a wide range of strain rates.

Wu, C. T.↗

NASA NTRS1993

Computation of Heat Transfer from Impinging Turbulent Jets

An axisymmetric jet impinging on a flat plate was simulated using a low-Reynolds number k-epsilon model. The accuracy or the numerical calculations was validated by comparing the predicted flowfields with experimental data for various nozzle-plate distance to jet diameter ratios (H/d) and Reynolds numbers. Heat transfer predictions for various H/d showed good agreement with experimental data in the wall jet region, and the complex behavior of heat transfer for small H/d is predicted. However, predictions in the neighborhood of the stagnation point were poor for small H/d The results suggest that improved modeling in the equation for the dissipation rate of the turbulence kinetic energy is required.

Chang, B. H.↗

NASA NTRS1976

Effect of anisotropy and rotation on turbulence production

The dynamical equations for the Reynolds stresses in a form which is suitable for incompressible homogeneous flows are used as a starting point in the investigation. It is assumed that the mean flow is two-dimensional. The equation for the rate of change of the kinetic energy of turbulence is derived. If the turbulence is isotropic, there is no turbulence production. However, the isotropic condition is not stable. The production mechanism is found to be autocatalytic. Rotation always inhibits production because it reduces anisotropy.

Ferziger, J. H.↗

NASA NTRS1999

The Impact of Buoyancy and Flame Structure on Soot, Radiation and NOx Emissions from a Turbulent Diffusion Flame

It is hypothesized that the spatial structure of a turbulent diffusion flame plays an important role in determining the emissions of radiative energy, soot and NO, from a combustor. This structure, manifested in the two point statistics, is influenced by buoyancy. Radiation, soot and NOx emissions are the cumulative result of processes that occur throughout a flame. For example, radiation fluxes along a line of sight can be found from summing up the contributions from sources in individual pockets of hot soot that emit, and from sinks in cold soot that absorb. Soot and NOx are both the results of slow chemistry and are not equilibrium products. The time that is available for production and burnout is crucial in determining the eventual emissions of these pollutants. Turbulence models generally rely on a single point closure of the appropriate time averaged equations. Hence, spatial information is lost and needs to be modeled using solution variables such as turbulence kinetic energy and dissipation rate, often with the assumption of isotropy. However, buoyancy can affect the physical structure of turbulent flames and can change the spatial extent of soot bearing regions. Theoretical comparisons with models are best done in the limit of infinite Froude number because the inclusion of buoyancy in flow models introduces significant uncertainties. Hence, LII measurements of soot, measurements of radiation fluxes from soot, Particle Imaging Velocimetry (PIV) of the flow field and measurements of post flame NOX will be carried out on the NASA Lewis 2.2 sec drop tower and eventually on the parabolic flight aircraft. The drop rig will be a modified version of a unit that has been successfully used at Lewis in the past.

Kennedy, I. M.↗

NASA NTRS1991

Analysis of two-equation turbulence models for recirculating flows

The two-equation kappa-epsilon model is used to analyze turbulent separated flow past a backward-facing step. It is shown that if the model constraints are modified to be consistent with the accepted energy decay rate for isotropic turbulence, the dominant features of the flow field, namely the size of the separation bubble and the streamwise component of the mean velocity, can be accurately predicted. In addition, except in the vicinity of the step, very good predictions for the turbulent shear stress, the wall pressure, and the wall shear stress are obtained. The model is also shown to provide good predictions for the turbulence intensity in the region downstream of the reattachment point. Estimated long time growth rates for the turbulent kinetic energy and dissipation rate of homogeneous shear flow are utilized to develop an optimal set of constants for the two equation kappa-epsilon model. The physical implications of the model performance are also discussed.

Thangam, S.↗

NASA NTRS1994

Asymptotic domination of cold relativistic MHD winds by kinetic energy flux

We study the conditions which lead to the conversion of most Poynting flux into kinetic energy flux in cold, relativistic hydromagnetic winds. It is shown that plasma acceleration along a precisely radial flow is extremely inefficient due to the near cancellation of the toroidal magnetic pressure and tension forces. However, if the flux tubes in a flow diverge even slightly faster than radially, the fast magnetosonic point moves inward from infinity to a few times the light cylinder radius. Once the flow becomes supermagnetosonic, further divergence of the flux tubes beyond the fast point can accelerate the flow via the 'magnetic nozzle' effect, thereby further converting Poynting flux to kinetic energy flux. We show that the Grad-Shafranov equation admits a generic family of kinetic energy-dominated asymptotic wind solutions with finite total magnetic flux. The Poynting flux in these solutions vanishes logarithmically with distance. The way in which the flux surfaces are nested within the flow depends only on the ratio of angular velocity to poliodal 4-velocity as a function of magnetic flux. Radial variations in flow structure can be expressed in terms of a pressure boundary condition on the outermost flux surface, provided that no external toriodal field surrounds the flow. For a special case, we show explicitly how the flux surfaces merge gradually to their asymptotes. For flows confined by an external medium of pressure decreasing to zero at infinity we show that, depending on how fast the ambient pressure declines, the final flow state could be either a collimated jet or a wind that fills the entire space. We discuss the astrophysical implications of our results for jets from active galactic nuclei and for free pulsar winds such as that believed to power the Crab Nebula.

Begelman, Mitchell C.↗

NASA NTRS2002

Decoupling the Role of Particle Inertia and Gravity on Particle Dispersion

Particle dispersion and the influence that particle momentum exchange has on the properties of a turbulent carrier flow in micro-gravity environments challenge present understanding and predictive schemes. The objective of this effort has been to develop and assess high-fidelity simulation tools for predicting particle transport within micro-gravity environments suspended in turbulent flows. The computational technique is based on Direct Numerical Simulation (DNS) of the incompressible Navier-Stokes equations. The particular focus of the present work is on the class of dilute flows in which particle volume fractions and inter-particle collisions are negligible. Particle motion is assumed to be governed by drag with particle relaxation times ranging from the Kolmogorov scale to the Eulerian timescale of the turbulence and particle mass loadings up to one. The velocity field was made statistically stationary by forcing the low wavenumbers of the flow. The calculations were performed using 96(exp 3) collocation points and the Taylor-scale Reynolds number for the stationary flow was 62. The effect of particles on the turbulence was included in the Navier-Stokes equations using the point-force approximation in which 96(exp 3) particles were used in the calculations. DNS results show that particles increasingly dissipate fluid kinetic energy with increased loading, with the reduction in kinetic energy being relatively independent of the particle relaxation time. Viscous dissipation in the fluid decreases with increased loading and is larger for particles with smaller relaxation times. Fluid energy spectra show that there is a non-uniform distortion of the turbulence with a relative increase in small-scale energy. The non-uniform distortion significantly affects the transport of the dissipation rate, with the production and destruction of dissipation exhibiting completely different behaviors. The spectrum of the fluid-particle energy exchange rate shows that the fluid drags particles at low wavenumbers while the converse is true at high wavenumbers for small particles. A spectral analysis shows that the increase of the high wavenumber portion of the fluid energy spectrum can be attributed to transfer of the fluid-particle covariance by the fluid turbulence. This in turn explains the relative increase of small-scale energy caused by small particles observed in the present simulations as well as those of others.

Squires, Kyle D.↗

NASA NTRS1986

Comparison between the South Pacific Convergence Zone and South Atlantic Convergence Zone in January 1979

Using one of the FGGE data sets, the eddy potential and eddy kinetic energy budgets during the period of January 10-27, 1979 were derived for the regions containing the South Pacific Convergence Zone (SPCZ) and the South Atlantic Convergence Zone. A complete set of energy equations developed by Brennan and Vincent (1980) was partitioned into zonal and eddy components; the eddy forms of energy were derived from a grid point's departure from the zonal average over a 5-deg latitude belt. The results of the analysis indicate that the eddy kinetic energy content (KE) is greater than the eddy available potential energy content (AE) throughout the period. Both AE and KE show large losses beginning when the SPCZ enters a decaying state: AE shows a gradual but slow decrease until after January 22, when it decreases rapidly; KE oscillates, reaching a maximum on January 22 before a rapid decrease.

Vincent, Dayton G.↗

NASA NTRS2016

Transient Growth Analysis of Compressible Boundary Layers with Parabolized Stability Equations

The linear form of parabolized linear stability equations (PSE) is used in a variational approach to extend the previous body of results for the optimal, non-modal disturbance growth in boundary layer flows. This methodology includes the non-parallel effects associated with the spatial development of boundary layer flows. As noted in literature, the optimal initial disturbances correspond to steady counter-rotating stream-wise vortices, which subsequently lead to the formation of stream-wise-elongated structures, i.e., streaks, via a lift-up effect. The parameter space for optimal growth is extended to the hypersonic Mach number regime without any high enthalpy effects, and the effect of wall cooling is studied with particular emphasis on the role of the initial disturbance location and the value of the span-wise wavenumber that leads to the maximum energy growth up to a specified location. Unlike previous predictions that used a basic state obtained from a self-similar solution to the boundary layer equations, mean flow solutions based on the full Navier-Stokes (NS) equations are used in select cases to help account for the viscous-inviscid interaction near the leading edge of the plate and also for the weak shock wave emanating from that region. These differences in the base flow lead to an increasing reduction with Mach number in the magnitude of optimal growth relative to the predictions based on self-similar mean-flow approximation. Finally, the maximum optimal energy gain for the favorable pressure gradient boundary layer near a planar stagnation point is found to be substantially weaker than that in a zero pressure gradient Blasius boundary layer.

Compressible boundary layer↗

NASA NTRS1999

Asymptotic Behavior of Ensemble-Averaged Linear Disturbances in Homogeneous Shear Flow

In order to expand the predictive capability of single-point turbulence closure models too account for the early-stage transition regime, a methodology for the formulation and calibration of model equations for the ensemble-averaged disturbance kinetic energy and energy dissipation rate is presented. The calibration is based on homogeneous shear flow where disturbances can be described by rapid distort,ion theory (RDT). The relationship between RDT and linear stability theory is exploit,c d in order to obtain a closed set, of modeled equations. The linear disturbance equations are solved directly so that, the numerical simulation yields a database from which the closure coefficient,s in the ensemble-averaged disturbance equations can he determined.

Thacker, W. D.↗