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All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Flight-measured pressure characteristics of aft-facing steps in high Reynolds number flow at Mach numbers of 2.20, 2.50, and 2.80 and comparison with other data

The YF-12 airplane was studied to determine the pressure characteristics associated with an aft-facing step in high Reynolds number flow for nominal Mach numbers of 2.20, 2.50, and 2.80. Base pressure coefficients were obtained for three step heights. The surface static pressures ahead of and behind the step were measured for the no-step condition and for each of the step heights. A boundary layer rake was used to determine the local boundary layer conditions. The Reynolds number based on the length of flow ahead of the step was approximately 10 to the 8th power and the ratios of momentum thickness to step height ranged from 0.2 to 1.0. Base pressure coefficients were compared with other available data at similar Mach numbers and at ratios of momentum thickness to step height near 1.0. In addition, the data were compared with base pressure coefficients calculated by a semiempirical prediction method. The base pressure ratios are shown to be a function of Reynolds number based on momentum thickness. Profiles of the surface pressures ahead of and behind the step and the local boundary layer conditions are also presented.

Powers, S. G.↗
NASA NTRS2003

Step Bunching and Solution Flow

Imagine a sequence of equidistant steps parallel to one another on a crystal face growing from solution. Steps may be one or part of a lattice spacing high. With such ideal morphology, the most perfect material is expected to be produced. Sometimes this happens. Much more often, however, steps form bunches, acquire wavy shapes and interlace. With time, these spontaneous perturbations may be increased in amplitude, i.e. the stepped surface becomes morphologically unstable. Interferometric studies of Y.G. Kuznetsov, L.N. Rashkovich, P.G. Vekilov and N.A. Booth and the author demonstrated that the step bunching depends at least on direction and rate of solution flow over the interface, supersaturation and presence of impurities. In particular, if solution and step flow are parallel to one another, the steps convene into bunches. If these flows are antiparallel, the bunches disappear. As the step train propagates, the overall bunch height often increases infinitely. However, we have found recently that if the flow rate is large enough, (approximately 1 meter per second), the bunch height may be limited. All these phenomena come from interaction between steps. The interaction mechanisms are still not fully understood. I plan to overview major approaches to the still unresolved problem on how these dissipative structures on growing crystal face appear and evolve.

Chernov, A. A.↗
NASA NTRS1997

On the Possibility of Ill-Conditioned Covariance Matrices in the First-Order Two-Step Estimator

The first-order two-step nonlinear estimator, when applied to a problem of orbital navigation, is found to occasionally produce first step covariance matrices with very low eigenvalues at certain trajectory points. This anomaly is the result of the linear approximation to the first step covariance propagation. The study of this anomaly begins with expressing the propagation of the first and second step covariance matrices in terms of a single matrix. This matrix is shown to have a rank equal to the difference between the number of first step states and the number of second step states. Furthermore, under some simplifying assumptions, it is found that the basis of the column space of this matrix remains fixed once the filter has removed the large initial state error. A test matrix containing the basis of this column space and the partial derivative matrix relating first and second step states is derived. This square test matrix, which has dimensions equal to the number of first step states, numerically drops rank at the same locations that the first step covariance does. It is formulated in terms of a set of constant vectors (the basis) and a matrix which can be computed from a reference trajectory (the partial derivative matrix). A simple example problem involving dynamics which are described by two states and a range measurement illustrate the cause of this anomaly and the application of the aforementioned numerical test in more detail.

Garrison, James L.↗
NASA NTRS2014

Effects of Forward- and Backward-Facing Steps on the Crossflow Receptivity and Stability in Supersonic Boundary Layers

The effects of forward- and backward-facing steps on the receptivity and stability of three-dimensional supersonic boundary layers over a swept wing with a blunt leading edge are numerically investigated for a freestream Mach number of 3 and a sweep angle of 30 degrees. The flow fields are obtained by solving the full Navier-Stokes equations. The evolution of instability waves generated by surface roughness is simulated with and without the forward- and backward-facing steps. The separation bubble lengths are about 5-10 step heights for the forward-facing step and are about 10 for the backward-facing step. The linear stability calculations show very strong instability in the separated region with a large frequency domain. The simulation results show that the presence of backward-facing steps decreases the amplitude of the stationary crossflow vortices with longer spanwise wavelengths by about fifty percent and the presence of forward-facing steps does not modify the amplitudes noticeably across the steps. The waves with the shorter wavelengths grow substantially downstream of the step in agreement with the linear stability prediction.

Balakumar, P.↗
NASA NTRSDate not supplied

Progress on the Development of a Step Height Sensor for the BOLT Flight Vehicle

This presentation will summarize progress on the development of a step height sensor for the BOLT flight vehicle. Two methods have been proposed to measure the step size in this effort.The first method involves the application of miniaturized camera embedded in the flight vehicle that views the step through a rearward-facing port (shown in Fig. 1a inset). The second method involves the application of a linear fiber optic array bundle to measure the intensity of light reflected back from the aft body step (concept shown in Fig. 1b). Preliminary testing with the miniaturized camera has been performed in the lab and shows that displacements of ≤10 μm can be measured using this method. Final testing with both methods will be performed on the test stand shown in Fig. 1a. This test stand will include a fine adjustment vertical translation stage that will be used to adjust the step height in steps of 1-2 μm. A high-magnification imaging system will also be used to verify the step height. The miniaturized camera and linear fiber optic array bundle will be mounted in one of several port holes with varying degrees of inclination relative to the top surface in the opposing aft-section slab. BOLT flight vehicle details and information on the steps can be found in Ref. [1].

BOLT↗
NASA NTRS2021

Modeling the Effects of a Backward-Facing Step on Boundary-Layer Transition

We model transition to turbulence in a two-dimensional boundary layer downstream of a backward-facing step (BFS) along a flat plate. With the goal of evaluating the available engineering models for predicting the effects of step excrescences on the transition characteristics, two separate methodologies are used to monitor the streamwise shift in the transition onset location as the step height and the flow speed are varied across the range of a previously reported experiment involving step-height-to-local-displacement-thickness ratios of 0 < h/δ* < 1.6. Unlike the variable N -factor method from the previous literature, both of these methods are general in scope and do not involve any empirical correlations that are specific to step excrescences. The first of these techniques involves an N -factor method that directly accounts for the change in boundary-layer instability characteristics due to the step. Stability computations using the harmonic linearized Navier-Stokes equations (HLNSE), which fully account for the nonparallel-mean-flow effects close to the BFS, indicate that the measured transition locations at nearly all test conditions ( h/δ* < 1.3) correlate well with a computed N -factor of N tr = 7.6, demonstrating a successful stability-based transition criterion related to step excrescences. Linear stability theory, which does not account for nonparallel effects, demonstrates reasonable agreement with the HLNSE results, yielding good predictions for the overall trends, but predicts a somewhat earlier onset of transition than HLNSE. The other methodology used in this work involves transport-equation-based transition models. We first show that the Langtry-Menter y - Re θt transition model cannot accurately predict the location of transition onset for moderate BFS heights because it is unable to accurately account for the flow history effects. Along with the Langtry-Menter transition model, we also show the amplification factor transport model does not produce accurate transition locations for subsonic flow over steps even though it accounts for some flow history effects.

Transition↗
NASA NTRS2021

Modeling the Effects of a Backward-Facing Step on Boundary-Layer Transition

We model transition to turbulence in a two-dimensional boundary layer downstream of a backward-facing step (BFS) along a flat plate. With the goal of evaluating the available engineering models for predicting the effects of step excrescences on the transition characteristics, two separate methodologies are used to monitor the streamwise shift in the transition onset location as the step height and the flow speed are varied across the range of a previously reported experiment involving step-height-to-local-displacement-thickness ratios of 0 < h/δ* < 1.6. Unlike the variable N -factor method from the previous literature, both of these methods are general in scope and do not involve any empirical correlations that are specific to step excrescences. The first of these techniques involves an N -factor method that directly accounts for the change in boundary-layer instability characteristics due to the step. Stability computations using the harmonic linearized Navier-Stokes equations (HLNSE), which fully account for the nonparallel-mean-flow effects close to the BFS, indicate that the measured transition locations at nearly all test conditions ( h/δ* < 1.3) correlate well with a computed N -factor of N tr = 7.6, demonstrating a successful stability-based transition criterion related to step excrescences. Linear stability theory, which does not account for nonparallel effects, demonstrates reasonable agreement with the HLNSE results, yielding good predictions for the overall trends, but predicts a somewhat earlier onset of transition than HLNSE. The other methodology used in this work involves transport-equation-based transition models. We first show that the Langtry-Menter y - Re θt transition model cannot accurately predict the location of transition onset for moderate BFS heights because it is unable to accurately account for the flow history effects. Along with the Langtry-Menter transition model, we also show the amplification factor transport model does not produce accurate transition locations for subsonic flow over steps even though it accounts for some flow history effects.

Transition↗
DOE OSTI2025

Development and application of two-step uncertainty propagation and sensitivity analysis methodology for fast reactor safety analysis

Uncertainty quantification (UQ) in nuclear reactors for transients is directly linked with safety assessment through the cross-sections uncertainties, provided as a covariance matrix, which are propagated through the reactor system to output of interest pertaining to reactor safety, such as peak temperatures in fuel/clad/coolant. Using a two-step approach, uncertainties are first quantified and propagated from basic input variables (such as reaction cross-sections) to intermediate quantities (such as reactivity feedback coefficients) through lattice level calculations. Uncertainties of intermediate quantities (from the first step) are then propagated through the system transient calculations, in the second step, to obtain uncertainties on reactor safety output parameters of interest. The scope of this work consists of Uncertainty Quantification & Propagation of nuclear data uncertainties that are highly correlated through unprotected transient overpower and unprotected loss of flow to assess their impact on core safety parameters. This two-step approach in the presence of covariance renders the sensitivity analysis very challenging. In fact, usually the sensitivity analysis is restricted to each step, which limits its application since the sensitivities between the system output quantities and the basic input variables are difficult to obtain. Here, in this work, we address this issue by proposing a simple, general methodology to combine the sensitivity indices obtained in each step by assuming the model behavior being linear. For the first step Generalized Perturbation theory based indices are used while in the second step the recently studied Johnson indices. The uncertainty quantification and sensitivity methodologies discussed here are demonstrated on a generic LFR design which is based on the 500 MWth demonstration Lead-cooled fast reactor (DLFR) using oxide fuel, developed by Westinghouse Electric Company (WEC).

42 - ENGINEERING↗
DOE OSTI2020

Experimental studies of the two-step scheme with an intense radioactive 132 Sn beam for next-generation production of very neutron-rich nuclei

The study of nuclei in the yet-unexplored, very neutron-rich, mid- to heavy-mass region of the nuclear chart, comprising perhaps half of all nuclei predicted to exist, is leading to new and/or upgraded facilities, as well as to research into the underlying production processes. In the present study, the usefulness of the two-step scheme, an alternate method to produce very neutron-rich nuclei, by a combination of an isotope-separation online (ISOL) system as a first step, and in-beam fragmentation of re-accelerated radioactive isotopes (RIs) as a second step, was investigated with a 132 Sn beam. In this work, very neutron-rich RIs around the neutron-rich neutron number N = 82 region were produced from the 278-MeV/nucleon 132 Sn beam impinging on a 5.97-mm Be target, and their production cross sections were measured. Yields were then estimated for the two-step scheme with the 132 Sn beam relative to the ones by a one-step scheme, in-flight fission of a 238 U beam, for 1-MW proton and 238 U beams at respective RI-beam facilities. This comparison suggests that the two-step scheme with the 132 Sn beam provides yields >40-times higher than those with the one-step scheme for the very neutron-rich N = 82 region. Moreover, by using various RI beams over the nuclear chart from ISOL, certain kinds of very neutron-rich RIs around the supernova r-process path can be produced with greater yields than by the one-step approach.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Quantifying and attributing time step sensitivities in present-day climate simulations conducted with EAMv1

Abstract. This study assesses the relative importance of time integration error in present-day climate simulations conducted with the atmosphere component of the Energy Exascale Earth System Model version 1 (EAMv1) at 1∘ horizontal resolution. We show that a factor-of-6 reduction of time step size in all major parts of the model leads to significant changes in the long-term mean climate. Examples of changes in 10-year mean zonal averages include the following: up to 0.5 K of warming in the lower troposphere and cooling in the tropical and subtropical upper troposphere, 1 %–10 % decreases in relative humidity throughout the troposphere, and 10 %–20 % decreases in cloud fraction in the upper troposphere and decreases exceeding 20 % in the subtropical lower troposphere. In terms of the 10-year mean geographical distribution, systematic decreases of 20 %–50 % are seen in total cloud cover and cloud radiative effects in the subtropics. These changes imply that the reduction of temporal truncation errors leads to a notable although unsurprising degradation of agreement between the simulated and observed present-day climate; to regain optimal climate fidelity in the absence of those truncation errors, the model would require retuning. A coarse-grained attribution of the time step sensitivities is carried out by shortening time steps used in various components of EAM or by revising the numerical coupling between some processes. Our analysis leads to the finding that the marked decreases in the subtropical low-cloud fraction and total cloud radiative effect are caused not by the step size used for the collectively subcycled turbulence, shallow convection, and stratiform cloud macrophysics and microphysics parameterizations but rather by the step sizes used outside those subcycles. Further analysis suggests that the coupling frequency between the subcycles and the rest of EAM significantly affects the subtropical marine stratocumulus decks, while deep convection has significant impacts on trade cumulus. The step size of the cloud macrophysics and microphysics subcycle itself appears to have a primary impact on cloud fraction in the upper troposphere and also in the midlatitude near-surface layers. Impacts of step sizes used by the dynamical core and the radiation parameterization appear to be relatively small. These results provide useful clues for future studies aiming at understanding and addressing the root causes of sensitivities to time step sizes and process coupling frequencies in EAM. While this study focuses on EAMv1 and the conclusions are likely model-specific, the presented experimentation strategy has general value for weather and climate model development, as the methodology can help researchers identify and understand sources of time integration error in sophisticated multi-component models.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1978

Flight-measured pressure characteristics of aft-facing steps in thick boundary layer flow for transonic and supersonic Mach numbers

Aft-facing step base pressure flight data were obtained for three step heights for nominal transonic Mach numbers of 0.80, 0.90, and 0.95, and for supersonic Mach numbers of 2.2, 2.5, and 2.8 with a Reynolds number, based on the fuselage length ahead of the step, of about 10 to the 8th power. Surface static pressures were measured ahead of the step, behind the step, and on the step face (base), and a boundary layer rake was used to obtain boundary layer reference conditions. A comparison of the data from the present and previous experiments shows the same trend of increasing base pressure ratio (decreasing drag) with increasing values of momentum thickness to step height ratios. However, the absolute level of these data does not always agree at the supersonic Mach numbers. For momentum thickness to height ratios near 1.0, the differences in the base pressure ratios appear to be primarily a function of Reynolds number based on the momentum thickness. Thus, for Mach numbers above 2, the data analyzed show that the base pressure ratio decreases (drag increases) as Reynolds number based on momentum thickness increases for a given momentum thickness and step height.

Powers, S. G.↗
NASA NTRS1935

The effect of depth of step on the water performance of a flying-boat hull model

NACA model 11-C was tested with four different depths of step to obtain information as to the effect of the depth of step on the water performance. The depths of step were selected to cover the practicable range of depths and in each case the included angle between the forebody and afterbody keels was kept the same 6-1/2 degrees. Small depths of step were found to give lower resistance at speeds below and at the hump speed of the model and greater depths of step lower resistance at high speeds. For low resistance throughout the speed range of the model investigated the most desirable depth of step is from 2.5 to 4.0 percent of the beam. The change of the best trim angle caused by variation of the depth of step was not appreciable. Increased depth of step caused increases in the maximum positive trimming moments at all trim angles investigated.

Bell, Joe W↗
NASA NTRS1997

Application of the Two-Step Filter to Process Ranging Measurements for Relative Navigation in an Elliptical Orbit

This estimator breaks a nonlinear estimation problem into a set of over determined 'first step' states which are linear in the observations and 'second step' states which are ultimately the states of interest. Linear estimation methods are applied to filter the observations and produce the optimal first step state estimate. The 'second step' states are obtained through iterative nonlinear parameter estimation considering the first step states as observations. It has been shown that this process exactly minimizes the least squares cost function for static problems and provides a better solution than the iterated extended Kalman filter (EKF) for dynamic problems. The two step filter is applied in this paper to process range and range rate measurements between the two spacecraft. Details of the application of the two step estimator to this problem will be given, highlighting the use of a test for ill-conditioned covariance estimates that can result from the first order covariance propagation. A comparison will be made between the performance of the two step filter and the IEKF.

Garrison, James L.↗
NASA NTRS1997

Unsteady Crystal Growth Due to Step-Bunch Cascading

Based on our experimental findings of growth rate fluctuations during the crystallization of the protein lysozym, we have developed a numerical model that combines diffusion in the bulk of a solution with diffusive transport to microscopic growth steps that propagate on a finite crystal facet. Nonlinearities in layer growth kinetics arising from step interaction by bulk and surface diffusion, and from step generation by surface nucleation, are taken into account. On evaluation of the model with properties characteristic for the solute transport, and the generation and propagation of steps in the lysozyme system, growth rate fluctuations of the same magnitude and characteristic time, as in the experiments, are obtained. The fluctuation time scale is large compared to that of step generation. Variations of the governing parameters of the model reveal that both the nonlinearity in step kinetics and mixed transport-kinetics control of the crystallization process are necessary conditions for the fluctuations. On a microscopic scale, the fluctuations are associated with a morphological instability of the vicinal face, in which a step bunch triggers a cascade of new step bunches through the microscopic interfacial supersaturation distribution.

Vekilov, Peter G.↗
NASA NTRS2003

Step Bunch Evolution on Vicinal Faces of KDP

For in-situ studies of the formation and evolution of step patterns in solution growth, we have assembled an experimental setup based on Michelson interferometry with the growing crystal surface as one of the reflective surfaces. The device allows data collection over a relatively large area (approximately 4 sq. mm) in situ and in real time during growth. The depth resolution is improved over traditional interferometry using phase-shifted images combining by a suitable algorithm. We achieve a depth resolution of approximately 50 Angstroms. Lateral resolution, dependent on the degree of magnification, is around 0.3 to 5 microns. The crystal chosen as a model in this work is potassium dihydrogen phosphate (KDP), the optically non-linear material widely used in frequency doubling applications. Kinetics of KDP crystallization is well studied so that KDP can serve as a benchmark for our investigations. We present quantitative results on the onset, initial stages and development of instabilities in moving step trains on vicinal crystal surfaces at varying supersaturation, flow rate, and flow direction. The kinetics data suggest that at low supersaturations, step bunching is caused by impurity retardation of the steps, while at higher supersaturations, we link the non-linearity during growth to interdependence of the velocity and density of the steps evidenced in independent experiments. The behavior on the surface is very dynamic, small bunches both merge and split from larger bunches as they travel across the facet. We present evidence that despite these dynamics, under steady conditions there exists a limiting value to step bunch height. This height is reached at distances between 600 and 1000 microns from the step source. In our experiments, we observed the retention of this step bunch height limit up to the path of 1500 microns.

Booth, N. A.↗
NASA NTRS1947

Aerodynamic Characteristics of Three Deep-Stepped Planing-Tail Flying-Boat Hulls

An investigation was made in the Langley 300 MPH 7- by 10-foot tunnel to determine the aerodynamic characteristics of three deep-stepped planing-tail flying-boat hulls differing only in the amount of step fairing. The hulls were derived by increasing the unfaired step depth of a planing-tail hull of a previous aerodynamic investigation to a depth about 92 percent of the hull beam. Tests were also made on a transverse-stepped hull with an extended afterbody for the purpose of comparison and in order to extend and verify the results of a previous investigation. The investigation indicated that the extended afterbody hull had a minimum drag coefficient about the same as a conventional hull, 0.0066, and an angle-of-attack range for minimum drag coefficient of 0.0057 which was 14 percent less than the transverse stepped hull with extended afterbody; the hulls with step fairing had up to 44 percent less minimum drag coefficient than the transverse-stepped hull, or slightly more drag than a streamlined body having approximately the same length and volume. Longitudinal and lateral instability varied little with step fairing and was about the same as a conventional hull.

Riebe, John M.↗
NASA NTRS2006

Recent Results from Epitaxial Growth on Step Free 4H-SiC Mesas

This paper updates recent progress made in growth, characterization, and understanding of high quality homoepitaxial and heteroepitaxial films grown on step-free 4H-SiC mesas. First, we report initial achievement of step-free 4H-SiC surfaces with carbon-face surface polarity. Next, we will describe further observations of how step-free 4H-SiC thin lateral cantilever evolution is significantly impacted by crystal faceting behavior that imposes non-uniform film thickness on cantilever undersides. Finally, recent investigations of in-plane lattice constant mismatch strain relief mechanisms observed for heteroepitaxial growth of 3C-SiC as well as 2H-AlN/GaN heterofilms on step-free 4H-SiC mesas will be reviewed. In both cases, the complete elimination of atomic heterointerface steps on the mesa structure enables uniquely well-ordered misfit dislocation arrays to form near the heterointerfaces with remarkable lack of dislocations threading vertically into the heteroepilayers. In the case of 3C-SiC heterofilms, it has been proposed that dislocation half-loops nucleate at mesa edges and glide laterally along the step-free 3C/4H interfaces. In contrast, 3C-SiC and 2H-AlN/GaN heterofilms grown on 4H-SiC mesas with steps exhibit highly disordered interface misfit dislocation structure coupled with 100X greater density of dislocations threading through the thickness of the heteroepilayers. These results indicate that the presence of steps at the heteroepitaxial interface (i.e., on the initial heteroepitaxial nucleation surface) plays a highly important role in the defect structure, quality, and relaxation mechanisms of single-crystal heteroepitaxial films.

Neudeck, Philip G.↗
DOE OSTI2022

High-order multirate explicit time-stepping schemes for the baroclinic-barotropic split dynamics in primitive equations

In order to treat the multiple time scales of ocean dynamics in an efficient manner, the baroclinic-barotropic splitting technique has been widely used for solving the primitive equations for ocean modeling. Based on the framework of strong stability-preserving Runge-Kutta approach, we propose two high-order multirate explicit time-stepping schemes (SSPRK2-SE and SSPRK3-SE) for the resulting split system in this paper. The proposed schemes allow for a large time step to be used for the three-dimensional baroclinic (slow) mode and a small time step for the two-dimensional barotropic (fast) mode, in which each of the two mode solves just need to satisfy their respective CFL conditions for numerical stability. Specifically, at each time step, the baroclinic velocity is first computed by advancing the baroclinic mode and fluid thickness of the system with the large time-step and the assistance of some intermediate approximations of the barotropicmode obtained by substepping with the small time step; then the barotropic velocity is corrected by using the small time step to re-advance the barotropic mode un-der an improved barotropic forcing produced by interpolation of the forcing terms from the preceding baroclinic mode solves; lastly, the fluid thickness is updated by coupling the baroclinic and barotropic velocities. Additionally, numerical inconsistencies on the discretized sea surface height caused by the mode splitting are relieved via a reconciliation process with carefully calculated flux deficits. Here, two benchmark tests from the “MPAS-Ocean” platform are carried out to numerically demonstrate the performance and parallel scalability of the proposed SSPRK-SE schemes.

54 ENVIRONMENTAL SCIENCES↗