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DOE OSTI2022

Utah FORGE Phase 3 Native State Model: 2022 Update

This is the Phase 3 native state model update. The Phase 3 numerical model represents a significant subsurface volume below the FORGE site footprint. The model domain of 4.0 km x 4.0 km x 4.2 km is located approximately between depths of 4000 to 4200 meters below land surface. This data archive consists of 10 files, 4 of which are simulation input files and the remaining 6 are simulation output files. There is an included readme.txt file that contains details on each of the data files. The input files include meshes, FALCON code inputs, tabulated data of water properties, temperature values, and model boundaries. The output files include simulation outfiles and point data of modeled material properties.

15 GEOTHERMAL ENERGY↗

NASA NTRS1990

Implicit solution of three-dimensional internal turbulent flows

The scalar form of the approximate factorization method was used to develop a new code for the solution of three-dimensional internal laminar and turbulent compressible flows. The Navier-Stokes equations in their Reynolds-averaged form are iterated in time until a steady solution is reached. Evidence is given to the implicit and explicit artificial damping schemes that proved to be particularly efficient in speeding up convergence and enhancing the algorithm robustness. A conservative treatment of these terms at domain boundaries is proposed in order to avoid undesired mass and/or momentum artificial fluxes. Turbulence effects are accounted for by the zero-equation Baldwin-Lomax turbulence model and the q-omega two-equation model. For the first, an investigation on the model behavior in case of multiple boundaries is performed. The flow in a developing S-duct is then solved in the laminar regime at Reynolds number (Re) 790 and in the turbulent regime at Re=40,000 using the Baldwin-Lomax model . The Stanitz elbow is then solved using an inviscid version of the same code at M(sub inlet)=0.4. Grid dependence and convergence rate are investigated showing that for this solver the implicit damping scheme may play a critical role for convergence characteristics. The same flow at Re=2.5x10(exp 6) is solved with the Baldwin-Lomax and the q-omega models. Both approaches showed satisfactory agreement with experiments, although the q-omega model is slightly more accurate.

Michelassi, V.↗

NASA NTRS1991

Implicit solution of three-dimensional internal turbulent flows

The scalar form of the approximate factorization method was used to develop a new code for the solution of three dimensional internal laminar and turbulent compressible flows. The Navier-Stokes equations in their Reynolds-averaged form were iterated in time until a steady solution was reached. Evidence was given to the implicit and explicit artificial damping schemes that proved to be particularly efficient in speeding up convergence and enhancing the algorithm robustness. A conservative treatment of these terms at the domain boundaries was proposed in order to avoid undesired mass and/or momentum artificial fluxes. Turbulence effects were accounted for by the zero-equation Baldwin-Lomax turbulence model and the q-omega two-equation model. The flow in a developing S-duct was then solved in the laminar regime in a Reynolds number (Re) of 790 and in the turbulent regime at Re equals 40,000 by using the Baldwin-Lomax model. The Stanitz elbow was then solved by using an invicid version of the same code at M sub inlet equals 0.4. Grid dependence and convergence rate were investigated, showing that for this solver the implicit damping scheme may play a critical role for convergence characteristics. The same flow at Re equals 2.5 times 10(exp 6) was solved with the Baldwin-Lomax and the q-omega models. Both approaches show satisfactory agreement with experiments, although the q-omega model was slightly more accurate.

Michelassi, V.↗

NASA NTRS1996

Time-Dependent Parabolic Finite Difference Formulation for Harmonic Sound Propagation in a Two-Dimensional Duct with Flow

An explicit finite difference real time iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for future large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable for a harmonic monochromatic sound field, a parabolic (in time) approximation is introduced to reduce the order of the governing equation. The analysis begins with a harmonic sound source radiating into a quiescent duct. This fully explicit iteration method then calculates stepwise in time to obtain the 'steady state' harmonic solutions of the acoustic field. For stability, applications of conventional impedance boundary conditions requires coupling to explicit hyperbolic difference equations at the boundary. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.

Kreider, Kevin L.↗

DOE OSTI2021

Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation

We report the Boltzmann equation with the Bhatnagar-Gross-Krook collision model (Boltzmann-BGK equation) has been employed to describe multiscale flows, i.e., from the hydrodynamic limit to free molecular flow. In this study we employ physics-informed neural networks (PINNs) to solve forward and inverse problems via the Boltzmann-BGK formulation (PINN-BGK), enabling PINNs to model flows in both the continuum and rarefied regimes. In particular, the PINN-BGK is composed of three sub-networks, i.e., the first for approximating the equilibrium distribution function, the second for approximating the non-equilibrium distribution function, and the third one for encoding the Boltzmann-BGK equation as well as the corresponding boundary/initial conditions. By minimizing the residuals of the governing equations and the mismatch between the predicted and provided boundary/initial conditions, we can approximate the Boltzmann-BGK equation for both continuous and rarefied flows. For forward problems, the PINN-BGK is utilized to solve various benchmark flows given boundary/initial conditions, e.g. Kovasznay flow, Taylor-Green flow, cavity flow, and micro Couette flow for Knudsen number up to 5. For inverse problems, we focus on rarefied flows in which accurate boundary conditions are difficult to obtain. We employ the PINN-BGK to infer the flow field in the entire computational domain given a limited number of interior scattered measurements on the velocity without using the (unknown) boundary conditions. Results for the two-dimensional micro Couette and micro cavity flows with Knudsen numbers ranging from 0.1 to 10 indicate that the PINN-BGK can infer the velocity field in the entire domain with good accuracy. Finally, we also present some results on using transfer learning to accelerate the training process. Specifically, we can obtain a three-fold speedup comparted to the standard training process (e.g., Adam plus L-BFG-B) for the two-dimensional flow problems considered in our work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2023

Split-Step Simulations to Assess the Effects of Atmospheric Boundary Layer Turbulence on the Dose Variability of N-Waves and Shaped Booms

The effects of atmospheric boundary layer turbulence on the loudness variability of a sonic boom N-wave and shaped boom are examined with split-step simulations. The shaped boom is representative of a design iteration of the NASA X-59 aircraft. Inhomogeneous atmospheric boundary layer turbulence is generated in the computational domain by a Fourier synthesis method. The N-wave and shaped boom are propagated through turbulent fields representing eight different convection levels measured at the NASA Kennedy Space Center and the NASA Armstrong Flight Research Center. Probability density functions of the formation of caustic regions along the propagation direction are computed from the N-wave results, and a parameter to collapse the caustic PDFs that accounts for both fluctuation intensities and length scales is proposed. Statistical results concerning loudness metric variability are presented, and the standard deviations of several metrics are shown to collapse across different convection levels of turbulence for small nondimensional propagation distances. The loudness metric distributions are observed to be well approximated by a normal distribution for a given range of propagation distances, and become increasingly skewed as distance increases. A model function for the dose variability is proposed, and the function parameters are found to be related to the convection level of the turbulence. The model for the dose variability distribution is compared to simulation data that were not used to find the regression parameters of the model. At several nondimensional propagation distances, agreement is observed between the model and the simulation data. These results indicate that the model may be suitable for providing quick estimates of noise dose variability in the primary carpet region across a wide range of atmospheric boundary layer conditions.

Sonic boom↗

NASA NTRS2015

RACORO Continental Boundary Layer Cloud Investigations: 1. Case Study Development and Ensemble Large-Scale Forcings

Observation-based modeling case studies of continental boundary layer clouds have been developed to study cloudy boundary layers, aerosol influences upon them, and their representation in cloud- and global-scale models. Three 60 h case study periods span the temporal evolution of cumulus, stratiform, and drizzling boundary layer cloud systems, representing mixed and transitional states rather than idealized or canonical cases. Based on in situ measurements from the Routine AAF (Atmospheric Radiation Measurement (ARM) Aerial Facility) CLOWD (Clouds with Low Optical Water Depth) Optical Radiative Observations (RACORO) field campaign and remote sensing observations, the cases are designed with a modular configuration to simplify use in large-eddy simulations (LES) and single-column models. Aircraft measurements of aerosol number size distribution are fit to lognormal functions for concise representation in models. Values of the aerosol hygroscopicity parameter, kappa, are derived from observations to be approximately 0.10, which are lower than the 0.3 typical over continents and suggestive of a large aerosol organic fraction. Ensemble large-scale forcing data sets are derived from the ARM variational analysis, European Centre for Medium-Range Weather Forecasts, and a multiscale data assimilation system. The forcings are assessed through comparison of measured bulk atmospheric and cloud properties to those computed in "trial" large-eddy simulations, where more efficient run times are enabled through modest reductions in grid resolution and domain size compared to the full-sized LES grid. Simulations capture many of the general features observed, but the state-of-the-art forcings were limited at representing details of cloud onset, and tight gradients and high-resolution transients of importance. Methods for improving the initial conditions and forcings are discussed. The cases developed are available to the general modeling community for studying continental boundary clouds.

Boundary layers↗

NASA NTRS1995

Flow simulations about steady-complex and unsteady moving configurations using structured-overlapped and unstructured grids

The limiting factor in simulating flows past realistic configurations of interest has been the discretization of the physical domain on which the governing equations of fluid flow may be solved. In an attempt to circumvent this problem, many Computational Fluid Dynamic (CFD) methodologies that are based on different grid generation and domain decomposition techniques have been developed. However, due to the costs involved and expertise required, very few comparative studies between these methods have been performed. In the present work, the two CFD methodologies which show the most promise for treating complex three-dimensional configurations as well as unsteady moving boundary problems are evaluated. These are namely the structured-overlapped and the unstructured grid schemes. Both methods use a cell centered, finite volume, upwind approach. The structured-overlapped algorithm uses an approximately factored, alternating direction implicit scheme to perform the time integration, whereas, the unstructured algorithm uses an explicit Runge-Kutta method. To examine the accuracy, efficiency, and limitations of each scheme, they are applied to the same steady complex multicomponent configurations and unsteady moving boundary problems. The steady complex cases consist of computing the subsonic flow about a two-dimensional high-lift multielement airfoil and the transonic flow about a three-dimensional wing/pylon/finned store assembly. The unsteady moving boundary problems are a forced pitching oscillation of an airfoil in a transonic freestream and a two-dimensional, subsonic airfoil/store separation sequence. Accuracy was accessed through the comparison of computed and experimentally measured pressure coefficient data on several of the wing/pylon/finned store assembly's components and at numerous angles-of-attack for the pitching airfoil. From this study, it was found that both the structured-overlapped and the unstructured grid schemes yielded flow solutions of comparable accuracy for these simulations. This study also indicated that, overall, the structured-overlapped scheme was slightly more CPU efficient than the unstructured approach.

Newman, James C., III↗

NASA NTRS2011

Three-Dimensional Modeling of the Solar Wind: From the Coronal Base to the Outer Heliosphere

We have developed a global fully three-dimensional magnetohydrodynamic solar wind model for the region that extends from the coronal base to 100 AU. The simulation domain consists of tree spherical shell subdomains with computational boundaries between them placed at 20 solar radii and 0.3 AU. The location of the first boundary ensures that the flow at the boundary is both supersonic and super-Alfvenic. A steady-state solution in the innermost (coronal) region is obtained by the time-relaxation method. The solution uses a tilted dipole model or solar magnetograms as the boundary condition at the coronal base and includes a flux of Alfven waves in the WKB approximation which provide additional acceleration for the coronal outflow in the open field regions. The intermediate region solution is constructed by the integration of steady-state equations along radius using a marching scheme. The outer region solution (0.3-100 AU) is obtained again by the time relaxation and takes into account turbulence transport and heating as well as heating, flow deceleration, and other effects due to the interstellar pickup protons treated as a separate fluid. We use the model to simulate the global steady-state structure of the solar wind from the coronal base to the heliospheric boundary and compare the results with Ulysses and Voyager observations.

Usmanov, A. V↗

NASA NTRSDate not supplied

An Extension of the Truncated Ingard-Myers Impedance Boundary Condition for High Mach Number Grazing Flows

The Ingard-Myers impedance boundary condition is widely recognized to be prone to hydrodynamic Kelvin-Helmholtz-type instability, primarily due to its use of a vortex sheet to model the flow at the boundary. Recently, a stabilized approximation of the Ingard-Myers condition, called the Truncated Ingard-Myers Impedance Boundary Condition (TIMIBC), has been introduced. This approximation offers a good representation of the Ingard-Myers condition for grazing flows characterized by low to mid subsonic Mach numbers. This paper explores an extension of the TIMIBC, referred to as TIMIBC-ext, designed for liners in grazing flows with high subsonic Mach numbers. The TIMIBC-ext introduces a tunable parameter and demonstrates that by judiciously selecting the parameter value, the accuracy of the TIMIBC can be improved for either upstream or downstream propagating waves in grazing flows with high subsonic Mach numbers. Consequently, the TIMIBC-ext represents an enhancement to the TIMIBC when the location of the source relative to the liner (upstream or downstream) is known. Time domain implementations of the TIMIBC-ext are also provided, employing a multipole expansion model for the impedance function. A numerical example is provided to assess the performance of the TIMIBC-ext, comparing computational results with measurements from a recent set of measurements in the NASA Langley Grazing Flow Impedance Tube.

time domain acoustic scattering↗

DOE OSTI2020

Dimits shift, avalanche-like bursts, and solitary propagating structures in the two-field flux-balanced Hasegawa–Wakatani model for plasma edge turbulence

We show that the recently introduced two-field flux-balanced Hasegawa–Wakatani (BHW) model captures the key features of drift-wave turbulent transport mediated by zonal flows observed in more complete and accurate gyrokinetic simulations, such as the existence of a nonlinear upshift of the threshold for drift wave turbulence driven transport, often called the Dimits shift, as well as non-local transport with avalanche bursts and solitary propagating structures. Because of the approximations made in the BHW model, these observations are made for the particle flux instead of the heat flux more commonly studied in ion temperature gradient (ITG) driven turbulence in fluid or gyrokinetic codes. Many of these features are not seen in other Hasegawa–Wakatani models, which confirm the critical role of the electron dynamics parallel to the magnetic field lines. To address questions regarding the role of boundary conditions on the drift-wave zonal flow dynamics, we apply our model to both a channel domain geometry and the more typical doubly periodic geometry. We only observe strong soliton-like solutions in the particle flux for the channel geometry, in the vicinity of the boundaries, where strong velocity shear and density gradients are generated, which are absent in the doubly periodic simulations. Changing the aspect ratio of the simulation domain also has a significant effect. In domains which are elongated in the radial direction, more complex multi-scale dynamics takes place, with multiple zonal jets interacting with each other, and large scale avalanches.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2001

Linear and Order Statistics Combiners for Pattern Classification

Several researchers have experimentally shown that substantial improvements can be obtained in difficult pattern recognition problems by combining or integrating the outputs of multiple classifiers. This chapter provides an analytical framework to quantify the improvements in classification results due to combining. The results apply to both linear combiners and order statistics combiners. We first show that to a first order approximation, the error rate obtained over and above the Bayes error rate, is directly proportional to the variance of the actual decision boundaries around the Bayes optimum boundary. Combining classifiers in output space reduces this variance, and hence reduces the 'added' error. If N unbiased classifiers are combined by simple averaging. the added error rate can be reduced by a factor of N if the individual errors in approximating the decision boundaries are uncorrelated. Expressions are then derived for linear combiners which are biased or correlated, and the effect of output correlations on ensemble performance is quantified. For order statistics based non-linear combiners, we derive expressions that indicate how much the median, the maximum and in general the i-th order statistic can improve classifier performance. The analysis presented here facilitates the understanding of the relationships among error rates, classifier boundary distributions, and combining in output space. Experimental results on several public domain data sets are provided to illustrate the benefits of combining and to support the analytical results.

Tumer, Kagan↗

DOE OSTI2020

Improvements to the Modeling of the TREAT Reactor and Experiments

This paper summarizes the latest improvements and lessons learned from the modeling and simulation of the transient test reactor at Idaho National Laboratory using the MAM- MOTH reactor physics application. MAMMOTH is a MOOSE-based, Finite Element Method application that specializes in the analysis of the spatial dynamics behavior of nuclear reactors. Since early 2018 several transient tests have been conducted at TREAT, thus providing the opportunity to apply and benchmark modern modeling and simulation tools. MAMMOTH was used to provide predictions of the power coupling factor between the core and the experiment for various experiments. Even though the power coupling factor predictions agree very well with the experimental data, within the bounds of the experimental uncertainty, one shortcoming was the underprediction of the total energy deposited in the core and in the experiment. Determination of the sources for this discrepancy are ongoing, but several key problems have been identified and resolved, thus providing valuable insights for future research. This paper discusses several of these lessons learned. First, the heat capacity data for the TREAT fuel has some significant problems due to limitations of the measurement techniques used circa 1960s. The sensitivity of the peak power and the total energy deposition to various representations of the heat capacity is approximately 5%. Second, the effects of the biological shield and thermal column on the modeling of the core are non-negligible, since they affect the mean generation time and the effective reflection of neutrons back into the core, which is suspected to be important during the core heat up. Matching the reactor period resolves the fact that the reduced spatial domain used in the MAMMOTH model underpredicts the mean generation time. The neutron reflection from these regions is marginally improved with the use of an albedo boundary condition. Third, modeling of the control rod movement with a multi-scheme method is introduced and its current limitations are exposed. Fourth, we explore the effects of using a homogenized model with Superhomogenization equivalence and how that differs from fully heterogeneous simulations. Finally, the energy condensation effects for this graphite core are significant. Solutions with 10 and 26 energy groups show the benefits of using a finer coarse group structure.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS2012

Modeling the Effects of Beam Size and Flaw Morphology on Ultrasonic Pulse/Echo Sizing of Delaminations in Carbon Composites

The size and shape of a delamination in a multi-layered structure can be estimated in various ways from an ultrasonic pulse/echo image. For example the -6dB contours of measured response provide one simple estimate of the boundary. More sophisticated approaches can be imagined where one adjusts the proposed boundary to bring measured and predicted UT images into optimal agreement. Such approaches require suitable models of the inspection process. In this paper we explore issues pertaining to model-based size estimation for delaminations in carbon fiber reinforced laminates. In particular we consider the influence on sizing when the delamination is non-planar or partially transmitting in certain regions. Two models for predicting broadband sonic time-domain responses are considered: (1) a fast "simple" model using paraxial beam expansions and Kirchhoff and phase-screen approximations; and (2) the more exact (but computationally intensive) 3D elastodynamic finite integration technique (EFIT). Model-to-model and model-to experiment comparisons are made for delaminations in uniaxial composite plates, and the simple model is then used to critique the -6dB rule for delamination sizing.

Margetan, Frank J.↗

DOE OSTI2020

Development and Validation of Passive Yaw in the Open-Source WEC-Sim Code

A passive yaw implementation is developed, validated, and explored for the WEC-Sim, an open-source wave energy converter modeling tool that works within MATLAB/Simulink. The Reference Model 5 (RM5) is selected for this investigation, and a WEC-Sim model of the device is modified to allow yaw motion. A boundary element method (BEM) code was used to calculate the excitation force coefficients for a range of wave headings. An algorithm was implemented in WEC-Sim to determine the equivalent wave heading from a body’s instantaneous yaw angle and interpolate the appropriate excitation coefficients to ensure the correct time-domain excitation force. This approach is able to determine excitation force for a body undergoing large yaw displacement. For the mathematically simple case of regular wave excitation, the dynamic equation was integrated numerically and found to closely approximate the results from this implementation in WEC-Sim. A case study is presented for the same device in irregular waves. In this case, computation time is increased by 32x when this interpolation is performed at every time step. To reduce this expense, a threshold yaw displacement can be set to reduce the number of interpolations performed. A threshold of 0.01° was found to increase computation time by only 22x without significantly affecting time domain results. Similar amplitude spectra for yaw force and displacements are observed for all threshold values less than 1°, for which computation time is only increased by 2.2x.

50 EE - Wind and Water Power Program - Water (EE-4↗

DOE OSTI2020

Development and Validation of Passive Yaw in the Open-Source WEC-Sim Code: Preprint

A passive yaw implementation is developed, validated, and explored for the Wave Energy Converter Simulator (WEC-Sim), an open-source wave energy converter modeling tool that works within MATLAB/Simulink. The Reference Model 5 (RM5) is selected for this investigation, and a WEC-Sim model of the device is modified to allow yaw motion. A boundary element method (BEM) code was used to calculate the excitation force coefficients for a range of wave headings. An algorithm was implemented in WEC-Sim to determine the equivalent wave heading from a body’s instantaneous yaw angle and interpolate the appropriate excitation coefficients to ensure the correct time-domain excitation force. This approach is able to determine excitation force for a body undergoing large yaw displacement. For the mathematically simple case of regular wave excitation, the dynamic equation was integrated numerically and found to closely approximate the results from this implementation in WEC-Sim. A case study is presented for the same device in irregular waves. In this case, computation time is increased by 32x when this interpolation is performed at every time step. To reduce this expense, a threshold yaw displacement can be set to reduce the number of interpolations performed. A threshold of 0.01 was found to increase computation time by only 22x without significantly affecting time domain results. Similar amplitude spectra for yaw force and displacements are observed for all threshold values less than or equal to 1, for which computation time is only increased by 2.2x.

50 EE - Wind and Water Power Program - Water (EE-4↗

NASA NTRS2004

Interaction of a Boundary Layer with a Turbulent Wake

The objective of this grant was to study the transition mechanisms on a flat-plate boundary layer interacting with the wake of a bluff body. This is a simplified configuration presented and designed to exemplify the phenomena that occur in multi-element airfoils, in which the wake of an upstream element impinges on a downstream one. Some experimental data is available for this configuration at various Reynolds numbers. The first task carried out was the implementation and validation of the immersed-boundary method. This was achieved by performing calculations of the flow over a cylinder at low and moderate Reynolds numbers. The low-Reynolds number results are discussed, which is enclosed as Appendix A. The high-Reynolds number results are presented in a paper in preparation for the Journal of Fluid Mechanics. We performed calculations of the wake-boundary-layer interaction at two Reynolds numbers, Re approximately equal to 385 and 1155. The first case is discussed and a comparison of the two calculations is reported. The simulations indicate that at the lower Reynolds number the boundary layer is buffeted by the unsteady Karman vortex street shed by the cylinder. This is shown: long streaky structures appear in the boundary layer in correspondence of the three-dimensionalities in the rollers. The fluctuations, however, cannot be self-sustained due to the low Reynolds-number, and the flow does not reach a turbulent state within the computational domain. In contrast, in the higher Reynolds-number case, boundary-layer fluctuations persist after the wake has decayed (due, in part, to the higher values of the local Reynolds number Re achieved in this case); some evidence could be observed that a self-sustaining turbulence generation cycle was beginning to be established. A third simulation was subsequently carried out at a higher Reynolds number, Re=3900. This calculation gave results similar to those of the Re=l155 case. Turbulence was established at fairly low Reynolds number, as a consequence of the high level of the free-stream perturbation. An instantaneous flow visualization for that case is shown. A detailed examination of flow statistics in the transitional and turbulent regions, including the evolution of the turbulent kinetic energy (TKE) budget and frequency spectra showed the formation and evolution of turbulent spots characteristic of the bypass transition mechanism. It was also observed that the turbulent eddies achieved an equilibrium, fully developed turbulent states first, as evidenced by the early agreement achieved by the terms in the TKE budget with those observed in turbulent flows. Once a turbulent Reynolds stress profile had been established, the velocity profile began to resemble a turbulent one, first in the inner region and later in the outer region of the wall layer. An extensive comparison of the three cases, including budgets, mean velocity and Reynolds stress profiles and flow visualization, is included. The results obtained are also presented.

Piomelli, Ugo↗

NASA NTRS1994

Backward-facing step measurements at low Reynolds number, Re(sub h)=5000

An experimental study of the flow over a backward-facing step at low Reynolds number was performed for the purpose of validating a direct numerical simulation (DNS) which was performed by the Stanford/NASA Center for Turbulence Research. Previous experimental data on back step flows were conducted at Reynolds numbers and/or expansion ratios which were significantly different from that of the DNS. The geometry of the experiment and the simulation were duplicated precisely, in an effort to perform a rigorous validation of the DNS. The Reynolds number used in the DNS was Re(sub h)=5100 based on step height, h. This was the maximum possible Reynolds number that could be economically simulated. The boundary layer thickness, d, was approximately 1.0 h in the simulation and the expansion ratio was 1.2. The Reynolds number based on the momentum thickness, Re(sub theta), upstream of the step was 610. All of these parameters were matched experimentally. Experimental results are presented in the form of tables, graphs and a floppy disk (for easy access to the data). An LDV instrument was used to measure mean velocity components and three Reynolds stresses components. In addition, surface pressure and skin friction coefficients were measured. LDV measurements were acquired in a measuring domain which included the recirculating flow region.

Jovic, Srba↗