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DOE OSTI2024

Rapidly convergent quantum Monte Carlo using a Chebyshev projector

The multireference coupled-cluster Monte Carlo (MR-CCMC) algorithm is a determinant-based quantum Monte Carlo (QMC) algorithm that is conceptually similar to Full Configuration Interaction QMC (FCIQMC). It has been shown to offer a balanced treatment of both static and dynamic correlation while retaining polynomial scaling, although application to large systems with significant strong correlation remained impractical. In this paper, we document recent algorithmic advances that enable rapid convergence and a more black-box approach to the multireference problem. These include a logarithmically scaling metric-tree-based excitation acceptance algorithm to search for determinants connected to the reference space at the desired excitation level and a symmetry-screening procedure for the reference space. We show that, for moderately sized reference spaces, the new search algorithm brings about an approximately 8-fold acceleration of one MR-CCMC iteration, while the symmetry screening procedure reduces the number of active reference space determinants with essentially no loss of accuracy. We also introduce a stochastic implementation of an approximate wall projector, which is the infinite imaginary time limit of the exponential projector, using a truncated expansion of the wall function in Chebyshev polynomials. Notably, this wall-Chebyshev projector can be used to accelerate any projector-based QMC algorithm. We show that it requires significantly fewer applications of the Hamiltonian to achieve the same statistical convergence. We benchmark these acceleration methods on the beryllium and carbon dimers, using initiator FCIQMC and MR-CCMC with basis sets up to cc-pVQZ quality.

Zhao, Zijun↗

NASA NTRS1980

On the calculation of turbulent heat transport downstream from an abrupt pipe expansion

A numerical study is reported of flow and heat transfer in the separated flow region created by an abrupt pipe expansion. Computations employed an adaptation of the TEACH-2E computer program with the standard model of turbulence. Emphasis is given to the simulation, from both a physical and numerical viewpoint, of the region in the immediate vicinity of the wall where turbulent transport gives way to molecular conduction and diffusion. Wall resistance laws or wall functions used to bridge this near-wall region are based on the idea that, beyond the viscous sublayer, the turbulent length scale is universal, increasing linearly with distance from the wall. Predictions of expermental data for a diameter ratio of 0.54 show generally encouraging agreement with experiment. At a diameter of 0.43 different trends are discernible between measurement and calculation though this appears to be due to effects unconnected with the wall region studied.

Chieng, C. C.↗

NASA NTRS1994

An analysis of supersonic flows with low-Reynolds number compressible two-equation turbulence models using LU finite volume implicit numerical techniques

A generalized flow solver using an implicit Lower-upper (LU) diagonal decomposition based numerical technique has been coupled with three low-Reynolds number kappa-epsilon models for analysis of problems with engineering applications. The feasibility of using the LU technique to obtain efficient solutions to supersonic problems using the kappa-epsilon model has been demonstrated. The flow solver is then used to explore limitations and convergence characteristics of several popular two equation turbulence models. Several changes to the LU solver have been made to improve the efficiency of turbulent flow predictions. In general, the low-Reynolds number kappa-epsilon models are easier to implement than the models with wall-functions, but require much finer near-wall grid to accurately resolve the physics. The three kappa-epsilon models use different approaches to characterize the near wall regions of the flow. Therefore, the limitations imposed by the near wall characteristics have been carefully resolved. The convergence characteristics of a particular model using a given numerical technique are also an important, but most often overlooked, aspect of turbulence model predictions. It is found that some convergence characteristics could be sacrificed for more accurate near-wall prediction. However, even this gain in accuracy is not sufficient to model the effects of an external pressure gradient imposed by a shock-wave/ boundary-layer interaction. Additional work on turbulence models, especially for compressibility, is required since the solutions obtained with base line turbulence are in only reasonable agreement with the experimental data for the viscous interaction problems.

Lee, J.↗

NASA NTRSDate not supplied

WMLES for the Fifth High-Lift PredictionWorkshop Cases Using FUN3D

This paper presents solution assessments and grid convergence studies for the test cases outlined in the Fifth High-Lift Prediction Workshop (HLPW-5), focusing on the high-lift Common Research Models (CRM-HL). The study utilizes a wall-modeled large-eddy simulation (WMLES) methodology developed in the unstructured-grid, node-centered flow solver FUN3D. The second-order accurate simulations conducted in this study utilize a finite-volume spatial discretization and an implicit temporal scheme. Large-scale turbulent features are resolved away from the wall, with small-scale effects captured by the Vreman subgrid-scale model. An equilibrium wall function uses the first grid point off the wall serving as the critical interface between the wall model and the large-eddy simulation region, thus requiring careful placement in grid design. WMLES solutions are assessed for HLPW-5 cases, including a clean wing-body configuration and geometry-buildup configurations corresponding to the 5.1\% ONERA CRM-HL model. Grid-convergence studies are systematically conducted using uniformly refined grids. Moreover, simulation results and grid sensitivity are presented for the NASA 5.2\% CRM-HL configuration at both moderate and flight-scale Reynolds numbers. Overall, WMLES results are satisfactory and agree well with available experimental data, especially on sufficiently fine grids.

high-lift aerodynamics↗

NASA NTRS1987

Investigation of turbulent flow in highly curved ducts with application to turbomachinery components

Numerical predictions were performed using a semi-elliptic calculation procedure for the case of turbulent flow in passage through a 90 deg bend of square cross section. Two versions of the isotropic turbulent viscosity two equation k-epsilon model were used. The first, the wall function model (WFM), employs the logarithmic law-of-the-wall relation and the notion of equilibrium flow to set all the necessary boundary conditions at the first grid point adjacent to a solid wall. The second model, the Van Driest model (VDM), employs Prandtl's original mixing length formulation, in conjunction with Van Driest's semi-empirical relation for the mixing length, to calculate the turbulent viscosity in the near wall regions of the flow. In this case, boundary conditions for k and epsilon, required to calculate these quantities in the core of the flow, are obtained by matching the mixing length and Reynolds number model formulations in an overlapping region of the flow near the walls. In both cases the results obtained show an improvement over earlier calculations using an elliptic numerical procedure. This is attributed to the finer grids possible in the present work. Of the two models, the VDM formulation shows better overall conformity with the mean flow measurements. Neither model reproduces well the details of the stress distribution as a result of the implied isotropic turbulent viscosity.

Humphrey, J. A. C.↗

NASA NTRS1987

Research on complex turbulent flows at the UW (overall effort)

Development of a pressure-strain model, an algebraic stress model, and wall functions appropriate for flows with spanwise variations in the local wall shear stress are accomplished. Furthermore, a hot-wire measurement technique was also developed for determining the local mean velocity and Reynolds stresses in a complex flow. Experiments were performed on supersonic and subsonic turbulent flow in a square duct, flow about a strut-endwall, flow within a transition duct, and on co-flowing annular jets with swirl. All results are presented in a viewgraph format.

Gessner, F. B.↗

NASA NTRS1998

Tetrahedral Finite-Volume Solutions to the Navier-Stokes Equations on Complex Configurations

A review of the algorithmic features and capabilities of the unstructured-grid flow solver USM3Dns is presented. This code, along with the tetrahedral grid generator, VGRIDns, is being extensively used throughout the U.S. for solving the Euler and Navier-Stokes equations on complex aerodynamic problems. Spatial discretization is accomplished by a tetrahedral cell-centered finite-volume formulation using Roe's upwind flux difference splitting. The fluxes are limited by either a Superbee or MinMod limiter. Solution reconstruction within the tetrahedral cells is accomplished with a simple, but novel, multidimensional analytical formula. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the near-wall region of the boundary layer. The issues of accuracy and robustness of USM3Dns Navier-Stokes capabilities are addressed for a flat-plate boundary layer, and a full F-16 aircraft with external stores at transonic speed.

Frink, Neal T.↗

NASA NTRS1998

Tetrahedral Finite-Volume Solutions to the Navier-Stokes Equations on Complex Configurations

Frink, N. T.↗

NASA NTRS1991

Modeling hypersonic boundary-layer flows with second-moment closure

An ongoing research effort designed to apply the best possible second-moment-closure model to simulate complex hypersonic flows is presented. The baseline model under consideration is the Launder-Reece-Rodi Reynolds stress transport turbulence model. Two add-ons accounting for wall effects, namely, the Launder-Shima low-Reynolds-number model and the compressible wall-function technique, are tested. Results are reported for flow over a flat plate, both adiabatic-wall and cooled-wall cases. It has been found that further improvements of the existing models are necessary to achieve accurate prediction in high Mach number flow range.

Huang, P. George↗

NASA NTRS1985

Calculation of flow about posts and powerhead model

A three dimensional analysis of the non-uniform flow around the liquid oxygen (LOX) posts in the Space Shuttle Main Engine (SSME) powerhead was performed to determine possible factors contributing to the failure of the posts. Also performed was three dimensional numerical fluid flow analysis of the high pressure fuel turbopump (HPFTP) exhaust system, consisting of the turnaround duct (TAD), two-duct hot gas manifold (HGM), and the Version B transfer ducts. The analysis was conducted in the following manner: (1) modeling the flow around a single and small clusters (2 to 10) of posts; (2) modeling the velocity field in the cross plane; and (3) modeling the entire flow region with a three dimensional network type model. Shear stress functions which will permit viscous analysis without requiring excessive numbers of computational grid points were developed. These wall functions, laminar and turbulent, have been compared to standard Blasius solutions and are directly applicable to the cylinder in cross flow class of problems to which the LOX post problem belongs.

Anderson, P. G.↗

NASA NTRS1992

The present state and the future direction of eddy viscosity models

Information is given in viewgraph form on the present state and future direction of eddy viscosity models. Topics covered include the eddy viscosity dilemma, two-equation models, equations of motion, free shear flows, incompressible free shear flows, model-predicted boundary layer structure, defect layer analysis, the effects of pressure gradients, viscous sublayer structure, wall functions and viscous damping, viscous damping for kappa-omega, the effects of compressibility, perturbation analysis of the wall layer, an alternative compressibility term, unsteady boundary layers, incompressible separation, backstep results, and compressible separation.

Wilcox, David C.↗

NASA NTRS2013

Computational Study of the CC3 Impeller and Vaneless Diffuser Experiment

Centrifugal compressors are compatible with the low exit corrected flows found in the high pressure compressor of turboshaft engines and may play an increasing role in turbofan engines as engine overall pressure ratios increase. Centrifugal compressor stages are difficult to model accurately with RANS CFD solvers. A computational study of the CC3 centrifugal impeller in its vaneless diffuser configuration was undertaken as part of an effort to understand potential causes of RANS CFD mis-prediction in these types of geometries. Three steady, periodic cases of the impeller and diffuser were modeled using the TURBO Parallel Version 4 code: 1) a k-epsilon turbulence model computation on a 6.8 million point grid using wall functions, 2) a k-epsilon turbulence model computation on a 14 million point grid integrating to the wall, and 3) a k-omega turbulence model computation on the 14 million point grid integrating to the wall. It was found that all three cases compared favorably to data from inlet to impeller trailing edge, but the k-epsilon and k-omega computations had disparate results beyond the trailing edge and into the vaneless diffuser. A large region of reversed flow was observed in the k-epsilon computations which extended from 70% to 100% span at the exit rating plane, whereas the k-omega computation had reversed flow from 95% to 100% span. Compared to experimental data at near-peak-efficiency, the reversed flow region in the k-epsilon case resulted in an under-prediction in adiabatic efficiency of 8.3 points, whereas the k-omega case was 1.2 points lower in efficiency.

Kulkarni, Sameer↗

NASA NTRS2013

Computational Study of the CC3 Impeller and Vaneless Diffuser Experiment

Centrifugal compressors are compatible with the low exit corrected flows found in the high pressure compressor of turboshaft engines and may play an increasing role in turbofan engines as engine overall pressure ratios increase. Centrifugal compressor stages are difficult to model accurately with RANS CFD solvers. A computational study of the CC3 centrifugal impeller in its vaneless diffuser configuration was undertaken as part of an effort to understand potential causes of RANS CFD mis-prediction in these types of geometries. Three steady, periodic cases of the impeller and diffuser were modeled using the TURBO Parallel Version 4 code: (1) a k-ε turbulence model computation on a 6.8 million point grid using wall functions, (2) a k-ε turbulence model computation on a 14 million point grid integrating to the wall, and (3) a k-ω turbulence model computation on the 14 million point grid integrating to the wall. It was found that all three cases compared favorably to data from inlet to impeller trailing edge, but the k-ε and k-ω computations had disparate results beyond the trailing edge and into the vaneless diffuser. A large region of reversed flow was observed in the k-ε computations which extended from 70 to 100 percent span at the exit rating plane, whereas the k-ω computation had reversed flow from 95 to 100 percent span. Compared to experimental data at near-peak-efficiency, the reversed flow region in the k-ε case resulted in an underprediction in adiabatic efficiency of 8.3 points, whereas the k-ω case was 1.2 points lower in efficiency.

Kulkarni, Sameer↗

NASA NTRS1985

Predictions and measurements of isothermal flowfields in axisymmetric combustor geometries

Numerical predictions, flow visualization experiments and time-mean velocity measurements were obtained for six basic nonreacting flowfields (with inlet swirl vane angles of 0 (swirler removed), 45 and 70 degrees and sidewall expansion angles of 90 and 45 degrees) in an idealized axisymmetric combustor geometry. A flowfield prediction computer program was developed which solves appropriate finite difference equations including a conventional two equation k-epsilon eddy viscosity turbulence model. The wall functions employed were derived from previous swirling flow measurements, and the stairstep approximation was employed to represent the sloping wall at the inlet to the test chamber. Recirculation region boundaries have been sketched from the entire flow visualization photograph collection. Tufts, smoke, and neutrally buoyant helium filled soap bubbles were employed as flow tracers. A five hole pitot probe was utilized to measure the axial, radial, and swirl time mean velocity components.

Rhodes, D. L.↗

DOE OSTI2020

Distinguishing Mesoscale Polar Order (Unidirectional vs Bidirectional) of Cellulose Microfibrils in Plant Cell Walls Using Sum Frequency Generation Spectroscopy

Cellulose in plant cell walls are synthesized as crystalline microfibrils with diameters of 3–4 nm and lengths of around 1–10 μm. These microfibrils are known to be the backbone of cell walls, and their multiscale three-dimensional organization plays a critical role in cell wall functions including plant growth and recalcitrance to degradation. The mesoscale organization of microfibrils over a 1–100 nm range in cell walls is challenging to resolve because most characterization techniques investigating this length scale suffer from low spatial resolution, sample preparation artifacts, or inaccessibility of specific cell types. Here, we report a sum frequency generation (SFG) study determining the mesoscale polarity of cellulose microfibrils in intact plant cell walls. SFG is a nonlinear optical spectroscopy technique sensitive to the molecular-to-mesoscale order of noncentrosymmetric domains in amorphous matrices. However, the quantitative theoretical model to unravel the effect of polarity in packing of noncentrosymmetric domains on SFG spectral features has remained unresolved. In this work, we show how the phase synchronization principle of the SFG process is used to predict the relative intensities of vibrational modes with different polar angles from the noncentrosymmetric domain axis. Applying this model calculation for the first time and employing SFG microscopy, we found that cellulose microfibrils in certain xylem cell walls are deposited unidirectionally (or biased in one direction) instead of the bidirectional polarity which was believed to be dominant in plant cell walls from volume-averaged characterizations of macroscopic samples. Here, with this advancement in SFG analysis, one can now determine the relative polarity of noncentrosymmetric domains such as crystalline biopolymers interspersed in amorphous polymer matrices, which will open opportunities to study new questions that have not been conceived in the past.

36 MATERIALS SCIENCE↗

NASA NTRS1989

Embedded function methods for compressible high speed turbulent flow

Fundamental issues relating to compressible turbulent flow are addressed. The focus has been on developing methods and testing concepts for attached flows rather than trying to force a conventional law of the wall into a zone of backflow. Although the dynamics of the near-wall flow in an attached turbulent boundary layer are relatively well documented, the dynamical features of a zone of reversed turbulent flow are not, nor are they well understood. Incompressibility introduces effects and issues that have been dealt with only marginally in the literature, therefore, the present work has been focussed on attached high-speed flows. The wall function method has been extended up through the supersonic to hypersonic speeds. Algorithms have been successfully introduced into the code that calculates the flow all the way to the wall, and testing is being carried out for progressively more complex flow situations.

Walker, J. D. A.↗

NASA NTRS1995

Development of a two-equation turbulence model for hypersonic flows: Evaluation of a low Reynolds number correction to the Kappa - epsilon two equation compressible turbulence model - Volume 1

The objective of the current research is the development of an improved k-epsilon two-equation compressible turbulence model for turbulent boundary layer flows experiencing strong viscous-inviscid interactions. The development of an improved model is important in the design of hypersonic vehicles such as the National Aerospace Plane (NASP) and the High Speed Civil Transport (HSCT). Improvements have been made to the low Reynolds number functions in the eddy viscosity and dissipation of solenoidal dissipation of the k-epsilon turbulence mode. These corrections offer easily applicable modifications that may be utilized for more complex geometries. The low Reynolds number corrections are functions of the turbulent Reynolds number and are therefore independent of the coordinate system. The proposed model offers advantages over some current models which are based upon the physical distance from the wall, that modify the constants of the standard model, or that make more corrections than are necessary to the governing equations. The code has been developed to solve the Favre averaged, boundary layer equations for mass, momentum, energy, turbulence kinetic energy, and dissipation of solenoidal dissipation using Keller's box scheme and the Newton spatial marching method. The code has been validated by removing the turbulent terms and comparing the solution with the Blasius solution, and by comparing the turbulent solution with an existing k-epsilon model code using wall function boundary conditions. Excellent agreement is seen between the computed solution and the Blasius solution, and between the two codes. The model has been tested for both subsonic and supersonic flat-plate turbulent boundary layer flow by comparing the computed skin friction with the Van Driest II theory and the experimental data of Weighardt; by comparing the transformed velocity profile with the data of Weighardt, and the Law of the Wall and the Law of the Wake; and by comparing the computed results of an adverse pressure gradient with the experimental data of Fernando and Smits. Good agreement is obtained with the experimental correlations for all flow conditions.

Knight, Doyle D.↗

NASA NTRS1991

Modeling turbulent boundary layers in adverse pressure gradients

Many of the turbulent layers encountered in practical flows develop in adverse pressure gradients; hence, the dynamics of the thickening and possible separation of the boundary layer has important implications for design practices. What are the key physical processes that govern how a turbulent boundary layer responds to an adverse pressure gradient, and how should these processes be modeled? Despite the ubiquity of such flows in engineering and nature, these equations remain largely unanswered. The turbulence closure models presently used to describe these flows commonly use 'wall functions' that have ad hoc corrections for the effects of pressure gradients. There is, therefore, a practical and theoretical need to examine the effects of adverse pressure gradients on wall bounded turbulent flows in order to develop models based on sound physical principle. The evolution of a turbulent boundary layer on a flat wall with an externally imposed pressure gradient is studied.

Belcher, Stephen E.↗