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Linear and nonlinear PSE for compressible boundary layers

Compressible stability of growing boundary layers is studied by numerically solving the partial differential equations under a parabolizing approximation. The resulting parabolized stability equations (PSE) account for nonparallel as well as nonlinear effects. Evolution of disturbances in compressible flat-plate boundary layers are studied for freestream Mach numbers ranging from 0 to 4.5. Results indicate that the effect of boundary-layer growth is important for linear disturbances. Nonlinear calculations are performed for various Mach numbers. Two-dimensional nonlinear results using the PSE approach agree well with those from direct numerical simulations using the full Navier-Stokes equations while the required computational time is less by an order of magnitude. Spatial simulation using PSE were carried out for both the fundamental and subharmonic type breakdown for a Mach 1.6 boundary layer. The promising results obtained show that the PSE method is a powerful tool for studying boundary-layer instabilities and for predicting transition over a wide range of Mach numbers.

Chang, Chau-Lyan

Investigation of Low-Energy Lattice Dynamics and Their Role in Superionic Na Diffusion and Ultralow Thermal Conductivity of Na 3 PSe 4 as a Solid-State Electrolyte

The atomic dynamics of Na 3 PSe 4 were investigated using a combination of neutron scattering experiments and ab initio and machine-learned molecular dynamics simulations to probe the interplay of fast ionic diffusion with atomic vibrations (phonons) of the host lattice. Our results reveal the existence of low-energy vibrational modes, simultaneously involving motions of Na + ions and framework polyanion subunits, and show that these modes become strongly overdamped in the superionic regime as they couple with the Na + hopping process. In particular, the Na+ migration energy landscape is strongly impacted by low-energy phonons derived from a soft acoustic branch of the host lattice, which modulates the diameter of the Na + diffusion channel at the bottleneck. We find that an additional factor for the enhanced Na + conductivity in Na 3 PSe 4 is the presence of Na-vacancies, which also affect the low-frequency dynamics and thermal vibration amplitudes, pointing to an interplay between Na + vacancies and host dynamics, jointly enhancing ionic diffusivity. Finally, we investigate the origin of ultralow thermal conductivities in Na 3 PSe 4 and Na 3 PS 4 using Green–Kubo simulations and find that low-energy acoustic phonon modes of the overall crystal framework provide a dominant contribution to the thermal conductivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Spatial Direct Numerical Simulation of Boundary-Layer Transition Mechanisms: Validation of PSE Theory

A study of instabilities in incompressible boundary-layer flow on a flat plate is conducted by spatial direct numerical simulation (DNS) of the Navier-Stokes equations. Here, the DNS results are used to critically evaluate the results obtained using parabolized stability equations (PSE) theory and to study mechanisms associated with breakdown from laminar to turbulent flow. Three test cases are considered: two-dimensional Tollmien-Schlichting wave propagation, subharmonic instability breakdown, and oblique-wave break-down. The instability modes predicted by PSE theory are in good quantitative agreement with the DNS results, except a small discrepancy is evident in the mean-flow distortion component of the 2-D test problem. This discrepancy is attributed to far-field boundary- condition differences. Both DNS and PSE theory results show several modal discrepancies when compared with the experiments of subharmonic breakdown. Computations that allow for a small adverse pressure gradient in the basic flow and a variation of the disturbance frequency result in better agreement with the experiments.

Joslin, R. D.

IDAES-PSE 2.5.0 Release

The Institute for the Design of Advanced Energy Systems (IDAES) Integrated Platform is a versatile computational environment offering extensive process systems engineering (PSE) capabilities for optimizing the design and operation of complex, interacting technologies and systems. IDAES enables users to efficiently search vast, complex design spaces to discover the lowest cost, most environmentally sustainable solutions while supporting the full process modeling lifecycle, from conceptual design to dynamic optimization and control. The extensible, open platform empowers users to create models of novel processes and rapidly develop custom analyses, workflows, and end-user applications. IDAES-PSE 2.5.0 Release Highlights Upcoming Changes IDAES will be switching to the new Pyomo solver interface in the next release. Whilst this will hopefully be a smooth transition for most users, there are a few important changes to be aware of. The new solver interface uses a different version of the IPOPT writer (“ipopt_v2”) and thus any custom configuration options you might have set for IPOPT will not carry over and will need to be reset. By default, the new Pyomo linear presolver will be activated with ipopt_v2. Whilst are working to identify any bugs in the presolver, it is possible that some edge cases will remain. IDAES will begin deploying a new set of scaling tools and APIs over the next few releases that make use of the new solver writers. The old scaling tools and APIs will remain for backward compatibility but will begin to be deprecated. New Models, Tools and Features New diagnostics check for near-parallel variables and constraints. New diagnostics tools for identifying causes of infeasibility in models. New example for creating a custom model of a liquid-liquid extractor unit operation. Bug Fixes Fixed bug in Gibbs reactor that caused it to appear to have additional spurious degrees of freedom. Fixed bug in the Modular Property Framework that would cause errors when trying to use phase-based material balances with phase equilibria. Fixed bug in Modular Properties Framework that caused errors when initializing models with non-vapor-liquid phase equilibria. Testing and Robustness Deployed the IDAES Diagnostics Toolbox to confirm that there are no structural or numerical issues in the core model libraries. Additional robustness tests for core model, and some associated improvements in the converge tester class. Fixed a number of issues that were causing unexpected warnings to be emitted during testing. Deprecations and Removals Removed examples for RIPE tool which has not been supported for a number of releases.

AS

IDAES-PSE 2.6.0 Release

The Institute for the Design of Advanced Energy Systems (IDAES) Integrated Platform is a versatile computational environment offering extensive process systems engineering (PSE) capabilities for optimizing the design and operation of complex, interacting technologies and systems. IDAES enables users to efficiently search vast, complex design spaces to discover the lowest cost solutions while supporting the full process modeling lifecycle, from conceptual design to dynamic optimization and control. The extensible, open platform empowers users to create models of novel processes and rapidly develop custom analyses, workflows, and end-user applications. IDAES-PSE 2.6.0 Release Highlights Upcoming Changes IDAES will be switching to the new Pyomo solver interface in the next release. Whilst this will hopefully be a smooth transition for most users, there are a few important changes to be aware of. The new solver interface uses a different version of the IPOPT writer (“ipopt_v2”) and thus any custom configuration options you might have set for IPOPT will not carry over and will need to be reset. By default, the new Pyomo linear presolver will be activated with ipopt_v2. Whilst are working to identify any bugs in the presolver, it is possible that some edge cases will remain. IDAES will begin deploying a new set of scaling tools and APIs over the next few releases that make use of the new solver writers. The old scaling tools and APIs will remain for backward compatibility but will begin to be deprecated. New Models, Tools and Features New Intersphinx extension automatically linking Jupyter notebook examples to project documentation New end-to-end diagnostics example demonstrated on a real problem New complementarity formulation for VLE with cubic equations of state, backward compatibility for old formulation New solver interface with presolve (ipopt_v2) in support of upcoming changes to the initialization and APIs methods, with default set to ipopt to maintain backwards compatibility; this will deprecate once all examples have been updated New forecaster and parameterized bidder methods within grid integration library Updated surrogates API and examples to support Keras 3, with backwards compatibility for older formats such as TensorFlow SavedModel (TFSM) Updated costing base dictionary to include the 2023 cost year index value Updated ProcessBlock to include information on the constructing block class Updated Flowsheet Visualizer to allow visualize() method to return value and functions Bug Fixes Fixed bug in the Modular Property Framework that would cause errors when trying to use phase-based material balances with phase equilibria. Fixed bug in Modular Properties Framework that caused errors when initializing models with non-vapor-liquid phase equilibria. Fixed typos flagged by June update to crate-ci/typos and removed DMF-related exceptions Minor corrections of units of measurement handling in power plant waste/transport costing expressions, control volume material holdup expressions, and BTX property package parameters Fixed throwing >7500 numpy deprecation warnings by replacing scalar value assignment with element extraction and item iteration calls Testing and Robustness Migrated slow tests (>10s) to integration, impacting test coverage but also yielding a nearly 30% decrease in local test runtime Pinned pint to avoid issues with older supported Python versions Pinned codecov versions to avoid tokenless upload behavior with latest version Bumped extensions to version 3.4.2 to allow pointing to non-standard install location Deprecations and Removals Python 3.8 is no longer supported. The supported Python versions are 3.9 through 3.12 The Data Management Framework (DMF) is no longer supported. Importing idaes.core.dmf will cause a deprecation warning to be displayed until the next release The SOFC Keras surrogates have been removed. The current version of the SOFC surrogate model in the examples repository is a PySMO Kriging model.

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IDAES-PSE 2.7.0 Release

The Institute for the Design of Advanced Energy Systems (IDAES) Integrated Platform is a versatile computational environment offering extensive process systems engineering (PSE) capabilities for optimizing the design and operation of complex, interacting technologies and systems. IDAES enables users to efficiently search vast, complex design spaces to discover the lowest cost solutions while supporting the full process modeling lifecycle, from conceptual design to dynamic optimization and control. The extensible, open platform empowers users to create models of novel processes and rapidly develop custom analyses, workflows, and end-user applications. IDAES-PSE 2.7.0 Release Highlights New features: AutoScaler and CustomScalerBase classes: Such tools are the core of the new scaling framework being implemented in IDAES. Wider adoption of scaling tools among users will result in quicker and more robust model solutions. Scaler for equilibrium reactor and saponification properties: These scaler models are examples to follow for how to use the new scaling tools. ONNX Surrogate support from Optimization & Machine Learning Toolkit (OMLT): ONNX is an open standard format to save and load ML/AI models that is widely supported by all major frameworks. This capability makes it easier for IDAES users to create surrogate models and use them without having to support each framework individually. 1D Membrane Model for CO2 Capture and Utilization: Supports ongoing efforts for modeling and optimizing polymer membrane processes for CO2 capture and conversion into formic acid. StreamScaler unit model: Unrelated to the CustomScalerBase, this unit model allows a stream’s extensive variables to be scaled by a fixed factor. This allows streams being processed by multiple units in parallel to be scaled down to unit scale and scaled back up to process scale. Bug fixes or improvements: Scaling, EoS, Diagnostics tool, Modular Properties, tests & documentation Deprecations: Old Cubic EoS

AS

Subsonic and Supersonic Jet Noise Calculations Using PSE and DNS

Noise radiated from a supersonic jet is computed using the Parabolized Stability Equations (PSE) method. The evolution of the instability waves inside the jet is computed using the PSE method and the noise radiated to the far field from these waves is calculated by solving the wave equation using the Fourier transform method. We performed the computations for a cold supersonic jet of Mach number 2.1 which is excited by disturbances with Strouhal numbers St=.2 and .4 and the azimuthal wavenumber m=l. Good agreement in the sound pressure level are observed between the computed and the measured (Troutt and McLaughlin 1980) results.

Balakumar, P.

The Langley Stability and Transition Analysis Code (LASTRAC) : LST, Linear and Nonlinear PSE for 2-D, Axisymmetric, and Infinite Swept Wing Boundary Layers

During the past two decades, our understanding of laminar-turbulent transition flow physics has advanced significantly owing to, in a large part, the NASA program support such as the National Aerospace Plane (NASP), High-speed Civil Transport (HSCT), and Advanced Subsonic Technology (AST). Experimental, theoretical, as well as computational efforts on various issues such as receptivity and linear and nonlinear evolution of instability waves take part in broadening our knowledge base for this intricate flow phenomenon. Despite all these advances, transition prediction remains a nontrivial task for engineers due to the lack of a widely available, robust, and efficient prediction tool. The design and development of the LASTRAC code is aimed at providing one such engineering tool that is easy to use and yet capable of dealing with a broad range of transition related issues. LASTRAC was written from scratch based on the state-of-the-art numerical methods for stability analysis and modem software technologies. At low fidelity, it allows users to perform linear stability analysis and N-factor transition correlation for a broad range of flow regimes and configurations by using either the linear stability theory (LST) or linear parabolized stability equations (LPSE) method. At high fidelity, users may use nonlinear PSE to track finite-amplitude disturbances until the skin friction rise. Coupled with the built-in receptivity model that is currently under development, the nonlinear PSE method offers a synergistic approach to predict transition onset for a given disturbance environment based on first principles. This paper describes the governing equations, numerical methods, code development, and case studies for the current release of LASTRAC. Practical applications of LASTRAC are demonstrated for linear stability calculations, N-factor transition correlation, non-linear breakdown simulations, and controls of stationary crossflow instability in supersonic swept wing boundary layers.

Chang, Chau-Lyan

Use of the SCIRun PSE for Coupled Fluid-Structure Analysis

The objective of this paper is to investigate the use of Problem Solving Environments (PSE) for tightly coupled fluid-structure control analysis of aerospace vehicles. The topics include: 1) Background; 2) The SCIRun PSE; 3) Projects Done with SCIRun; 4) Research Procedures; 5) Installtion; 6) Installation Problems on NAS; 7) Module Development; 8) Module Testing Framework; 9) Time Testing of SCIRun; and 10) Time Test Results. This paper is in viewgraph form.

Cheung, Christopher

Detailed Comparison of DNS to PSE for Oblique Breakdown at Mach 3

A pair of oblique waves at low amplitudes is introduced in a supersonic flat-plate boundary layer. Their downstream development and the concomitant process of laminar to turbulent transition is then investigated numerically using Direct Numerical Simulations (DNS) and Parabolized Stability Equations (PSE). This abstract is the last part of an extensive study of the complete transition process initiated by oblique breakdown at Mach 3. In contrast to the previous simulations, the symmetry condition in the spanwise direction is removed for the simulation presented in this abstract. By removing the symmetry condition, we are able to confirm that the flow is indeed symmetric over the entire computational domain. Asymmetric modes grow in the streamwise direction but reach only small amplitude values at the outflow. Furthermore, this abstract discusses new time-averaged data from our previous simulation CASE 3 and compares PSE data obtained from NASA's LASTRAC code to DNS results.

Mayer, Christian S. J.

IDAES-PSE 2.8.0 Release

The Institute for the Design of Advanced Energy Systems (IDAES) Integrated Platform is a versatile computational environment offering extensive process systems engineering (PSE) capabilities for optimizing the design and operation of complex, interacting technologies and systems. IDAES enables users to efficiently search vast, complex design spaces to discover the lowest cost solutions while supporting the full process modeling lifecycle, from conceptual design to dynamic optimization and control. The extensible, open platform empowers users to create models of novel processes and rapidly develop custom analyses, workflows, and end-user applications.

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IDAES-PSE Software Tools for Optimizing Energy Systems and Market Interactions

Modern power grids coordinate electricity production and consumption via multi-scale wholesale energy markets. Historically, levelized cost metrics were the de facto standard for techno-eco-nomic analyses of energy systems and comparison of technology options. However, these metrics neglect the complexity of energy infrastructure including the time-varying value of electricity. An emerging alternative is multi-period optimization, which considers the locational marginal price of electricity as input data (parameters). In this work, we present a general interface for multi-period optimization with time-varying energy prices to facilitate rapid analysis and comparison of potential energy systems models. The PriceTakerModel class is written in the IDAES-PSE platform and allows users to generate a multi-period, price-taker model instance, as well as automatically generate common operational constraints for their model, such as start-up and shutdown. We show this interface successfully generates multi-period price-taker models, facilitates model discrimination, and aids in analyzing various technologies for deployment in unique energy markets.

Laky, Daniel

Analysis of the linear stability of compressible boundary layers using the PSE

The application of linearized parabolic stability equations (PSE) to compressible flow is considered. The effect of mean-flow nonparallelism is found to be weak on 2D waves and strong on 3D waves. Results for a single choice of free-stream parameters that corresponds to the atmospheric conditions at 15,000 m above sea level are presented.

Bertolotti, F. P.

PSE-Based Aerodynamic Flow Transition Prediction Using Automated Unstructured CFD Integration

Accurate, robust, and efficient prediction of transition in viscous flows is a significant challenge in computational fluid dynamics. We present a coupled, high-fidelity, iterative approach that leverages the FUN3D flow solver and the LASTRAC stability code to predict transition in low-disturbance environments, initiated by the linear growth of boundary-layer instability modes. Our method integrates the ability of FUN3D to compute mixed laminar-transitional-turbulent mean flows via transition-sensitized Reynolds-Averaged Navier-Stokes equations with the ability of LASTRAC to perform linear stability analysis, all within an automated framework that requires no intermediate user involvement. Unlike conventional frameworks that rely on classical stability theory or reduced-order metamodels, our approach employs the parabolized stability equations to provide more accurate and reliable estimates of disturbance growth for multiple instability mechanisms, including Tollmien-Schlichting, Kelvin-Helmholtz, and crossflow modes. By accounting for the effects of mean-flow nonparallelism as well as the surface curvature, this approach lays the foundation for improved N-factor correlations for transition onset prediction in a broad class of flows. We apply this method to three distinct flow configurations: 1) flow over a zero-pressure-gradient flat plate, 2) the NLF-0416 airfoil with both natural and separation-induced transitions, and 3) a 6:1 prolate spheroid, where transition is primarily driven by crossflow instability. For the two-dimensional cases, a formulated intermittency distribution is used to model the transition zone in between the laminar and fully turbulent flows. The results include comparisons with experimental measurements, similar numerical approaches, and transport-equations-based models, demonstrating good agreement in surface pressure coefficients, transition onset locations, and skin-friction coefficients for all three configurations. Besides contributing a couple of new insights into boundary-layer transition in these canonical cases, this study provides a powerful tool for transition modeling in both research and design applications in aerodynamics.

Transition Prediction

Electron density profiles in the background of LF absorption during Forbush-decrease and PSE

Based on the simulation of different Forbush decrease and particle precipitation effects in the D region, electron density profiles in the mid-latitudes the ionospheric absorption of low frequency (LF) radio waves was determined. The absorption variations at different frequenceis are strongly affected by the shape of the electron density profile. A structure appears which sometimes resembles the letter S (in a sloping form). Both the height (around 70 to 72 km) and the depth of the local minimum in the electron density contribute to the computed absorption changes of various degree at different frequencies. In this way several observed special absorption events can be interpreted.

Satori, G.

The transition prediction toolkit: LST, SIT, PSE, DNS, and LES

The e(sup N) method for predicting transition onset is an amplitude ratio criterion that is on the verge of full maturation for three-dimensional, compressible, real gas flows. Many of the components for a more sophisticated, absolute amplitude criterion are now emerging: receptivity theory, secondary instability theory, parabolized stability equations approaches, direct numerical simulation and large-eddy simulation. This paper will provide a description of each of these new theoretical tools and provide indications of their current status.

Zang, Thomas A.

Development of a Three-Dimensional PSE Code for Compressible Flows: Stability of Three-Dimensional Compressible Boundary Layers

A program is developed to investigate the linear stability of three-dimensional compressible boundary layer flows over bodies of revolutions. The problem is formulated as a two dimensional (2D) eigenvalue problem incorporating the meanflow variations in the normal and azimuthal directions. Normal mode solutions are sought in the whole plane rather than in a line normal to the wall as is done in the classical one dimensional (1D) stability theory. The stability characteristics of a supersonic boundary layer over a sharp cone with 50 half-angle at 2 degrees angle of attack is investigated. The 1D eigenvalue computations showed that the most amplified disturbances occur around x(sub 2) = 90 degrees and the azimuthal mode number for the most amplified disturbances range between m = -30 to -40. The frequencies of the most amplified waves are smaller in the middle region where the crossflow dominates the instability than the most amplified frequencies near the windward and leeward planes. The 2D eigenvalue computations showed that due to the variations in the azimuthal direction, the eigenmodes are clustered into isolated confined regions. For some eigenvalues, the eigenfunctions are clustered in two regions. Due to the nonparallel effect in the azimuthal direction, the eigenmodes are clustered into isolated confined regions. For some eigenvalues, the eigenfunctions are clustered in two regions. Due to the nonparallel effect in the azimuthal direction, the most amplified disturbances are shifted to 120 degrees compared to 90 degrees for the parallel theory. It is also observed that the nonparallel amplification rates are smaller than that is obtained from the parallel theory.

Balakumar, P.