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At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Advanced Computational Aeroacoustics Methods for Fan Noise Prediction

Direct computation of fan noise is presently not possible. One of the major difficulties is the geometrical complexity of the problem. In the case of fan noise, the blade geometry is critical to the loading on the blade and hence the intensity of the radiated noise. The precise geometry must be incorporated into the computation. In computational fluid dynamics (CFD), there are two general ways to handle problems with complex geometry. One way is to use unstructured grids. The other is to use body fitted overset grids. In the overset grid method, accurate data transfer is of utmost importance. For acoustic computation, it is not clear that the currently used data transfer methods are sufficiently accurate as not to contaminate the very small amplitude acoustic disturbances. In CFD, low order schemes are, invariably, used in conjunction with unstructured grids. However, low order schemes are known to be numerically dispersive and dissipative. dissipative errors are extremely undesirable for acoustic wave problems. The objective of this project is to develop a high order unstructured grid Dispersion-Relation-Preserving (DRP) scheme. would minimize numerical dispersion and dissipation errors. contains the results of the funded portion of the project. scheme on an unstructured grid has been developed. constructed in the wave number space. The characteristics of the scheme can be improved by the inclusion of additional constraints. Stability of the scheme has been investigated. Stability can be improved by adopting the upwinding strategy.

Envia, Edmane↗
DOE OSTI2022

FSVPy: A python-based package for fluorescent streak velocimetry (FSV)

Predictive constitutive equations that connect easy-to-measure transport properties (e.g., viscosity and conductivity) with system performance variables (e.g., power consumption and efficiency) are needed to design advanced thermal and electrical systems. In this work, we explore the use of fluorescent particle-streak analysis to directly measure the local velocity field of a pressure-driven flow, introducing a new Python package (FSVPy) to perform the analysis. Fluorescent streak velocimetry combines high-speed imaging with highly fluorescent particles to produce images that contain fluorescent streaks, whose length and intensity can be related to the local flow velocity. By capturing images throughout the sample volume, the three-dimensional velocity field can be quantified and reconstructed. We demonstrate this technique by characterizing the channel flow profiles of several non-Newtonian fluids: micellar Cetylpyridinium Chloride solution, Carbopol 940, and Polyethylene Glycol. We then explore more complex flows, where significant acceleration is created due to microscale features encountered within the flow. We demonstrate the ability of FSVPy to process streaks of various shapes and use the variable intensity along the streak to extract position-specific velocity measurements from individual images. Thus, we demonstrate that FSVPy is a flexible tool that can be used to extract local velocimetry measurements from a wide variety of fluids and flow conditions.

Mechanics↗
NASA NTRS1988

Hormone purification by isoelectric focusing in space

The objective of the program was the definition and development of optimal methods for electrophoretic separations in microgravity. The approach is based on a triad consisting of ground based experiments, mathematical modeling and experiments in microgravity. Zone electrophoresis is a rate process, where separation is achieved in uniform buffers on the basis of differences in electrophoretic mobilities. Optimization and modeling of continuous flow electrophoresis mainly concern the hydrodynamics of the flow process, including gravity dependent fluid convection due to density gradients and gravity independent electroosmosis. Optimization of focusing requires a more complex model describing the molecular transport processes involved in electrophoresis of interacting systems. Three different focusing instruments were designed, embodying novel principles of fluid stabilization. Fluid stability was achieved by: (1) flow streamlining by means of membrane elements in combination with rapid fluid recycling; (2) apparatus rotation in combination with said membrane elements; and (3) shear stress induced by rapid recycling through a narrow gap channel.

Bier, M.↗
NASA NTRS1998

A Generalized Fluid System Simulation Program to Model Flow Distribution in Fluid Networks

This paper describes a general purpose computer program for analyzing steady state and transient flow in a complex network. The program is capable of modeling phase changes, compressibility, mixture thermodynamics and external body forces such as gravity and centrifugal. The program's preprocessor allows the user to interactively develop a fluid network simulation consisting of nodes and branches. Mass, energy and specie conservation equations are solved at the nodes; the momentum conservation equations are solved in the branches. The program contains subroutines for computing "real fluid" thermodynamic and thermophysical properties for 33 fluids. The fluids are: helium, methane, neon, nitrogen, carbon monoxide, oxygen, argon, carbon dioxide, fluorine, hydrogen, parahydrogen, water, kerosene (RP-1), isobutane, butane, deuterium, ethane, ethylene, hydrogen sulfide, krypton, propane, xenon, R-11, R-12, R-22, R-32, R-123, R-124, R-125, R-134A, R-152A, nitrogen trifluoride and ammonia. The program also provides the options of using any incompressible fluid with constant density and viscosity or ideal gas. Seventeen different resistance/source options are provided for modeling momentum sources or sinks in the branches. These options include: pipe flow, flow through a restriction, non-circular duct, pipe flow with entrance and/or exit losses, thin sharp orifice, thick orifice, square edge reduction, square edge expansion, rotating annular duct, rotating radial duct, labyrinth seal, parallel plates, common fittings and valves, pump characteristics, pump power, valve with a given loss coefficient, and a Joule-Thompson device. The system of equations describing the fluid network is solved by a hybrid numerical method that is a combination of the Newton-Raphson and successive substitution methods. This paper also illustrates the application and verification of the code by comparison with Hardy Cross method for steady state flow and analytical solution for unsteady flow.

Majumdar, Alok↗
DOE OSTI2021

Machine learning to discover mineral trapping signatures due to CO 2 injection

Mineral trapping is pursued as a geological CO 2 sequestration (GCS) mechanism because it permanently stores CO 2 in solid phases or minerals. However, CO 2 mineral-trapping mechanisms are poorly understood due to (1) lack of sufficient field and laboratory data characterizing these complex processes, and (2) challenges to develop site-specific reactive-transport models coupling fluid flow and geochemical reactions occurring at various temporal (from milliseconds to years) and spatial (from pore (millimeters) to field (kilometers)) scales. Reactive transport with additional complexities such as heterogeneity can make the simulation outputs even more difficult to interpret because of complex nonlinearity and multi-scale interdependencies. Furthermore, the values of model outputs such as concentrations can vary by several orders of magnitude, making it harder to correlate and characterize the impact of the variables via traditional data interpretation techniques such as exploratory data analyses. Recently, machine learning (ML) has shown promise in feature discovery and in highlighting hidden mechanisms that cannot be obtained by existing data-analytics and statistical methods. In this study, we applied an unsupervised ML approach, non-negative matrix factorization with custom -means clustering (NMF) to the data generated by reactive-transport simulations of GCS. The reactive-transport data consisted of 19 attributes, including four physio-chemical variables (pH, porosity, aqueous CO 2 , and sequestered CO 2 ), six chemical species (K + , Na + , HCO, Ca 2+ , Mg 2+ , Fe 2+ ), and four carbonate minerals (calcite, dolomite, siderite, and ankerite), a feldspar mineral (albite), and four clay minerals (illite, clinochlore, kaolinite, and smectite) over a period of 200 years of simulation time. Furthermore, the simulation data used was for Morrow B sandstone at the Farnsworth hydrocarbon unit in Texas. Data are sampled at two locations within the model domain: (1) at the injection well and (2) 200 m west of the injection well. The injection was performed for a period of 10 years. Using NMF, we estimated the temporal interdependencies among the 19 attributes over a span of 200 years. We found that NMF was able to identify four reaction stages and their dominant attributes; these cannot be directly discerned through traditional visualization (e.g., line plots, Pareto analysis, Glyph-based visualization methods) or exploratory data analysis tools of the simulation data. The four stages were: reactions in the injection phase followed by short-, mid-, and long-term reactions. The NMF analysis also revealed that 10 among the 19 attributes are dominant. These dominant attributes for mineral trapping include calcite, dolomite at injection well, siderite at 200 m away from the injection well, clinochlore, kaolinite, Na + , K + , Ca 2+ , Mg 2+ , pH, and aqeuous CO 2 . Finally, at late times (65–200 years), our results showed that calcite plays a major role in mineral trapping with insignificant contribution from siderite, ankerite, and clay minerals. These findings make the proposed unsupervised ML-model attractive for reactive-transport sensing towards real-time GCS monitoring.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

A quantum liquid of magnetic octupoles on the pyrochlore lattice

Spin liquids are highly correlated yet disordered states formed by the entanglement of magnetic dipoles. Theories define such states using gauge fields and deconfined quasiparticle excitations that emerge from a local constraint governing the ground state of a frustrated magnet. For example, the ‘2-in–2-out’ ice rule for dipole moments on a tetrahedron can lead to a quantum spin ice in rare-earth pyrochlores. However, $f$-electron ions often carry multipole degrees of freedom of higher rank than dipoles, leading to intriguing behaviours and ‘hidden’ orders. In this paper we show that the correlated ground state of a Ce 3+ -based pyrochlore, Ce 2 Sn 2 O 7 , is a quantum liquid of magnetic octupoles. Our neutron scattering results are consistent with a fluid-like state where degrees of freedom have a more complex magnetization density than that of magnetic dipoles. The nature and strength of the octupole–octupole couplings, together with the existence of a continuum of excitations attributed to spinons, provides further evidence for a quantum ice of octupoles governed by a ‘2-plus–2-minus’ rule. Our work identifies Ce 2 Sn 2 O 7 as a unique example of frustrated multipoles forming a ‘hidden’ topological order, thus generalizing observations on quantum spin liquids to multipolar phases that can support novel types of emergent fields and excitations.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Investigating the Interaction Between Circulating Tumor Cells and Local Hydrodynamics via Experiment and Simulations

Introduction: The biological and mechanical properties of circulating tumor cells (CTCs) in combination with the hemodynamics affect the preference of metastatic sites in the vasculature. Despite the extensive literature on the effects of biological properties on cell adhesion, the effects of hydrodynamic forces on primary attachment remains an active area of research. Here, using simulations in conjunction with experimentation, we provide new insight into the interplay of CTCs dynamics and local hydrodynamics. Methods: A flow experiment of CTC attachment was performed within a bioprinted, double branching endothelialized vessel. Simulations of fluid flow and CTC transport in the reconstructed and idealized bifurcated vessel were respectively performed by HARVEY, our in-house massively parallel computational fluid dynamics solver. HARVEY is based on the lattice Boltzmann and finite element methods to model the fluid and cells dynamics. The immersed boundary method is employed for resolving the fluid–structure interaction. Results: CTC attachment was quantified experimentally at all regions of the complex vessel. The results demonstrate a clear preference for CTCs to attach at the branch points. To elucidate the effect of the vessel topology on the location of attachment, a fluid-only simulation was performed assessing the differences in the hydrodynamics along the vessel. CTC transport in idealized bifurcated vessels was subsequently studied to examine the effects of cell deformability on the local hydrodynamics patterns and, thus, the preference of attachment sites. Conclusions: The current work provides evidence on the correlation of the hydrodynamics forces arising from the vessel topology and CTC properties on the attachment regions.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1995

The VOrtex Ring Transit EXperiment (VORTEX) GAS project

Get Away Special (GAS) payload G-093, also called VORTEX (VOrtex Ring Transit EXperiment), is an investigation of the propagation of a vortex ring through a liquid-gas interface in microgravity. This process results in the formation of one or more liquid droplets similar to earth based liquid atomization systems. In the absence of gravity, surface tension effects dominate the drop formation process. The Shuttle's microgravity environment allows the study of the same fluid atomization processes as using a larger drop size than is possible on Earth. This enables detailed experimental studies of the complex flow processes encountered in liquid atomization systems. With VORTEX, deformations in both the vortex ring and the fluid surface will be measured closely for the first time in a parameters range that accurately resembles liquid atomization. The experimental apparatus will record images of the interactions for analysis after the payload has been returned to earth. The current design of the VORTEX payload consists of a fluid test cell with a vortex ring generator, digital imaging system, laser illumination system, computer based controller, batteries for payload power, and an array of housekeeping and payload monitoring sensors. It is a self-contained experiment and will be flown on board the Space Shuttle in a 5 cubic feet GAS canister. The VORTEX Project is entirely run by students at the University of Michigan but is overseen by a faculty advisor acting as the payload customer and the contact person with NASA. This paper summarizes both the technical and programmatic aspects of the VORTEX Project.

Bilen, Sven G.↗
NASA NTRS1993

Computational reacting gas dynamics

In the study of high speed flows at high altitudes, such as that encountered by re-entry spacecrafts, the interaction of chemical reactions and other non-equilibrium processes in the flow field with the gas dynamics is crucial. Generally speaking, problems of this level of complexity must resort to numerical methods for solutions, using sophisticated computational fluid dynamics (CFD) codes. The difficulties introduced by reacting gas dynamics can be classified into three distinct headings: (1) the usually inadequate knowledge of the reaction rate coefficients in the non-equilibrium reaction system; (2) the vastly larger number of unknowns involved in the computation and the expected stiffness of the equations; and (3) the interpretation of the detailed reacting CFD numerical results. The research performed accepts the premise that reacting flows of practical interest in the future will in general be too complex or 'untractable' for traditional analytical developments. The power of modern computers must be exploited. However, instead of focusing solely on the construction of numerical solutions of full-model equations, attention is also directed to the 'derivation' of the simplified model from the given full-model. In other words, the present research aims to utilize computations to do tasks which have traditionally been done by skilled theoreticians: to reduce an originally complex full-model system into an approximate but otherwise equivalent simplified model system. The tacit assumption is that once the appropriate simplified model is derived, the interpretation of the detailed numerical reacting CFD numerical results will become much easier. The approach of the research is called computational singular perturbation (CSP).

Lam, S. H.↗
NASA NTRS2010

Simulation of Propellant Loading System Senior Design Implement in Computer Algorithm

Propellant loading from the Storage Tank to the External Tank is one of the very important and time consuming pre-launch ground operations for the launch vehicle. The propellant loading system is a complex integrated system involving many physical components such as the storage tank filled with cryogenic fluid at a very low temperature, the long pipe line connecting the storage tank with the external tank, the external tank along with the flare stack, and vent systems for releasing the excess fuel. Some of the very important parameters useful for design purpose are the prediction of pre-chill time, loading time, amount of fuel lost, the maximum pressure rise etc. The physics involved for mathematical modeling is quite complex due to the fact the process is unsteady, there is phase change as some of the fuel changes from liquid to gas state, then conjugate heat transfer in the pipe walls as well as between solid-to-fluid region. The simulation is very tedious and time consuming too. So overall, this is a complex system and the objective of the work is student's involvement and work in the parametric study and optimization of numerical modeling towards the design of such system. The students have to first become familiar and understand the physical process, the related mathematics and the numerical algorithm. The work involves exploring (i) improved algorithm to make the transient simulation computationally effective (reduced CPU time) and (ii) Parametric study to evaluate design parameters by changing the operational conditions

Bandyopadhyay, Alak↗
DOE OSTI2020

Effect of cold cap coverage and emissivity on the plenum temperature in a pilot-scale waste vitrification melter

Integrated computational fluid dynamics (CFD) models are being developed to model the complex physics occurring within the high-level waste melter for vitrification of legacy tank waste at the Hanford site. Here, we present a validation of the integrated CFD model by using data from two experimental runs in a pilot-scale melter. While the model uses several simplifying assumptions (such as constant heat sinks from a cooling jacket and inleakage of ambient air, steady state feed-to-batch conversion heat, and a cold cap model with a simplified shape), it closely predicts the molten glass (1150°C and 1175°C) and plenum temperatures (550°C) obtained from thermocouples during two pilot-scale tests, with an average cold cap coverage of 80%. Additional simulations were performed to explore the sensitivity of the predicted plenum temperatures to variations in cold cap coverage (fraction of melt surface covered by the glass batch) and batch emissivity. The plenum temperature was found to be in the range of 606°C when cold cap coverage decreased from 95% to 70%. Cold cap emissivity had a smaller effect, increasing the plenum temperature by as much as 179°C when cold cap emissivity increased from 0.2 to 0.8. Maintaining a high cold cap coverage without overfeeding is important for a sustained melter operation with high glass throughput. This work provides a tool for achieving that goal in terms of correlating the plenum temperature with the cold cap coverage.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
NASA NTRS1990

Thermal buoyancy and Marangoni convection in a two fluid layered system - A numerical study

Thermal buoyancy and surface tension driven convection is numerically investigated in a system with two, immiscible fluids. The geometry investigated, has an open cavity configuration with the lighter fluid situated on top of the heavier fluid, forming a stable layered system. The upper fluid meniscus and the interface are assumed to be flat and undeformable in the calculations. The governing equations and boundary/interface conditions are solved by a control volume based finite difference scheme for two pairs of immiscible fluids; the water-hexadecane system and a so called generic system. The steady state calculations show, that dramatically different flows are predicted when the interfacial tension effects are included or excluded from the system model. These differences are particularly appreciable in surface tension dominated flows, that are typical of microgravity situations. Complex flow patterns, with induced secondary flows are noticed in both the fluids. In general, the overall system heat transfer is found to increase with increases in the thermal buoyancy and surface tension effects, but the behavior of the system flow and thermal fields is not easy to characterize, when different combinations of these forces are considered.

Ramachandran, N.↗
NASA NTRS2004

Computation of Sensitivity Derivatives of Navier-Stokes Equations using Complex Variables

Accurate computation of sensitivity derivatives is becoming an important item in Computational Fluid Dynamics (CFD) because of recent emphasis on using nonlinear CFD methods in aerodynamic design, optimization, stability and control related problems. Several techniques are available to compute gradients or sensitivity derivatives of desired flow quantities or cost functions with respect to selected independent (design) variables. Perhaps the most common and oldest method is to use straightforward finite-differences for the evaluation of sensitivity derivatives. Although very simple, this method is prone to errors associated with choice of step sizes and can be cumbersome for geometric variables. The cost per design variable for computing sensitivity derivatives with central differencing is at least equal to the cost of three full analyses, but is usually much larger in practice due to difficulty in choosing step sizes. Another approach gaining popularity is the use of Automatic Differentiation software (such as ADIFOR) to process the source code, which in turn can be used to evaluate the sensitivity derivatives of preselected functions with respect to chosen design variables. In principle, this approach is also very straightforward and quite promising. The main drawback is the large memory requirement because memory use increases linearly with the number of design variables. ADIFOR software can also be cumber-some for large CFD codes and has not yet reached a full maturity level for production codes, especially in parallel computing environments.

Vatsa, Veer N.↗
DOE OSTI2021

The solubility of thorium in carbonate-bearing solutions at hydrothermal conditions

Thorium mineralization is frequently hosted in carbonate-bearing rocks, and thorium commonly substitutes into the structures of carbonate-bearing minerals that have precipitated from or been modified by hydrothermal fluids. Given this common association, it is reasonable to consider the hypothesis that the presence of carbonate ligands in hydrothermal solutions promotes the transport of Th through the formation of stable aqueous complexes. Our ability to evaluate this hypothesis, however, is hindered by the lack of experimental data for Th-carbonate species at conditions beyond ambient. The low-temperature data indicate that carbonate is a strong complexing agent for Th. In this contribution, we investigate the solubility of Th in carbonate-bearing fluids relevant to natural systems (0.05–0.5 m NaHCO 3 /Na 2 CO 3 ; pH T ~ 7.8–9.8) at elevated temperature (175–250 °C). We demonstrate that, in contrast to the behavior of Th at low temperature, the stability of Th-carbonate complexes is not sufficient for them to predominate at these conditions. Instead, the solubility of Th is governed by hydrolysis reactions. Under the experimental conditions investigated, the predominant hydroxyl complexes are Th(OH) 4 0 and Th(OH) 5 -. Furthermore, thermodynamic formation constants were derived for these species at the temperatures considered in our experiments (log β 4 = 43.34 and 44.31 at 175 and 200 °C, respectively, and log β 5 = 46.15 and 47.9 at 225 and 250 °C, respectively) to permit forward modeling of Th mobility in natural systems. Our study indicates that carbonate ions are unlikely to play a role in transporting Th in hydrothermal fluids. Summarizing the results of this study and our previous studies of the solubility of Th in hydrothermal fluids, we conclude that SO 4 2- is the primary ligand responsible for the hydrothermal transport of Th.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Uranium carbonate complexes demonstrate drastic decrease in stability at elevated temperatures

Quantitative understanding of uranium transport by high temperature fluids is crucial for confident assessment of its migration in a number of natural and artificially induced contexts, such as hydrothermal uranium ore deposits and nuclear waste stored in geological repositories. An additional recent and atypical context would be the seawater inundated fuel of the Fukushima Daiichi Nuclear Power Plant. Given its wide applicability, understanding uranium transport will be useful regardless of whether nuclear power finds increased or decreased adoption in the future. The amount of uranium that can be carried by geofluids is enhanced by the formation of complexes with inorganic ligands. Carbonate has long been touted as a critical transporting ligand for uranium in both ore deposit and waste repository contexts. However, this paradigm has only been supported by experiments conducted at ambient conditions. We have experimentally evaluated the ability of carbonate-bearing fluids to dissolve (and therefore transport) uranium at high temperature, and discovered that in fact, at temperatures above 100 °C, carbonate becomes almost completely irrelevant as a transporting ligand. This demands a re-evaluation of a number of hydrothermal uranium transport models, as carbonate can no longer be considered key to the formation of uranium ore deposits or as an enabler of uranium transport from nuclear waste repositories at elevated temperatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Same-sided successive-shock HED instability experiments

Inertial confinement fusion (ICF) and high-energy density (HED) physics experiments experience complicated forcing for instability growth and mix due to the ubiquitous presence of multiple shocks interacting with perturbations on multiple material interfaces. One common driver of instability growth is successive shocks from the same direction. However, there is a severe lack of analytic work and modeling validation for same-sided successive shocks since they are extremely difficult to achieve with conventional (non-HED) drivers. Successive shocks access a large instability parameter space; idealized fluid theory [K. O. Mikaelian, Phys. Rev. A 31, 410 (1985)] predicts 15 different interface evolution scenarios for a sinusoidal perturbation. Growth becomes more complex for multi-mode, compressible HED systems. The Mshock campaign is the first experiment in any fluid regime to probe a wide portion of successive shock parameter space. This is enabled by our development of a hybrid direct/indirect drive platform capable of creating independently controllable successive shocks on the National Ignition Facility. These experiments have delivered the first data capable of rigorously challenging our models and their ability to accurately capture Richtmyer–Meshkov growth under successive shocks. Single-mode and two-mode experiments have successfully demonstrated the ability to access and control the various growth scenarios of the shocked interface, including re-inversion, freeze out, and continued growth. Simulations and theoretical modeling are shown to accurately capture the experimental observations in the linear growth phase, giving us confidence in our ICF/HED design codes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2011

Extension of Generalized Fluid System Simulation Program's Fluid Property Database

This internship focused on the development of additional capabilities for the General Fluid Systems Simulation Program (GFSSP). GFSSP is a thermo-fluid code used to evaluate system performance by a finite volume-based network analysis method. The program was developed primarily to analyze the complex internal flow of propulsion systems and is capable of solving many problems related to thermodynamics and fluid mechanics. GFSSP is integrated with thermodynamic programs that provide fluid properties for sub-cooled, superheated, and saturation states. For fluids that are not included in the thermodynamic property program, look-up property tables can be provided. The look-up property tables of the current release version can only handle sub-cooled and superheated states. The primary purpose of the internship was to extend the look-up tables to handle saturated states. This involves a) generation of a property table using REFPROP, a thermodynamic property program that is widely used, and b) modifications of the Fortran source code to read in an additional property table containing saturation data for both saturated liquid and saturated vapor states. Also, a method was implemented to calculate the thermodynamic properties of user-fluids within the saturation region, given values of pressure and enthalpy. These additions required new code to be written, and older code had to be adjusted to accommodate the new capabilities. Ultimately, the changes will lead to the incorporation of this new capability in future versions of GFSSP. This paper describes the development and validation of the new capability.

Patel, Kishan↗
NASA NTRS1999

Overview of Sensitivity Analysis and Shape Optimization for Complex Aerodynamic Configurations

This paper presents a brief overview of some of the more recent advances in steady aerodynamic shape-design sensitivity analysis and optimization, based on advanced computational fluid dynamics (CFD). The focus here is on those methods particularly well-suited to the study of geometrically complex configurations and their potentially complex associated flow physics. When nonlinear state equations are considered in the optimization process, difficulties are found in the application of sensitivity analysis. Some techniques for circumventing such difficulties are currently being explored and are included here. Attention is directed to methods that utilize automatic differentiation to obtain aerodynamic sensitivity derivatives for both complex configurations and complex flow physics. Various examples of shape-design sensitivity analysis for unstructured-grid CFD algorithms are demonstrated for different formulations of the sensitivity equations. Finally, the use of advanced, unstructured-grid CFDs in multidisciplinary analyses and multidisciplinary sensitivity analyses within future optimization processes is recommended and encouraged.

Newman, James C., III↗