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NASA NTRS1987

Investigation, development and application of optimal output feedback theory. Vol. 4: Measures of eigenvalue/eigenvector sensitivity to system parameters and unmodeled dynamics

Some measures of eigenvalue and eigenvector sensitivity applicable to both continuous and discrete linear systems are developed and investigated. An infinite series representation is developed for the eigenvalues and eigenvectors of a system. The coefficients of the series are coupled, but can be obtained recursively using a nonlinear coupled vector difference equation. A new sensitivity measure is developed by considering the effects of unmodeled dynamics. It is shown that the sensitivity is high when any unmodeled eigenvalue is near a modeled eigenvalue. Using a simple example where the sensor dynamics have been neglected, it is shown that high feedback gains produce high eigenvalue/eigenvector sensitivity. The smallest singular value of the return difference is shown not to reflect eigenvalue sensitivity since it increases with the feedback gains. Using an upper bound obtained from the infinite series, a procedure to evaluate whether the sensitivity to parameter variations is within given acceptable bounds is developed and demonstrated by an example.

Halyo, Nesim↗
DOE OSTI2023

Impact of Thermal Scattering Law on Similarity Assessment in Light-Water or Polyethylene-Moderated Systems

A collaborative effort between Pacific Northwest National Laboratory (PNNL) and Oak Ridge National Laboratory (ORNL) is underway to provide a technical basis and methodology for the criticality safety community to use the sum of fractions (SoF) method for generating limits for mixtures of “selected actinide nuclides” included in the ANSI/ANS 8.15 standard. The PNNL scope in this project is to define a range of mixtures of 233 U, 235 U, and 239 Pu moderated with either light water or polyethylene and to examine the critical masses for these mixtures. The ORNL scope is primarily to provide validation support for these studies. More complete discussion of the project and its validation aspects will be presented at the upcoming International Conference on Nuclear Criticality Safety (ICNC) this Fall in Sendai, Japan. Clear differences in benchmark similarity to application systems as assessed by the integral parameter ck are noted in the validation studies performed as part of this project as a function of moderator. The c k value is a correlation coefficient that represents that amount of shared uncertainty in k eff due to cross sections between two systems. Individual nuclide-reaction contributions between the two systems can be simply summed to arrive at the total c k value. Specifically, the c k values for light-water–moderated solution experiments are higher for a water-moderated application than for a polyethylene-moderated application. This result is neither totally unexpected nor surprising, but the magnitude of the difference was difficult to anticipate. The TSUNAMI sequence, in the SCALE 6.2.4 code package developed by ORNL, was used to generate eigenvalues and reactivity effects with perturbation-theory based approach through sensitivity coefficients for all nuclides in the system with all reactions and energy groups. The TSUNAMI-Indices and Parameters (IP) sequence then uses the sensitivity data generated through TSUNAMI to generate relational parameters (i.e., c k ) to determine the degree of similarity between systems. One detail of the SCALE material and data implementation must be discussed at this point. Several thermal scattering laws (TSLs) are available for 1 H. SCALE uses a different nuclide ID number for each TSL; essentially, each version of 1 H is treated as a unique nuclide. For example, 1 H bound in water ( 1 H-H2O) is assigned the nuclide ID 1001, whereas 1 H bound in polyethylene (h-poly) is assigned the nuclide ID 9001001. The same cross section data are used for all reactions in 1 H, regardless of TSL, except for scattering below the TSL cutoff energy. TSUNAMI-IP treats different nuclide IDs as different nuclides; thus, no uncertainty is shared between 1 H-H2O and h-poly, despite much of the same data, including covariance data, being used for both nuclides. This presents a question: how much of the difference in assessed similarity between water- and polyethylene-moderated systems is due to the moderators, and how much is caused by the treatment of 1 H-H2O and h poly with cross section and covariance data. The extended edits generated by TSUANMI-IP allow for an investigation of this issue specifically, as well as a demonstration of the general techniques available within TSUNAMI to understand the results of the similarity assessment. This paper presents and analyzes the similarity assessment of both water- and polyethylene-moderated systems for a single benchmark: PST-002-001.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Deep Learning for Multigroup Cross-Section Representation in Two-Step Core Calculations

Here we investigate using deep learning, a type of machine-learning algorithm employing multiple layers of artificial neurons, for the mathematical representation of multigroup cross sections for use in the Griffin reactor multiphysics code for two-step deterministic neutronics calculations. A three-dimensional fuel element typical of a high-temperature gas reactor as well as a two-dimensional sodium-cooled fast reactor lattice are modeled using the Serpent Monte Carlo code, and multigroup macroscopic cross sections are generated for various state parameters to produce a training data set and a separate validation data set. A fully connected, feedforward neural network is trained using the open-source PyTorch machine-learning framework, and its accuracy is compared against the standard piecewise linear interpolation model. Additionally, we provide in this work a generic technique for propagating the cross-section model errors up to the k eff using sensitivity coefficients with the first-order uncertainty propagation rule. Quantifying the eigenvalue error due to the cross-section regression errors is especially practical for appropriately selecting the mathematical representation of the cross sections. We demonstrate that the artificial neural network model produces lower errors and therefore enables better accuracy relative to the piecewise linear model when the cross sections exhibit nonlinear dependencies; especially when a coarse grid is employed, where the errors can be halved by the artificial neural network. However, for linearly dependent multigroup cross sections as found for the sodium-cooled fast reactor case, a simpler linear regression outperforms deeper networks.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

CE TSUNAMI-3D Algorithm Improvements in SCALE 6.2

The TSUNAMI (Tools for Sensitivity and Uncertainty Analysis Methodology Implementation) capabilities within the SCALE code system make use of sensitivity coefficients for an extensive number of criticality safety applications such as quantifying the data-induced uncertainty in the eigenvalue of critical systems, assessing the neutronic similarity between different systems, quantifying computational biases, and guiding nuclear data adjustment studies. The continuous-energy (CE) TSUNAMI-3D code is a new tool included in SCALE 6.2 that allows for eigenvalue and generalized response sensitivity calculations using high-fidelity CE Monte Carlo methods. This paper describes several improvements to CE TSUNAMI-3D beyond those previously published. These improvements primarily consist of - A multi-response capability for the CE TSUNAMI generalized response sensitivity calculation mode; and - Efficiency improvements in CE TSUNAMI's Iterated Fission Probability (IFP)-based algorithms. This paper documents several improvements to the CE TSUNAMI-3D sensitivity algorithms included in the SCALE 6.2 release. These improvements have enabled the simulation of multiple GPT responses within a single CE TSUNAMI simulation, a feature that increases the memory footprint of the simulations by approximately 1-3% per response and the runtime by approximately 1-2%, per response. These algorithmic improvements have also significantly improved the computational efficiency of CE TSUNAMI IFP-based sensitivity calculations, reducing the memory footprints approximately by a factor of 3 and the simulation runtimes by 10-70%. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

IAEA Coordinated Research Project on HTGR Physics, Thermal Hydraulics, and Depletion Uncertainty Analysis: PHISICS/RELAP5-3D Results for the Phase III Coupled Core Exercises

This report details the Parallel and Highly Innovative Simulation for INL Code System (PHISICS)/Reactor Excursions and Leak Analysis Program (RELAP5)-3D results obtained for the neutronics stand-alone core exercises defined for Phase II of the International Atomic Energy Agency (IAEA) Coordinated Research Project (CRP) on high-temperature gas cooled reactor (HTGR) uncertainty analysis in modeling (UAM). The Phase II models and results are linked to the earlier Standardized Computer Analyses for Licensing Evaluation (SCALE)/Sampler/New ESC-based Weighting Transport (NEWT) data generated for the lattice physics (lattice) stage Phase I of the CRP. The focus of this report is the propagation of cross-section uncertainties from the lattice to the core calculation (core) phase of the prismatic 350 megawatt (MW) General Atomics (GA) Modular HTGR (MHTGR). The Phase II neutronics exercises consist of two sub-cases (II-2a and II-2b) specified for the fresh and mixed core loading of the MHTGR-350 prismatic high-temperature reactor design. Exercises II-2a and II-2b are performed without temperature feedback using isothermal temperature profiles. For the nominal lattice physics (i.e., best-estimate) model, a series of fresh and depleted single block and super cell SCALE/KENO and SCALE/NEWT models were developed at Idaho National Laboratory (INL) to assess the impact of spectral effects on the few-group cross sections. A combination of these lattice cells were used in a super cell calculation to construct 8-group cross-section libraries for use in the INL-developed PHISICS/RELAP5-3D code suite. The block-level homogenized libraries were assigned to the 220 fuel zones utilized in the MHTGR-350 PHISICS core model, according to the fresh and mixed fresh/depleted core loading pattern. In order to evaluate the effect of uncertainty propagation, several sets consisting of 1,000 perturbed NEWT lattice and PHISICS/RELAP5-3D core calculations were performed using the SCALE 6.2 ENDF/B-VII.1 cross-section co-variance data and the stochastic sampling module Sampler in SCALE 6.2.0. The Figures of Merit (FOM) investigated include the mean and standard deviation uncertainty values obtained for the eigenvalues, control rod worth values, block-averaged power profiles, power axial offsets, and isothermal temperature feedback coefficients. A sensitivity study on the main nuclide reaction contributors to the FOM uncertainties has not yet been performed since the SCALE/PHISICS/RAVEN coupling with ENDF/B-VII co-variance data is still being developed. It was found that uncertainties in the cross sections lead to uncertainties in the local power values of up to 1.5%. The variances between the fresh and mixed/depleted core models are not as large as the axial variations between the top and bottom within each core model. The core eigenvalue uncertainty is approximately 0.5%, which is significant in comparison to typical eigenvalue difference targets (less than ~0.1% for LWRs). The power peaking and axial offset uncertainties are smaller (0.10% – 0.15%) and probably below the level of significance in typical core design metrics. The use of an 8-group energy structure slightly under-estimates some of the uncertainties, but in absolute terms, the uncertainty results are reasonably close to the 26-group results. The 26- and 8-group mean and nominal results differ by a larger degree, and if it can be afforded in terms of calculation resources, the 26-group structure should be used for HTGR calculations. The 8-group structure can, however, still be useful for reasonably accurate uncertainty assessments of transient cases where computational time is important. It was furthermore found that the use of a super cell during the cross-section generation process for better representation of the spectral environment at the core periphery did not lead to significant changes in the core eigenvalues, axial offset, and power peaking uncertainties. The impact of the super cell cross sections on the nominal and mean eigenvalues is, however, important enough (0.6% – 1.1% lower) to justify the use of these super cells for HTGR core simulation to represent the softer spectral environment in the core peripheral regions for nominal best-estimate calculations. The use of super cells for HTGR uncertainty studies is, therefore, not strictly necessary, but the improvements in nominal results could justify their use.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Extension of SCALE/Sampler’s sensitivity analysis

Nuclear data are a major source of uncertainties in reactor physics calculations. The propagation of nuclear data uncertainties to important system responses is instrumental when determining appropriate safety margins in reactor safety analyses. It is also important to understand the major contributors to the observed uncertainties to make recommendations for further measurements and evaluations and aid in the understanding of the studied system. The SCALE code system allows for nuclear data uncertainty analysis based on the random sampling approach as implemented in SCALE’s Sampler sequence. Sampler was recently extended by a sensitivity analysis in terms of the calculation of two correlation-based sensitivity indices. This analysis allows for the identification of the top contributing nuclear reactions to any analyzed output uncertainty. This paper presents the sensitivity indices, along with their interpretation and limitations. It demonstrates the application in an eigenvalue and decay heat analysis for a boiling water reactor fuel assembly.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Impact of Increased Latent Generations on Sensitivity Calculations with SCALE [Slides]

Depending on the system, energy, and/or nuclide, altering the number of latent generations can significantly impact generated sensitivity coefficients. In general, as the number of latent generations increases, the accuracy of the generated sensitivity value compared with the DP value increases and there is a significant increase in the uncertainty with generated sensitivity values. IFP generated sensitivities appear to be more stable than those with CLUTCH. Complex systems, even with IFP and increased latent generations can still produce poor results (i.e., MPC- 32). This reiterates the importance of performing DPs to confirm sensitivities. IFP-Shift and CLUTCH can take advantage of parallel computing abilities. Work continues in this area as additional parameters and calculational methods are examined to provide analysts insights to successfully generating sensitivity coefficients for confirmatory analyses and validation efforts.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Automated Direct Perturbation Calculations with SCALE TSUNAMI [Abstract]

In nuclear criticality safety analysis, the sensitivity of the eigenvalue keff to uncertainties in nuclear data and its evaluation are crucial. The TSUNAMI sequences within the SCALE code system offer users various options with both multigroup (MG) and continuous-energy (CE) 3D Monte Carlo (MC) transport capabilities for calculating keff sensitivity coefficients and storing them in a sensitivity data file (SDF). Each methodology available in TSUNAMI offers distinct advantages and limitations, and its effectiveness can vary based on the specific problem being solved. As a best practice, practitioners typically use the direct perturbation (DP) method as a confirmatory step alongside their sensitivity calculations to verify the accuracy of the sensitivity data generated. In this process, DP calculations are usually performed on select nuclides, those considered most important for validating their total sensitivities. However, because of code limitations, analysts use a workaround method when conducting DP calculations for a single nuclide: rather than perturbing the nuclide's microscopic cross section, an equivalent number density for this nuclide is calculated to reflect the effect of a change in the macroscopic cross section due to a perturbation in the microscopic cross section. The current approach requires rerunning the CSAS criticality calculation several times with model changes. Although this method can yield results with acceptable accuracy, it is labor-intensive and prone to errors.

AZURE: SAMMY↗
NASA NTRS1972

Spectral factorization in periodically time-varying systems and application to navigation problems.

Spectral factorization has been used previously to derive the steady-state solution of Kalman filtering equations without iteration for constant coefficient systems. The present work extends the spectral factorization algorithm to time-varying systems having periodic coefficient matrices for cases of both discrete and continuous systems. Time-consuming, expensive iterations of sequential covariance equations are not required to reach the final solution since this is an algebraic algorithm employing existing eigenvalue, eigenvector subroutines. The computer program incorporating the algorithm is suitable for sensitivity studies in formulating navigation and guidance strategies of low-thrust interplanetary missions. The determination of an optimum tracking pattern from an earth station is examined as an example.

Nishimura, T.↗
NASA NTRS1989

Flutter suppression using eigenspace freedoms to meet requirements

A constrained optimization methodology has been developed which allows specific use of eigensystem freedoms to meet design requirements. A subset of the available eigenvector freedoms was employed. The eigenvector freedoms associated with a particular closed-loop eigenvalue are coefficients of basis vectors which span the subspace in which that closed-loop vector must lie. Design requirements are included as a vector of inequality constraints. The procedure was successfully applied to develop an unscheduled controller which stabilizes symmetric flutter of an aeroelastic vehicle to a dynamic pressure 44 percent above the open-loop flutter point. The design process proceeded from full-state feedback to the inclusion of a full-order observer to the selection of an eighth-order controller which preserved the full-state sensitivity characteristics. Only a subset of the design freedoms was utilized (i.e., assuming full-state feedback only four out of 26 eigenvectors were used, and no variations were made in the closed-loop eigenvalues). Utilization of additional eigensystem freedoms could further improve the controller.

Adams, William M., Jr.↗
DOE OSTI2022

Implementation and testing of the GPT sensitivities in TRIPOLI-4

Computing the sensitivity of given reactor parameters with respect to nuclear data is mandatory in key applications such as the assessment of reactor safety or core design. In recent years, the development of Monte Carlo methods capable of estimating sensitivity coefficients based on the Standard or Generalized Perturbation Theory (SPT and GPT, respectively) has attracted intensive research efforts, especially in view of having reference golden standard simulations to be compared to faster but approximate deterministic calculations. Following our previous implementation and validation of the SPT functionalities in the Monte Carlo TRIPOLI-4, devoted to the sensitivity of the k eigenvalue, in this work we detail the development of GPT methods for ratios of reaction rates, and validate them against a few relevant benchmark results. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Expanded Intercomparison of Nuclear Data Libraries Using Jupiter and Jupiter High-240 Experiments

There is a limited availability of plutonium experiments with sensitivity to lead in the ICSBEP (International Handbook of Evaluated Criticality Safety Benchmark Experiments) Handbook. The Jupiter and Jupiter High-240 experiments were performed at the National Criticality Experiments Research Center as a collaborative effort between Los Alamos National Laboratory and the Japan Atomic Energy Agency to assess lead void coefficients in a plutonium-lead system containing weapons- and reactor-grade plutonium, respectively. Concurrent with benchmark development, an intercomparison of calculations using different nuclear data libraries has been performed to assess the usability of the experimental data for nuclear data adjustment in a “softer-that-fast” neutron energy spectrum. Eigenvalue calculations using MCNP with the ENDF/B-VIII.0 and TENDL-2021 nuclear data libraries calculate closest to the benchmark values for Jupiter. Calculations using JENDL-5 and ENDF/B-VIII.1 match best with the Jupiter High-240 values. Lead void worth calculations using the various nuclear data libraries are all within 3σ of their respective measured values. Perturbation studies between ENDF/B-VIII.0 and ENDF/B-VIII.1 demonstrate an approximate increase in calculated eigenvalues for the Jupiter series experiments by ~240 pcm for plutonium (mostly 239 Pu) and ~120 pcm for lead accompanied by a decrease contributed by ~113 pcm for copper and ~13 pcm for stainless steel. Nuclear data sensitivities and uncertainties investigated using Whisper show slightly lower sensitivity to scatter than a lead-reflected plutonium sphere but greater sensitivity to neutron capture. The sensitivities between Jupiter and Jupiter High-240 for lead are very similar for both ENDF/B-VIII.0 and ENDF/B-VIII.1 nuclear data. These benchmarks are more sensitive to neutron capture in lead than other plutonium benchmark experiments and would be useful for both lead and 240 Pu validation. In conclusion, with the high degree of compensating effects between copper, lead, and plutonium cross sections, additional isolated Pb-Pu and Cu-Pu benchmarks would be beneficial in improving these nuclear data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2019

Verification and validation of integrated simulation of energetic particles in fusion plasmas

Here, we report on verification and validation of linear simulations of Alf´ven eigenmodes in the current ramp phase of DIII-D L-mode discharge #159243 using gyrokinetic, gyrokinetic-MHD hybrid, and eigenvalue codes. Using a classical fast ion profile, all simulation codes find that reversed shear Alf´ven eigenmodes (RSAE) are the dominant instability. The real frequencies from all codes have a coefficient of variation of less than 5% for the most unstable modes with toroidal mode number n = 4 and 5. Due to uncertainty in the experimentally measured minimum safety factor (q min ) and the sensitivity of the RSAE’s frequency to q min , the average difference in frequency between simulated and measured is df/f = 14.7%, 22.6%, for n = 4 and 5, respectively. If qmin is adjusted slightly, within experimental errors, an agreement of within 4.5% and 3.1%, for n = 4 and 5 respectively, is found for all codes. The simulated growth rates exhibit greater variation, and simulations find that pressure gradients of thermal plasmas make a significant contribution to the growth rates. Mode structures of the dominant modes agree well among all codes. Using a calculated fast ion profile that takes into account the action of the spectrum of multiple unstable modes, a toroidal Alf´ven eigenmode (TAE) with n = 6 is found to be unstable in the outer edge, consistent with the experimental data. Variations of the real frequencies and growth rates of the TAE are slightly larger than those of the RSAE. Lastly, electron temperature fluctuations and radial phase shifts from simulations show no significant differences with the experimental data for the strong n = 4 RSAE, but significant differences for the weak n = 6 TAE. The verification and validation for the linear simulations of Alf´ven eigenmodes is the first step to determine an integrated simulation of energetic particles confinement in burning plasmas incorporating multiple physical processes with kinetic effects of both energetic and thermal particles on an equal footing.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Impact of Increased Latent Generations on Sensitivity Calculations with SCALE

Analyses of cross section sensitivity data from systems with fissile material allow analysts to associate an importance for each material, nuclide, reaction, and neutron energy by simulating real world criticality scenarios. Although criticality safety validation efforts can be guided by the cross-section sensitivity and uncertainty data generated for a particular system, these calculations can often be computationally expensive and sometimes cumbersome without proper guidance. The TSUNAMI suite within the SCALE code package has several methods for generating sensitivity data, including multigroup and continuous energy (CE) capabilities. The release of SCALE 6.3 has three different CE methods for generating cross section sensitivity data: (1) the Iterated Fission Probability (IFP) method with the KENO Monte Carlo transport solver, (2) the IFP method with the Shift Monte Carlo transport solver, and (3) the Contributon-Linked eigenvalue sensitivity/Uncertainty estimation via Tracklength importance CHaracterization (CLUTCH) method with the KENO Monte Carlo transport solver. Although the CLUTCH method has additional parameters for generating sensitivity data files relative to the IFP method, all three methods use latent generations, which are the generations between an event (i.e., fission) and the assessment of importance based on the asymptotic population of progeny neutrons. Increasing the number of latent generations in a calculation leads to increased discrimination of the sensitivity coefficients but at the cost of the increased uncertainty associated with those generated values. Analysts must balance the accuracy of the sensitivity calculations and its uncertainty with the associated computational cost involved in generating the values. This paper discusses the impact of adjusting the latent generation parameter for a range of sensitivity values and how these changes compare with the direct perturbation values obtained from a change of ±0.5% Δ k in both benchmark and safety application models. Two benchmarks from the International Handbook of Evaluated Criticality Safety Benchmark Experiments and the MPC-32 dual purpose canister for spent nuclear fuel are used for analysis.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

SCALE Modeling of the Fast Spectrum Heat Pipe Reactor

As part of the severe accident analysis collaboration with Sandia National Laboratories (SNL) and the Nuclear Regulatory Commission (NRC), SCALE models were developed for a fast-spectrum heat pipe reactor. These models were based on the Idaho National Laboratory (INL) Design A concept, which is an alternative design to the Los Alamos National Laboratory (LANL) Special Purpose Reactor (SPR), also known as the Megapower reactor. The model contains 1,134 heat pipes, surrounded by hexagonal fuel elements, with a potassium working fluid; the fuel is UO 2 with 19.75 wt% 235 U enrichment. The model contains axial beryllium oxide (BeO) reflectors above and below the active fuel region along with a radial alumina reflector containing 12 B 4 C control drums. The center of the core is left unfueled to make room for two shutdown control rods, one annular and one solid. The active region of the core was discretized into twenty axial and five radial zones to analyze spatial variations in power and burnup. Infinite lattice unit cell sensitivity studies were used to perform verification between the SCALE and INL models. The eigenvalue results agreed well with the reported results to within roughly 50 percent mille (pcm). Full-core model verification was performed by analyzing system eigenvalues with differing configurations of control drum and shutdown rod positions. These full core results all had eigenvalue differences less than 310 pcm. Control drum and shutdown rod worths were also compared, with differences of 3.2% or less. Using the verified model, the isotopic inventory and decay heat, as well as temperature feedback coefficients, were calculated and provided to SNL as input to the MELCOR severe accident code to analyze potential releases from this class of reactor. The results of the MELCOR analysis are provided in a different report.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRSDate not supplied

Aerodynamic Design Optimization for Natural Laminar Flow Airfoils

Natural laminar flow technology is a passive laminar flow control (LFC) strategy that seeks to delay the onset of boundary-layer transition (BLT) through shape optimization to reduce the drag of the aerodynamic vehicle. Adjoint-based design optimization for LFC is proposed in an integrated multidisciplinary framework, which includes the computational fluid dynamics (CFD), geometry and grid deformation, and linear stability analysis (LSA) for transition prediction. In particular, the BLT location is predicted using the dual N-factor method that is based on a linear stability theory (LST) eigenvalue problem. The dual N-factor criterion accounts for the amplification of planar Tollmien-Schlichting (TS) and stationary crossflow (CF) boundary-layer instabilities to predict the transition location in three-dimensional boundary-layer flows. The adjoint-based shape optimization procedure is based on an iteratively coupled CFD and LSA methodology to converge the transition location and flow solutions, as well as to calculate the sensitivities of the aerodynamic metrics of interest with respect to the flow and shape design parameters. The RAE 2822 airfoil at 0 and 30 degrees yaw angles, an angle of attack of 0.72 degrees, and subsonic conditions (M∞ = 0.19, Rec = 5.6 × 106 ) are used as baseline configurations for design optimization. The angle of attack and the vertical displacement of free-form-deformation control points are used as design variables to reduce the drag coefficient while reaching a specified lift coefficient. The optimized unswept airfoil designs achieve a 30% drag reduction accompanied by a downstream shift of the transition locations over both suction and pressure sides of the airfoil. The initial design iterations for the swept case also show a favorable trend in the drag reduction with transition delay over both sides.

Transition↗
DOE OSTI2017

The structure and propagation of laminar flames under autoignitive conditions

The laminar flame speed s l is an important reference quantity for characterising and modelling combustion. Experimental measurements of laminar flame speed require the residence time of the fuel/air mixture (τ f ) to be shorter than the autoignition delay time (τ). This presents a considerable challenge for conditions where autoignition occurs rapidly, such as in compression ignition engines. As a result, experimental measurements in typical compression ignition engine conditions do not exist. Simulations of freely propagating premixed flames, where the burning velocity is found as an eigenvalue of the solution, are also not well posed in such conditions, since the mixture ahead of the flame can autoignite, leading to the so called “cold boundary problem”. In this paper, a numerical method for estimating a reference flame speed, s R , is proposed that is valid for laminar flame propagation at autoignitive conditions. Two isomer fuels are considered to test this method: ethanol, which in the considered conditions is a single-stage ignition fuel; and dimethyl ether, which has a temperature-dependent single- or two-stage ignition and a negative temperature coefficient regime for τ. Calculations are performed for the flame position in a one-dimensional computational domain with inflow-outflow boundary conditions, as a function of the inlet velocity U I and for stoichiometric fuel–air premixtures. The response of the flame position, L F , to U I shows distinct stabilisation regimes. For single-stage ignition fuels, at low U I the flame speed exceeds U I and the flame becomes attached to the inlet. Above a critical U I value, the flame detaches from the inlet and L f becomes extremely sensitive to U I until, for sufficiently high U I , the sensitivity decreases and L f corresponds to the location expected from a purely autoignition stabilised flame. The transition from the attached to the autoignition regimes has a corresponding peak dL f /dU I value which is proposed to be a unique reference flame speed s R for single-stage ignition fuels. For two-stage ignition fuels, there is an additional stable regime where a high-temperature flame propagates into a pool of combustion intermediates generated by the first stage of autoignition. This results in two peaks in dL f /dU I and therefore two reference flame speed values. The lower value corresponds to the definition of s R for single-stage ignition fuels, while the higher value exists only for two-stage ignition fuels and corresponds to a high temperature flame propagating into the first stage of autoignition and is denoted s R ' . Finally, a transport budget analysis for low- and high-temperature radical species is also performed, which confirms that the flame structures at U I = s R and U I = s R ' do indeed correspond to premixed flames (deflagrations), as opposed to spontaneous ignition fronts which do not have a unique propagation speed.

33 ADVANCED PROPULSION SYSTEMS↗