Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Model predictive control”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Numerical Modeling of Cavitating Venturi: A Flow Control Element of Propulsion System

In a propulsion system, the propellant flow and mixture ratio could be controlled either by variable area flow control valves or by passive flow control elements such as cavitating venturies. Cavitating venturies maintain constant propellant flowrate for fixed inlet conditions (pressure and temperature) and wide range of outlet pressures, thereby maintain constant, engine thrust and mixture ratio. The flowrate through the venturi reaches a constant value and becomes independent of outlet pressure when the pressure at throat becomes equal to vapor pressure. In order to develop a numerical model of propulsion system, it is necessary to model cavitating venturies in propellant feed systems. This paper presents a finite volume model of flow network of a cavitating venturi. The venturi was discretized into a number of control volumes and mass, momentum and energy conservation equations in each control volume are simultaneously solved to calculate one-dimensional pressure, density, and flowrate and temperature distribution. The numerical model predicts cavitations at the throat when outlet pressure was gradually reduced. Once cavitation starts, with further reduction of downstream pressure, no change in flowrate is found. The numerical predictions have been compared with test data and empirical equation based on Bernoulli's equation.

Majumdar, Alok↗
NASA NTRS2008

Enhanced Pseudo-Waypoint Guidance for Spacecraft Maneuvers

An enhanced version of the scheme reported in "Pseudo-Waypoint Guidance for Proximity Spacecraft Maneuvers" (NPO-42753), NASA Tech Briefs, Vol. 31, No. 6 (June 2007), page 73 was developed. To recapitulate: the scheme provides algorithms for guidance and control (G&C) of a spacecraft maneuvering near a small astronomical body. The open-loop guidance problem is solved in advance or in real time by use of the pseudo-waypoint generation (PWG) method. Feedback control is implemented to track PWG trajectories, in a manner that enables updating of G&C in a model-predictive manner. The scheme includes silent periods following each thruster firing. The original version of the scheme provides for a fire-first, followed-by-silence sequence, which is disadvantageous in that the silence after final firing precludes reduction of any remaining velocity error -- an unacceptable result in the case of a maneuver for which a specific final velocity is required. In the enhanced version, the scheme is augmented with a fire-second technique, so that the final velocity can be established with a much higher precision because both the guidance and feedback firing can be performed and ceased at the final maneuver time.

Carson, John↗
NASA NTRS2012

Impact of Calibrated Land Surface Model Parameters on the Accuracy and Uncertainty of Land-Atmosphere Coupling in WRF Simulations

Land-atmosphere (L-A) interactions play a critical role in determining the diurnal evolution of both planetary boundary layer (PBL) and land surface temperature and moisture budgets, as well as controlling feedbacks with clouds and precipitation that lead to the persistence of dry and wet regimes. Recent efforts to quantify the strength of L-A coupling in prediction models have produced diagnostics that integrate across both the land and PBL components of the system. In this study, we examine the impact of improved specification of land surface states, anomalies, and fluxes on coupled WRF forecasts during the summers of extreme dry (2006) and wet (2007) land surface conditions in the U.S. Southern Great Plains. The improved land initialization and surface flux parameterizations are obtained through the use of a new optimization and uncertainty estimation module in NASA's Land Information System (LIS-OPT/UE), whereby parameter sets are calibrated in the Noah land surface model and classified according to a land cover and soil type mapping of the observation sites to the full model domain. The impact of calibrated parameters on the a) spinup of the land surface used as initial conditions, and b) heat and moisture states and fluxes of the coupled WRF simulations are then assessed in terms of ambient weather and land-atmosphere coupling along with measures of uncertainty propagation into the forecasts. In addition, the sensitivity of this approach to the period of calibration (dry, wet, average) is investigated. Finally, tradeoffs of computational tractability and scientific validity, and the potential for combining this approach with satellite remote sensing data are also discussed.

Santanello, Joseph A., Jr.↗
NASA NTRSDate not supplied

Final Thermal Design and Thermal Vacuum Testing of the StarBurst Instrument

The StarBurst Multimessenger Pioneer is a small satellite mission serving as a wide-field gamma-ray observatory designed to capture the initial emissions of short gamma-ray bursts, electromagnetic signatures of neutron star mergers. This paper presents the final thermal design and analysis of the StarBurst Instrument, comprising the bus-to-instrument interface plate, control electronics, and twelve crystal detector units, which form the core of the mission’s science capability. The passive thermal control system design requires consideration of restrictive keep-out zones, unknown orbital parameters, and narrow temperature limits of the detectors. Also summarized is the instrument level thermal vacuum cycle test, correlated model refinements, and updated model results. Following successful completion of the instrument test campaign, the hardware was integrated with the spacecraft bus for spacecraft level testing, including additional thermal vacuum testing. The results from the spacecraft level thermal vacuum test will further inform the instrument thermal model, ensuring accurate flight temperature predictions. StarBurst launches as a secondary payload in 2027 and has a mission duration of at least one year.

StarBurst↗
NASA NTRS1982

Applications of system identification methods to the prediction of helicopter stability, control and handling characteristics

A set of results on rotorcraft system identification is described. Flight measurements collected on an experimental Puma helicopter are reviewed and some notable characteristics highlighted. Following a brief review of previous work in rotorcraft system identification, the results of state estimation and model structure estimation processes applied to the Puma data are presented. The results, which were obtained using NASA developed software, are compared with theoretical predictions of roll, yaw and pitching moment derivatives for a 6 degree of freedom model structure. Anomalies are reported. The theoretical methods used are described. A framework for reduced order modelling is outlined.

Padfield, G. D.↗
NASA NTRS1994

USAF single-event sonic boom prediction model: PCBoom3

The Air Force has developed PCBoom3, a general-purpose, single-event sonic boom prediction model. The model operates on an IBM PC or compatible, under DOS or Windows. It is accessed via an integrated environment which controls building of input cases, running boom calculations, displaying contours and signatures, and managing all associated data. The primary boom calculation is via a variation of FOBOOM, the focus-boom extension of Thomas's program. Aircraft input is either via a user-provided F-function, or simple N-wave F-functions tabulated for about 20 current aircraft. A fast boom calculation, based on Plotkin's SBORT algorithms, is included for simple N-wave F-functions in a windless atmosphere and flight altitudes up to 60,000 feet. After a run is complete, the user can access an index identifying significant events (focal zones, beginning of footprint, etc.), then plot boom amplitude contours and signatures or spectra at any point in the footprint. The primary uses of this program are expected to be operational planning and boom incident investigation. However, because of the commonality between FOBOOM and the MDBOOM program currently being used for low boom configuration design, this program is of interest to the HSCT community, especially as supersonic route planning activity increases. The Air Force recently conducted a flight test program to evaluate the focal zone capabilities of PCBoom3. Initial results of that program validate the prediction of focal zone geometry, amplitudes, and waveforms.

Plotkin, Kenneth J.↗
NASA NTRS2019

Sketch-To-Solution: An Exploration of Viscous CFD with Automatic Grids

Numerical simulation of the Reynolds-averaged Navier–Stokes (RANS) equations has become a critical tool for the design of aerospace vehicles. However, the issues that affect the grid convergence of three dimensional RANS solutions are not completely understood, as documented in the AIAA Drag Prediction Workshop series. Grid adaption methods have the potential for increasing the automation and discretization error control of RANS solutions to impact the aerospace design and certification process. The realization of the CFD Vision 2030 Study includes automated management of errors and uncertainties of physics-based, predictive modeling that can set the stage for ensuring a vehicle is in compliance with a regulation or specification by using analysis without demonstration in flight test (i.e., certification or qualification by analysis). For example, the Cart3D inviscid analysis package has automated Cartesian cut-cell gridding with output-based error control. Fueled by recent advances in the fields of anisotropic grid adaptation, error estimation, and geometry modeling, a similar work flow is explored for viscous CFD simulations; where a CFD application engineer provides geometry, boundary conditions, and flow parameters, and the sketch-to-solution process yields a CFD simulation through automatic, error-based, grid adaptation.

Kleb, William L.↗
NASA NTRS2001

Adaptive Multi-Layer LMS Controller Design and Application to Active Vibration Suppression on a Truss and Proposed Impact Analysis Technique

This research develops an adaptive controller that actively suppresses a single frequency disturbance source at a remote position and tests the system on the NPS Space Truss. The experimental results are then compared to those predicted by an ANSYS finite element model. The NPS space truss is a 3.7-meter long truss that simulates a space-borne appendage with sensitive equipment mounted at its extremities. One of two installed piezoelectric actuators and an Adaptive Multi-Layer LMS control law were used to effectively eliminate an axial component of the vibrations induced by a linear proof mass actuator mounted at one end of the truss. Experimental and analytical results both demonstrate reductions to the level of system noise. Vibration reductions in excess of 50dB were obtained through experimentation and over 100dB using ANSYS, demonstrating the ability to model this system with a finite element model. This report also proposes a method to use distributed quartz accelerometers to evaluate the location, direction, and energy of impacts on the NPS space truss using the dSPACE data acquisition and processing system to capture the structural response and compare it to known reference Signals.

Barney, Timothy A.↗
NASA NTRS1997

Computational Models of Human Performance: Validation of Memory and Procedural Representation in Advanced Air/Ground Simulation

The Man-Machine Interaction Design and Analysis System (MIDAS) under joint U.S. Army and NASA cooperative is intended to assist designers of complex human/automation systems in successfully incorporating human performance capabilities and limitations into decision and action support systems. MIDAS is a computational representation of multiple human operators, selected perceptual, cognitive, and physical functions of those operators, and the physical/functional representation of the equipment with which they operate. MIDAS has been used as an integrated predictive framework for the investigation of human/machine systems, particularly in situations with high demands on the operators. We have extended the human performance models to include representation of both human operators and intelligent aiding systems in flight management, and air traffic service. The focus of this development is to predict human performance in response to aiding system developed to identify aircraft conflict and to assist in the shared authority for resolution. The demands of this application requires representation of many intelligent agents sharing world-models, coordinating action/intention, and cooperative scheduling of goals and action in an somewhat unpredictable world of operations. In recent applications to airborne systems development, MIDAS has demonstrated an ability to predict flight crew decision-making and procedural behavior when interacting with automated flight management systems and Air Traffic Control. In this paper, we describe two enhancements to MIDAS. The first involves the addition of working memory in the form of an articulatory buffer for verbal communication protocols and a visuo-spatial buffer for communications via digital datalink. The second enhancement is a representation of multiple operators working as a team. This enhanced model was used to predict the performance of human flight crews and their level of compliance with commercial aviation communication procedures. We show how the data produced by MIDAS compares with flight crew performance data from full mission simulations. Finally, we discuss the use of these features to study communication issues connected with aircraft-based separation assurance.

Corker, Kevin M.↗
NASA NTRS2011

Multiple Damage Progression Paths in Model-Based Prognostics

Model-based prognostics approaches employ domain knowledge about a system, its components, and how they fail through the use of physics-based models. Component wear is driven by several different degradation phenomena, each resulting in their own damage progression path, overlapping to contribute to the overall degradation of the component. We develop a model-based prognostics methodology using particle filters, in which the problem of characterizing multiple damage progression paths is cast as a joint state-parameter estimation problem. The estimate is represented as a probability distribution, allowing the prediction of end of life and remaining useful life within a probabilistic framework that supports uncertainty management. We also develop a novel variance control mechanism that maintains an uncertainty bound around the hidden parameters to limit the amount of estimation uncertainty and, consequently, reduce prediction uncertainty. We construct a detailed physics-based model of a centrifugal pump, to which we apply our model-based prognostics algorithms. We illustrate the operation of the prognostic solution with a number of simulation-based experiments and demonstrate the performance of the chosen approach when multiple damage mechanisms are active

Daigle, Matthew↗
NASA NTRS2006

Momentum Transfer in a Spinning Fuel Tank Filled with Xenon

Transient spin-up and spin-down flows inside of spacecraft fuel tanks need to be analyzed in order to properly design spacecraft control systems. Knowledge of the characteristics of angular momentum transfer to and from the fuel is used to size the de-spin mechanism that places the spacecraft in a controllable in-orbit state. In previous studies, several analytical models of the spin-up process were developed. However, none have accurately predicted all of the flow dynamics. Several studies have also been conducted using Navier-Stokes based methods. These approaches have been much more successful at simulating the dynamic processes in a cylindrical container, but have not addressed the issue of momentum transfer. In the current study, the spin-up and spin-down of a fuel tank filled with gaseous xenon has been investigated using a three-dimensional unsteady Navier-Stokes code. Primary interests have been concentrated on the spin-up/spin-down time constants and the initial torque imparted on the system. Additional focus was given to the relationship between the dominant flow dynamics and the trends in momentum transfer. Through the simulation of both a cylindrical and a spherical tank, it was revealed that the transfer of angular momentum is nonlinear at early times and tends toward a linear pattern at later times. Further investigation suggests that the nonlinear spin up is controlled by the turbulent transport of momentum, while the linear phase is controlled by a Coriolis driven (Ekman) flow along the outer wall. These results indicate that the spinup and spin-down processes occur more quickly in tanks with curved surfaces than those with defined top, bottom, and side walls. The results also provide insights for the design of spacecraft de-spin mechanisms.

Peugeot, John W.↗
NASA NTRS2011

Base Flow Investigation of the Apollo AS-202 Command Module

In recent years, both Europe and the US are developing hypersonic research and operational vehicles. These include (re)entry capsules (both ballistic and lifting) and lifting bodies such as ExoMars, EXPERT, ARV, CEV and IXV. The research programs are meant to enable technology and engineering capabilities to support during the next decade the development of affordable (possibly reusable) space transportation systems as well as hypersonic weapons systems for time critical targets. These programs have a broad range of goals, ranging from the qualification of thermal protection systems, the assessment of RCS performances, the development of GNC algorithms, to the full demonstration of the performance and operability of the integrated vehicles. Since the aerothermodynamic characteristics influence nearly all elements of the vehicle design, the accurate prediction of the aerothermal environment is a prerequisite for the design of efficient hypersonic systems. Significant uncertainties in the prediction of the hypersonic aerodynamic and the aerothermal loads can lead to conservative margins in the design of the vehicle including its Outer Mould Line (OML), thermal protection system, structure, and required control system robustness. The current level of aerothermal prediction uncertainties results therefore in reduced vehicle performances (e.g., sub-optimal payload to mass ratio, increased operational constraints). On the other hand, present computational capabilities enable the simulation of three dimensional flow fields with complex thermo-chemical models over complete trajectories and ease the validation of these tools by, e.g., reconstruction of detailed wind tunnel tests performed under identified and controlled conditions (flow properties and vehicle attitude in particular). These controlled conditions are typically difficult to achieve when performing in flight measurements which in turn results in large associated measurement uncertainties. Similar problems arise when attempting to rebuild measurements performed in "hot" ground facilities, where the difficulty level is increased by the addition of the free-flow characterization itself. The implementation of ever more sophisticated thermochemical models is no obvious cure to the aforementioned problems since their effect is often overwhelmed by the large measurement uncertainties incurred in both flight and ground high enthalpy facilities. Concurrent to the previous considerations, a major contributor to the overall vehicle mass of re-entry vehicles is the afterbody thermal protection system. This is due to the large acreage (equal or bigger than that of the forebody) to be protected. The present predictive capabilities for base flows are comparatively lower than those for windward flowfields and offer therefore a substantial potential for improving the design of future re-entry vehicles. To that end, it is essential to address the accuracy of high fidelity CFD tools exercised in the US and EU, which motivates a thorough investigation of the present status of hypersonic flight afterbody heating. This paper addresses the predictive capabilities of after body flow fields of re-entry vehicles investigated in the frame of the NATO/RTO - RTG-043 Task Group and is structured as follows: First, the verification of base flow topologies on the basis of available wind-tunnel results performed under controlled supersonic conditions (i.e., cold flows devoid of reactive effects) is performed. Such tests address the detailed characterization of the base flow with particular emphasis on separation/reattachment and their relation to Mach number effects. The tests have been performed on an Apollo-like re-entry capsule configuration. Second, the tools validated in the frame of the previous effort are exercised and appraised against flight-test data collected during the Apollo AS-202 re-entry.

Walpot, Louis M. G.↗
NASA NTRS1998

A Cognitive-System Model for En Route Air Traffic Management

NASA Ames Research Center has been engaged in the development of advanced air traffic management technologies whose basic form is cognitive aiding systems for air traffic controller and flight deck operations. In the design and evaluation of such systems the dynamic interaction between the airborne aiding system and the ground-based aiding systems forms a critical coupling for control. The human operator is an integral control element in the system and the optimal integration of human decision and performance parameters with those of the automation aiding systems offers a significant challenge to cognitive engineering. This paper presents a study in full mission simulation and the development of a predictive computational model of human performance. We have found that this combination of methodologies provide a powerful design-aiding process. We have extended the computational model Man Machine Integrated Design and Analysis System (N13DAS) to include representation of multiple cognitive agents (both human operators and intelligent aiding systems), operating aircraft airline operations centers and air traffic control centers in the evolving airspace. The demands of this application require the representation of many intelligent agents sharing world-models, and coordinating action/intention with cooperative scheduling of goals and actions in a potentially unpredictable world of operations. The operator's activity structures have been developed to include prioritization and interruption of multiple parallel activities among multiple operators, to provide for anticipation (knowledge of the intention and action of remote operators), and to respond to failures of the system and other operators in the system in situation-specific paradigms. We have exercised this model in a multi-air traffic sector scenario with potential conflict among aircraft at and across sector boundaries. We have modeled the control situation as a multiple closed loop system. The inner and outer loop alerting structure of air traffic management has many implications that need to be investigated to assure adequate design. First, there are control and stability factors implicit in the design. As the inner loop response time approaches that of the outer loop, system stability may be compromised in that controllers may be solving a problem the nature of which has already been changed by pilot action. Second, information exchange and information presentation for both air and ground must be designed to complement as opposed to compete with each other. Third, the level of individual and shared awareness in trajectory modification and flight conformance needs to be defined. Fourth, the level of required awareness and performance impact of mixed fleet operations and failed-mode recovery must be explored.

Corker, Kevin M.↗
NASA NTRS2009

Aerothermal Testing for Project Orion Crew Exploration Vehicle

The Project Orion Crew Exploration Vehicle aerothermodynamic experimentation strategy, as it relates to flight database development, is reviewed. Experimental data has been obtained to both validate the computational predictions utilized as part of the database and support the development of engineering models for issues not adequately addressed with computations. An outline is provided of the working groups formed to address the key deficiencies in data and knowledge for blunt reentry vehicles. The facilities utilized to address these deficiencies are reviewed, along with some of the important results obtained thus far. For smooth wall comparisons of computational convective heating predictions against experimental data from several facilities, confidence was gained with the use of algebraic turbulence model solutions as part of the database. For cavities and protuberances, experimental data is being used for screening various designs, plus providing support to the development of engineering models. With the reaction-control system testing, experimental data were acquired on the surface in combination with off-body flow visualization of the jet plumes and interactions. These results are being compared against predictions for improved understanding of aftbody thermal environments and uncertainties.

Berry, Scott A.↗
NASA NTRS2011

Core Noise: Implications of Emerging N+3 Designs and Acoustic Technology Needs

This presentation is a summary of the core-noise implications of NASA's primary N+3 aircraft concepts. These concepts are the MIT/P&W D8.5 Double Bubble design, the Boeing/GE SUGAR Volt hybrid gas-turbine/electric engine concept, the NASA N3-X Turboelectric Distributed Propulsion aircraft, and the NASA TBW-XN Truss-Braced Wing concept. The first two are future concepts for the Boeing 737/Airbus A320 US transcontinental mission of 180 passengers and a maximum range of 3000 nm. The last two are future concepts for the Boeing 777 transpacific mission of 350 passengers and a 7500 nm range. Sections of the presentation cover: turbofan design trends on the N+1.5 time frame and the already emerging importance of core noise; the NASA N+3 concepts and associated core-noise challenges; the historical trends for the engine bypass ratio (BPR), overall pressure ratio (OPR), and combustor exit temperature; and brief discussion of a noise research roadmap being developed to address the core-noise challenges identified for the N+3 concepts. The N+3 conceptual aircraft have (i) ultra-high bypass ratios, in the rage of 18 - 30, accomplished by either having a small-size, high-power-density core, an hybrid design which allows for an increased fan size, or by utilizing a turboelectric distributed propulsion design; and (ii) very high OPR in the 50 - 70 range. These trends will elevate the overall importance of turbomachinery core noise. The N+3 conceptual designs specify the need for the development and application of advanced liners and passive and active control strategies to reduce the core noise. Current engineering prediction of core noise uses semi-empirical methods based on older turbofan engines, with (at best) updates for more recent designs. The models have not seen the same level of development and maturity as those for fan and jet noise and are grossly inadequate for the designs considered for the N+3 time frame. An aggressive program for the development of updated noise prediction tools for integrated core assemblies as well as and strategies for noise reduction and control is needed in order to meet the NASA N+3 noise goals. The NASA Fundamental Aeronautics Program has the principal objective of overcoming today's national challenges in air transportation. The SFW Reduced-Perceived-Noise Technical Challenge aims to develop concepts and technologies to dramatically reduce the perceived aircraft noise outside of airport boundaries. This reduction of aircraft noise is critical to enabling the anticipated large increase in future air traffic.

Hultgren, Lennart S.↗
NASA NTRSDate not supplied

Summary of the First AIAA Stability and Control Prediction Workshop

Results from the First AIAA Stability and Control Prediction Workshop are summarized in this paper. The workshop series was developed in support of three primary objectives: (1) to establish best practices for the prediction of stability and control derivatives using industry-standard Computational Fluid Dynamics (CFD) solvers, (2) to provide an impartial forum for evaluating the effectiveness of Reynolds-averaged-Navier-Stokes- and Detached-Eddy-Simulation-based modeling techniques, and (3) to identify areas in need of additional research and development. To address these objectives, the inaugural workshop focused on generating computational aerodynamic predictions for the ONERA version of the NASA/Boeing Common Research Model. The configuration includes the wing, body, horizontal tail, and a vertical tail designed by ONERA. While longitudinal wind tunnel test data for the model had been previously documented, unpublished lateral test data at small sideslip angles provided a unique opportunity for participants to generate blind computational predictions for wind tunnel data comparisons. Additional test cases included assessments of the Mach number effect on static lateral/directional stability and the impact of the wind tunnel sting on longitudinal stability. Participants were invited to generate solutions using two workshop-provided series of structured overset and unstructured grids, in addition to any participant custom grids of interest. Total and component-level breakdowns for the force and moment coefficients for each test case are presented, as well as sectional pressure distribution data on the wing and tail components, to assess the agreement between several different Reynolds-averaged Navier-Stokes CFD solvers.

CFD↗
NASA NTRS1999

Numerical Modeling and In-Situ Observations of the Dynamics of the Solid/Liquid Interface Morphology During Directional Solidification of Alloys

The departure from interface planarity and the subsequent evolution to a periodic array of cells or dendrites is a fundamental process that characterizes most microstructures in solidified alloys. The growing demand for high quality alloys and semiconductor crystals requires a precise methodology to predict and subsequently control both the interface morphology and the distribution of impurities, additives, and phases in the grown crystal. Apart from its practical significance, the study of morphological evolution has also been viewed as a means to unearth a general paradigm for pattern formation in nature. A previously developed 2D numerical model for the solid/liquid interface tracking has been further refined and used to simulate the time-evolution of the perturbations on the interface. The dynamics of the local growth velocity, interface undercooling and solute concentration at the interface has been theoretically predicted by means of the numerical model for Al-Cu and Pb-Sn alloys. The model shows that perturbations with a wavelengths, lambda greater than a critical wavelength lambda(sub c) continue to grow in time whereas perturbations with lambda < lambda(sub c) cease to propagate. The model further predicts that under certain conditions perturbation can also propagate along the interface. Comparison of these predictions with existing theories of pattern formation and experimental results will be discussed.

Catalina, Adrian V.↗
NASA NTRS1976

Linear and nonlinear analysis of orbital telescope/space shuttle dynamics and control

Work completed on the design and study of an annular suspension and pointing (ASP) system for the space shuttle was presented. This system makes use of a magnetically suspended vernier pointing assembly. The following objectives were pursued in this study: (1) development of a detailed mathematical model of the Space Shuttle/ASP system, (2) design of control laws in order to obtain the desired pointing performance, and (3) prediction of the statistical pointing accuracies in the presence of stochastic disturbances such as crew-motion, and sensor and actuator noise. The first two of these objectives are documented in this report.

Roberts, A. S., Jr.↗