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At least 289 records · Page 16

Features and applications of the Groove Analysis Program (GAP)

An IBM Personal Computer (PC) version of the Groove Analysis program (GAP) was developed to predict the steady state heat transport capability of an axially grooved heat pipe for a specified groove geometry and working fluid. In the model, the capillary limit is determined by the numerical solution of the differential equation for momentum conservation with the appropriate boundary conditions. This governing equation accounts for the hydrodynamic losses due to friction in liquid and vapor flows and due to liquid/vapor shear interaction. Back-pumping in both 0-g and 1-g is accounted for in the boundary condition at the condenser end. Slug formation in 0-g and puddle flow in 1-g are also considered in the model. At the user's discretion, the code will perform the analysis for various fluid inventories (undercharge, nominal charge, overcharge, or a fixed fluid charge) and heat pipe elevations. GAP will also calculate the minimum required heat pipe wall thickness for pressure containment at design temperatures that are greater than or lower than the critical temperature of the working fluid. This paper discusses the theory behind the development of the GAP model. It also presents the many useful and powerful capabilities of the model. Furthermore, a correlation of flight test performance data and the predictions using GAP are presented and discussed.

Ku, Jentung↗

Technology Estimating 2: A Process to Determine the Cost and Schedule of Space Technology Research and Development

As a leader in space technology research and development, NASA is continuing in the development of the Technology Estimating process, initiated in 2012, for estimating the cost and schedule of low maturity technology research and development, where the Technology Readiness Level is less than TRL 6. NASA' s Technology Roadmap areas consist of 14 technology areas. The focus of this continuing Technology Estimating effort included four Technology Areas (TA): TA3 Space Power and Energy Storage, TA4 Robotics, TA8 Instruments, and TA12 Materials, to confine the research to the most abundant data pool. This research report continues the development of technology estimating efforts completed during 2013-2014, and addresses the refinement of parameters selected and recommended for use in the estimating process, where the parameters developed are applicable to Cost Estimating Relationships (CERs) used in the parametric cost estimating analysis. This research addresses the architecture for administration of the Technology Cost and Scheduling Estimating tool, the parameters suggested for computer software adjunct to any technology area, and the identification of gaps in the Technology Estimating process.

Cole, Stuart K.↗

An Overview of the Patch Integral Method (PIM), a New Heat Transfer Analysis Tool for Hypersonic Wind Tunnel Facilities at NASA Langley

NASA Langley’s hypersonic wind tunnels are heavily leveraged for planetary missions. The data collection method in these tunnels is thermography, and surface temperature measurements of the model surface are collected and reduced to produce surface heating data, as seen in Fig 1. However, during model injection, no temperature data are collected, and thus conventional, integral heat transfer methods cannot be used to solve for surface heating. A method was developed in the 1990’s to reduce this data despite the data gap, known as the step approximation method. The method assumes that the film coefficient behaves as a step function, the model is semi-infinite, and thermal properties are constant. With these simplifying assumptions, a Laplace transform can be performed to result in an equation that takes the initial temperature of the model and a temperature at some point in time to back out the film coefficient at that time. This is the method that is used in the current thermographic data reduction software, IHEAT. While computationally light-weight, the step approximation has several issues associated with it. The time-history of temperature is not accounted for, which is vital as heat transfer is an integral process. Additionally, the required semi-infinite assumption is unnecessary and might be violated during runtime. Thermal variation of material properties can have a sizeable impact on heating results and are not modeled by the method. This method also takes multiple seconds to “collapse” to a steady state, which is undesirable from both a facility and data reduction standpoint. The method is also very sensitive to the “effective time” approximation, an approximation of when heating instantaneously starts (which is a nonphysical simplification), and a small variation in this value can result in an error in heating results.

J. S. Cheatwood↗

An analysis of the back end of the nuclear fuel cycle with emphasis on high-level waste management, volume 1

The programs and plans of the U.S. government for the "back end of the nuclear fuel cycle" were examined to determine if there were any significant technological or regulatory gaps and inconsistencies. Particular emphasis was placed on analysis of high-level nuclear waste management plans, since the permanent disposal of radioactive waste has emerged as a major factor in the public acceptance of nuclear power. The implications of various light water reactor fuel cycle options were examined including throwaway, stowaway, uranium recycle, and plutonium plus uranium recycle. The results of this study indicate that the U.S. program for high-level waste management has significant gaps and inconsistencies. Areas of greatest concern include: the adequacy of the scientific data base for geological disposal; programs for the the disposal of spent fuel rods; interagency coordination; and uncertainties in NRC regulatory requirements for disposal of both commercial and military high-level waste.

Source record↗

Multi-Disciplinary Design Optimization Using WAVE

The current preliminary design tools lack the product performance, quality and cost prediction fidelity required to design Six Sigma products. They are also frequently incompatible with the tools used in detailed design, leading to a great deal of rework and lost or discarded data in the transition from preliminary to detailed design. Thus, enhanced preliminary design tools are needed in order to produce adequate financial returns to the business. To achieve this goal, GEAE has focused on building the preliminary design system around the same geometric 3D solid model that will be used in detailed design. With this approach, the preliminary designer will no longer convert a flowpath sketch into an engine cross section but rather, automatically create 3D solid geometry for structural integrity, life, weight, cost, complexity, producibility, and maintainability assessments. Likewise, both the preliminary design and the detailed design can benefit from the use of the same preliminary part sizing routines. The design analysis tools will also be integrated with the 3D solid model to eliminate manual transfer of data between programs. GEAE has aggressively pursued the computerized control of engineering knowledge for many years. Through its study and validation of 3D CAD programs and processes, GEAE concluded that total system control was not feasible at that time. Prior CAD tools focused exclusively on detail part geometry and Knowledge Based Engineering systems concentrated on rules input and data output. A system was needed to bridge the gap between the two to capture the total system. With the introduction of WAVE Engineering from UGS, the possibilities of an engineering system control device began to formulate. GEAE decided to investigate the new WAVE functionality to accomplish this task. NASA joined GEAE in funding this validation project through Task Order No. 1. With the validation project complete, the second phase under Task Order No. 2 was established to develop an associative control structure (framework) in the UG WAVE environment enabling multi-disciplinary design of turbine propulsion systems. The capabilities of WAVE were evaluated to assess its use as a rapid optimization and productivity tool. This project also identified future WAVE product enhancements that will make the tool still more beneficial for product development.

Irwin, Keith↗

Microshutter Arrays for the NGST NIRSpec

We are developing a programmable multiobject field selector for the NGST NIRSpec. This device is a microshutter array, a close-packed 2000 x 2000 array of 100 micrometer x 100 micrometer shutters fabricated with Micro-ElectroMechanical Systems (MEMS) technologies. The shutters are opened using a magnet scanned over the array. The shutters are held open by electrostatic potentials on adjacent vertical electrodes. Modeling of the magnetic actuation of the microshutters allowed optimization of the magnetic field configuration, the distance between magnet and shutters, and the force and torque produced by the magnet. The results of laboratory tests are consistent with our modeling. We have demonstrated actuation, latching and addressing. We are able to rotate shutters out of the plane up to 90 degree and more, to latch them electrostatically to the walls and release them selectively. During the last six month all critical elements of the array have been demonstrated. Fabrication processes were developed to deposit vertical electrodes on support grid side walls and insulated light-shields that block the gaps between shutters and the support grid. Physical optics analysis was performed to assess the expected optical performance of the microshutters. A preliminary Fourier optics analysis on the microshutter array performance has been carried out. More detailed analysis of wave propagation through 3D structures is a next step. An optical test station for verifying optical parameters of the shutter array at room temperature has been developed. It allows to measure parameters, such as transmission, scattering, contrast ratio, and diffraction of the array structure. Initial data have been acquired and are being analyzed and compared to theoretical predictions.

Moseley, Harvey↗

Safe Affordable Fission Engine (SAFE 30) Module Conductivity Test Thermal Model Correlation

Two SAFE 30 modules were tested to determinate the thermal conductivity efficiency of the tri-cusps filled between the heat pipe and the heater cores. The modules consisted of four one-inch diameter tubes with heaters joined to an empty 1 inch diam. tube. The test was conducted on a vacuum chamber with 4 configurations: tri-cusps filled with and without radiation shielding and non-filled tri-cusps with and without radiation shielding. The tri-cusps material helps the bonding of the heat pipe to the four electric heater cores, filling the gap between the pipes. The baseline configuration is a brazed joint between the pipe. The test consisted of controlling the power applied to the heaters until a set surface temperature is reach. The temperatures varied between a max. of 800 C to 500 C. Test data, input energy and chamber surface temperature from each individual test, was used as boundary conditions for the model. Nodes located on the same location as the test thermocouples were plotted again test data to determinate the accuracy of the analysis. The unknown n variables on the analysis are the radiation emissivity of the pipe and chamber and the radiation view factor between the module and the chamber. A correlation was determined using a parametric analysis varying the surface emissivity and view factor until a good match was reach.

Roman, Jose↗

Reanalysis of Rat Data from Spacelab Life Sciences 2 (SLS-2) to Reveal Research Gaps in Spaceflight Data

Using and analyzing the legacy data obtained in space life sciences missions has the potential to provide researchers a complete picture of the molecular changes associated with space without further experimentation. This project’s objective is to extract, filter, organize, and analyze all Rattus norvegicus data and metadata obtained from Columbia’s Spacelab Life Sciences 2 (SLS-2, STS-58) mission to explore the ways that we can compile information from model organisms, in our case rats, to create a reliable model to understand biological mechanisms in response to these space flight changes. By reusing rare space legacy data coupled with data analysis techniques, we can combine individual preexisting datasets with current ones to gain new, comprehensive insights about the effects of spaceflight on our bodies. Our methods can also lead to the creation of a standardized pipeline that could be applied to other space life science datasets for analysis. In this review, every biological experiment conducted on rats in the SLS-2 Mission was studied with our pipeline to create a new biological library and model that could be used by scientists from around the world to make novel discoveries and develop new hypotheses from this priceless information without the limitation of the costs of spaceflight experimentation.

rats↗

Passive Orbital Disconnect Strut (PODS 3), structural and thermal test program

A test program is undertaken to verify that the lifetime of a shuttle launchable dewar can be increased by using passive orbital disconnect struts (PODS). A detailed design is performed on the cold end (PODS-III) portion of the strut. Structural analysis of the thin-wall fiberglass tube allows selection of the optimum winding angle and tube dimensions. Structural tests on the thin-wall fiberglass tube measure both the tension and compression modulus at ambient and LN2 temperatures, the radial deflection versus side load, and the ultimate compression strength of the tube at LN2 temperature. The thermal expansion of the fiberglass tube plus Invar is also measured down to 78 K. The axial gap at the wedge portion of the stem is set based on these data. The PODS-III test article parts are fabricated and assembled using a detailed assembly procedure. The thermal conductants in the orbital configuration was measured for body temperatures between 5 and 40 K. This temperature range covers the predicted ground hold and orbit temperatures for vapor-cooled supports. The test results are then compared with heat leak values predicted before the test began. Side load, axial compression load, and tension load tests conclude the test program.

Parmley, R. T.↗

NASA ACC High Energy Dynamic Impact Methodology and Outcomes

High fidelity analysis methods known as Progressive Damage Analysis (PDA) methods, capable of reliably predicting the onset and progression of damage in composite materials, are being developed for HEDI event simulation. Four state-of-the-art PDA methods are being investigated: LS-DYNA MAT162, LS-DYNA MAT261, Smooth-Particle Galerkin (SPG), and EMU Peridynamics. Validation of these PDA models aims to follow a building block approach, starting with coupon- and component-level development. As part of the overall effort, material characterization testing was performed to bridge gaps between existing experimental data and the material property inputs required to predict ballistic impact behavior at the component-level. The material models were updated with the results of the coupon-level testing and were then used to predict panel behavior and damage in ballistic impact events. To assess the accuracy of the PDA methods, these pre-test predictions were compared to the results of ballistic impact testing.

Hunziker, Kenneth J.↗

Synergistic Use of Hyperspectral UV-Visible OMI and Broadband Meteorological Imager MODIS Data for a Merged Aerosol Product

The retrieval of optimal aerosol datasets by the synergistic use of hyperspectral ultraviolet(UV)–visible and broadband meteorological imager (MI) techniques was investigated. The Aura Ozone Monitoring Instrument (OMI) Level 1B (L1B) was used as a proxy for hyperspectral UV–visible instrument data to which the Geostationary Environment Monitoring Spectrometer (GEMS) aerosol algorithm was applied. Moderate-Resolution Imaging Spectroradiometer (MODIS) L1B and dark target aerosol Level 2 (L2) data were used with a broadband MI to take advantage of the consistent time gap between the MODIS and the OMI. First, the use of cloud mask information from the MI infrared (IR) channel was tested for synergy. High-spatial-resolution and IR channels of the MI helped mask cirrus and sub-pixel cloud contamination of GEMS aerosol, as clearly seen in aerosol optical depth (AOD) validation with Aerosol Robotic Network (AERONET) data. Second, dust aerosols were distinguished in the GEMS aerosol-type classification algorithm by calculating the total dust confidence index (TDCI) from MODIS L1B IR channels. Statistical analysis indicates that the Probability of Correct Detection (POCD) between the forward and inversion aerosol dust models (DS) was increased from 72% to 94% by use of the TDCI for GEMS aerosol-type classification, and updated aerosol types were then applied to the GEMS algorithm. Use of the TDCI for DS type classification in the GEMS retrieval procedure gave improved single-scattering albedo (SSA) values for absorbing fine pollution particles (BC) and DS aerosols. Aerosol layer height (ALH) retrieved from GEMS was compared with Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) data, which provides high-resolution vertical aerosol profile information. The CALIOP ALH was calculated from total attenuated backscatter data at 1064 nm, which is identical to the definition of GEMS ALH. Application of the TDCI value reduced the median bias of GEMS ALH data slightly. The GEMS ALH bias approximates zero, especially for GEMS AOD values of>~0.4 and GEMS SSA values of<~0.95.Finally, the AOD products from the GEMS algorithm and MI were used in aerosol merging with the maximum-likelihood estimation method, based on a weighting factor derived from the standard deviation of the original AOD products. With the advantage of the UV–visible channel in retrieving aerosol properties over bright surfaces, the combined AOD products demonstrated better spatial data availability than the original AOD products, with comparable accuracy. Furthermore, pixel-level error analysis of GEMS AOD data indicates improvement through MI synergy.

aerosol↗

Steady internal flow and aerodynamic loads analysis of shuttle thermal protection system

An analytical model for calculation of ascent steady state tile loading was developed and validated with wind tunnel data. The analytical model is described and results are given. Results are given for loading due to shocks and skin friction. The analysis included calculation of internal flow (porous media flow and channel flow) to obtain pressures and integration of the pressures to obtain forces and moments on an insulation tile. A heat transfer program was modified by using analogies between heat transfer and fluid flow so that it could be used for internal flow calculation. The type of insulation tile considered was undensified reusable surface insulation (RSI) without gap fillers, and the location studied was the lower surface of the orbiter. Force and moment results are reported for parameter variations on surface pressure distribution, gap sizes, insulation permeability, and tile thickness.

Petley, D. H.↗

Edge discrimination as applied to Thematic Mapper data

An evaluation of suitable edge discrimination techniques and their application to image segmentation is reported. From an analysis of Thematic Mapper Simulator data, it is concluded that segmentation by automated edge discrimination is a valuable technique which can be used in the development of per-field classifiers. A Laplacian convolution operator appears to be the most cost-effective high-pass filter. Spatial frequency domain filtering is more versatile in its ability to enhance different edge types. A simple global gray value threshold can produce good edge discrimination from an enhanced image which may be improved by using a local thresholding technique. A gap-fill postprocessing technique is necessary for useful segmentation. Gradient and other directionally dependent techniques are unsuitable for segmentation.

Hall, J. R.↗

NESSUS (Numerical Evaluation of Stochastic Structures Under Stress)/EXPERT: Bridging the gap between artificial intelligence and FORTRAN

The development of a probabilistic structural analysis methodology (PSAM) is described. In the near-term, the methodology will be applied to designing critical components of the next generation space shuttle main engine. In the long-term, PSAM will be applied very broadly, providing designers with a new technology for more effective design of structures whose character and performance are significantly affected by random variables. The software under development to implement the ideas developed in PSAM resembles, in many ways, conventional deterministic structural analysis code. However, several additional capabilities regarding the probabilistic analysis makes the input data requirements and the resulting output even more complex. As a result, an intelligent front- and back-end to the code is being developed to assist the design engineer in providing the input data in a correct and appropriate manner. The type of knowledge that this entails is, in general, heuristically-based, allowing the fairly well-understood technology of production rules to apply with little difficulty. However, the PSAM code, called NESSUS, is written in FORTRAN-77 and runs on a DEC VAX. Thus, the associated expert system, called NESSUS/EXPERT, must run on a DEC VAX as well, and integrate effectively and efficiently with the existing FORTRAN code. This paper discusses the process undergone to select a suitable tool, identify an appropriate division between the functions that should be performed in FORTRAN and those that should be performed by production rules, and how integration of the conventional and AI technologies was achieved.

Fink, Pamela K.↗

Evaluating SAR Radiometric Terrain Correction Solutions: Optimal products for applied users

Operational applications of Synthetic Aperture Radar (SAR) are under development around the world, driven by the regularly-acquired, free-and-open source C-band SAR observations provided by ESA’s Sentinel-1 sensor constellation since 2014. Groups like SERVIR, a joint NASA and USAID initiative, are at the forefront of remote sensing applications for societal benefit. A takeaway from SERVIR’s experience is the need for appropriately geocoded and fully calibrated SAR data that is ready to use for a range of ecosystems-related applications. Radiometric Terrain Corrected (RTC) data are key entry-level products for multiple applications that range from ecosystems to hazards. This work fills a gap in current research by evaluating several RTCs produced by open-source software solutions (SNAP-7 and ISCE-2), the gold standard commercial software (GAMMA), a Google Earth Engine (GEE) based workflow, and the uncorrected GRD products currently available in GEE. RTCs were analyzed for geolocation quality, absolute radiometric calibration, and fidelity of the radiometric terrain flattening over ten sites representing varied terrains. In addition, a time series analysis was conducted over two locations. Overall, no significant differences for radiometric calibration were found across RTC products. However, all RTCs performed better than uncorrected GRD products. The main differences between products were found in geolocation quality. These results not only demonstrate the need for the uptake and distribution of RTC products for ecosystems applications, but demonstrate the ability to do so with open source methods, adding value to developing affordable operational applications.

Helen Blue Parache↗

Active Sensing of CO2 Emissions over Nights, Days, and Seasons (ASCENDS): Final Report of the ASCENDS Ad Hoc Science Definition Team

Improved remote sensing observations of atmospheric carbon dioxide (CO2) are critically needed to quantify, monitor, and understand the Earth's carbon cycle and its evolution in a changing climate. The processes governing ocean and terrestrial carbon uptake remain poorly understood,especially in dynamic regions with large carbon stocks and strong vulnerability to climate change,for example, the tropical land biosphere, the northern hemisphere high latitudes, and the Southern Ocean. Because the passive spectrometers used by GOSAT (Greenhouse gases Observing SATellite) and OCO-2 (Orbiting Carbon Observatory-2) require sunlit and cloud-free conditions,current observations over these regions remain infrequent and are subject to biases. These short comings limit our ability to understand and predict the processes controlling the carbon cycle on regional to global scales.In contrast, active CO2 remote-sensing techniques allow accurate measurements to be taken day and night, over ocean and land surfaces, in the presence of thin or scattered clouds, and at all times of year. Because of these benefits, the National Research Council recommended the National Aeronautics and Space Administration (NASA) Active Sensing of CO2 Emissions over Nights,Days, and Seasons (ASCENDS) mission in the 2007 report Earth Science and Applications from Space: National Imperatives for the Next Decade and Beyond. The ability of ASCENDS to collect low-bias observations in these key regions is expected to address important gaps in our knowledge of the contemporary carbon cycle.The ASCENDS ad hoc Science Definition Team (SDT), comprised of carbon cycle modeling and active remote sensing instrument teams throughout the United States (US), worked to develop the mission's requirements and advance its readiness from 2008 through 2018. Numerous scientific investigations were carried out to identify the benefit and feasibility of active CO2 remote sensing measurements for improving our understanding of CO2 sources and sinks. This report summarizes their findings and recommendations based on mission modeling studies, analysis of ancillary meteorological data products, development and demonstration of candidate technologies, anddesign studies of the ASCENDS mission concept.

Kawa, S. Randolph↗

Fully Coupled Aeroelastic Stability Analysis of Adaptive Shape Memory Alloy Structural Technologies for Airframe Noise Reduction

This final report documents work performed by ATA Engineering, Inc., (ATA) to develop computational models and analyze the coupled fluid-structure response of two types of noise treatments applied to the leading-edge-slat component of a high-lift system typical of modern transport aircraft. The first treatment is a slat-gap filler (SGF), which closes the gap between the suction surfaces of a deployed slat and an aircraft main wing, and the second treatment is a slat-cove filler (SCF), which replaces the recirculating flow on the slat cove with a surface that promotes flow attachment. The representative airframe chosen for this work was NASA’s High-Lift Common Research Model (CRM-HL) in a baseline high-lift configuration. Superelastic shape memory alloys (SMAs) have been identified as enabling materials for these structural treatments. Since the technology elements rely upon having a highly reconfigurable structure, designs were assessed for their static aeroelastic deflection as well as their dynamic aeroelastic stability using coupled computational fluid dynamics (CFD) and nonlinear computational structural dynamics (NL-CSD) tools. Specifically, fluid-structure interaction (FSI) problems were solved computationally using the CFD solver Loci/CHEM and the NL-CSD solver Abaqus. As a part of the overall project, a similar capability was implemented using the CFD solver FUN3D coupled to Abaqus, although that work is documented in a separate report and that FSI framework was not used to analyze any of NASA’s SGF and SCF configurations. The technical approach consisted of solving for the flow field around the entire vehicle using a global CFD model, followed by extraction of relevant local subdomain data for CFD and NL-CSD co-simulations. The SGF design was analyzed using both 2D and 3D co-simulations to predict quasi-static aeroelastic deformations and to assess dynamic aeroelastic stability, whereas the SCF was analyzed in 2D only. SGF static aeroelastic response predictions focused on characterizing the deformed shape, with maximum displacements predicted to be on the order of magnitude of the technology element panel thickness. SGF dynamic aeroelastic response predictions used Partial Floquet analysis of the temporal evolution of selected nodal displacements to quantify the sign and magnitude of aeroelastic damping. Results suggest that the CRM-HL operating conditions would result in a dynamically stable response. The simulated dynamic pressure was also increased up to a factor of about four, and resulting responses suggest that predicted dynamic stability would be achieved with some margin.

Fluid Structure Interaction↗

Contracting Quality Early in the Lifecycle Using AS9145 Data Deliverables

Development schedules and a highly dynamic supply chain are a challenge to developers of complex systems produced at low volume. Flaws in designs, parts and materials availability problems, poor manufacturability, and a lack of knowledge about critical items and key process attributes can be realized well before traditional second-party quality assurance activities begin. Supplier audits and product inspections may have little mitigating effect once these foundational problems have been realized. Their impacts can be significant lifecycle disruption, cost overruns, inability to deliver to plan, and even project cancellation. AS9145, Requirements for Advanced Product Quality Planning and Production Part Approval Process, can be used to drive quality engineering practices into early development lifecycles to significantly reduce this late-cycle risk and to reduce the cost of quality overall. Since its initial publication in 2016, it has had very limited adoption by the DoD, no adoption by NASA, and sparse adoption in the aerospace and defense supply chain. A task group within the Aerospace Industries Association's (AIA) Joint Strategic Quality Council (JSQC) identified that both acquirers and suppliers see as AS9145 as a cost-adder and are hesitant to use it as an alternative to late-stage-heavy quality assurance approaches. A lack of prior use creates large capability gaps in request-for-proposal (RFP) teams, proposal teams, suppliers’ quality management systems (QMS), and in experienced personnel executing the early lifecycle approach. To create a more realizable on-ramp for using AS9145 in the space and defense sectors, the AIA JSQC task team created five deliverable requirements descriptions (DRDs) that can be used in a contract to begin to engage both parties in early lifecycle quality engineering and quality assurance activities, that reduce exposure to late-stage cost and schedule collapse due to unidentified risks in design, supply chain, and manufacturability. These DRDs drive the parties to engage in planning and analysis discussions early on to understand what production risks can be known and how they will focus resources based on safety criticality and the key elements of design and construction. The suppliers and acquirers who will produce the data and information required by the DRD will be able to incrementally evolve their QMS and the acquirer will incrementally be able to track and understand the benefits of cost shifting from late to early development phases. A white paper describing this approach and the five recommended DRDs will be published by the AIA in late 2024 or early 2025.

Jeannette Plante↗