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At least 343 records · Page 19

Adaptive PV Frequency Control Strategy Based on Real-time Inertia Estimation

The declining cost of solar Photovoltaics (PV) generation is driving its worldwide deployment. As conventional generation with large rotating masses is being replaced by renewable energy such as PV, the power system’s inertia will be affected. As a result, the system’s frequency may vary more dramatically in the case of a disturbance, and the frequency nadir may be low enough to trigger protection relays such as under-frequency load shedding. The existing frequency-watt function mandated in power inverters cannot provide grid frequency support in a loss-of-generation event, as PV plants usually do not have power reserves. Here, a novel adaptive PV frequency control strategy is proposed to reserve the minimum power required for grid frequency support. A machine learning model is trained to predict system frequency response under varying system conditions, and an adaptive allocation of PV headroom reserves is made based on the machine learning model as well as real-time system conditions including inertia. Case studies show the proposed control method meets the frequency nadir requirements using minimal power reserves compared to a fixed headroom control approach.

14 SOLAR ENERGY↗

California Price Response Potential Study

California's energy landscape is undergoing a significant transformation, driven by the increasing integration of renewable energy sources, the increased adoption of distributed energy resources, the electrification of end-use loads, and the growing need for grid efficiency. To address these challenges, recent revisions to the State’s Load Management Standards (LMS) require all of California’s large utilities and community choice aggregators (CCAs) to offer dynamic electricity pricing options to customers by 2027. Dynamic pricing, which involves varying electricity rates based on real-time supply and demand conditions, offers a promising solution for optimizing grid operations, reducing costs, and incentivizing efficient use of grid capacity. Effective implementation of dynamic pricing requires understanding the potential impacts on customer bills, system load, and the cost-effectiveness of automation technologies. This study aims to evaluate the load response of various end-use devices to hourly dynamic prices. The end-uses studied here are space cooling, space heating, water heating, crop irrigation, pool and spa pumps, and electric vehicle (EV) charging, all for both residential and commercial applications, except for crop irrigation. In 2030, these end uses are forecasted to account for 18% of annual electricity demand in the state, but 40% of demand in the peak net load hour. By modeling possible price-responsive load dispatch algorithms and assessing the resulting impacts on both individual bills and the overall grid, we seek to inform policymakers and utilities about the potential benefits and challenges associated with dynamic pricing, and considerations for the design of dynamic pricing tariffs. Additionally, we will explore the cost effectiveness of adopting automation technologies to enable devices to respond more effectively to real-time price signals. This study considers a range of price profiles, accounting for differences across utilities and customer classes, and presents scenarios for dynamic price design via variation in the percentage of total customer electric costs that are allocated dynamically (versus constituting a fixed portion of the hourly volumetric price). We present results focused primarily on 2030, forecasting electricity prices under both low and high-cost scenarios, to inform longer-term tariff design considerations. We design tariffs by starting with 2019 prices that were calculated according to CalFUSE guidance (CPUC, 2022) and that have been used in recent studies; these prices are all-in volumetric rates that vary by utility and are revenue-neutral to each customer class. They are developed by considering six electricity cost components that are allocated hourly based on system load indicators (gross and net load, and wholesale prices). These prices are forecasted to 2030 for low and high cost scenarios, considering recent trends in total electricity costs with and without years of substantial wildfire mitigation investments. These tariffs, which allocate all costs on an hourly basis, are considered our “Full” dynamic tariff design scenario, while two additional scenarios explore allocating a portion of costs as a flat volumetric charge: the “Medium” scenario allocates 50% of revenue dynamically (and keeps 50% flat), while the “Mild” scenario allocates 20% of revenue dynamically. The 20% dynamic allocation on the Mild scenario aims to represent a case where only the marginal operating costs of the grid are included in the dynamic price.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

A Consistent Representation of Cloud Overlap and Cloud Subgrid Vertical Heterogeneity

Many global climate models underestimate the cloud cover and overestimate the cloud albedo, especially for low-level clouds. We determine how a correct representation of the vertical structure of clouds can fix part of this bias. We use the 1D McICA framework and focus on low-level clouds. Using Large Eddy Simulations results as reference, we propose a method based on exponential-random overlap that represents the cloud overlap between layers and the subgrid cloud properties over several vertical scales, with a single value of the overlap parameter. Starting from a coarse vertical grid, representative of atmospheric models, this algorithm is used to generate the vertical profile of the cloud fraction with a finer vertical resolution, or to generate it on the coarse grid but with subgrid heterogeneity and cloud overlap that ensures a correct cloud cover. Doing so we find decorrelation lengths are dependent on the vertical resolution, except if the vertical subgrid heterogeneity and interlayer overlap are taken into account coherently. We confirm that the frequently used maximum-random overlap leads to a significant error by underestimating the low-level cloud cover with a relative error of about 50%, that can lead to an error of SW cloud albedo as big as 70%. Not taking into account the subgrid vertical heterogeneity of clouds can cause a relative error of 20% in brightness, assuming the cloud cover is correct.

54 ENVIRONMENTAL SCIENCES↗

A comparative study of the parabolized Navier-Stokes code using various grid-generation techniques

The parabolized Navier-Stokes (PNS) equations are used to calculate the flow-field characteristics about the hypersonic research aircraft X-24C. A comparison of the results obtained using elliptic, hyperbolic and algebraic grid generators is presented. The outer bow shock is treated as a sharp discontinuity, and the discontinuities within the shock layer are captured. Surface pressures and heat-transfer results at angles of attack of 6 deg and 20 deg, obtained using the three grid generators, are compared. The PNS equations are marched downstream over the body in both Cartesian and cylindrical base coordinate systems, and the results are compared. A robust marching procedure is demonstrated by successfully using large marching-step sizes with the implicit shock fitting procedure. A correlation is found between the marching-step size, Reynolds number and the angle of attack at fixed values of smoothing and stability coefficients for the marching scheme.

Kaul, U. K.↗

The System Modeling and Analysis of Resiliency in STEReO (SMARt-STEReO)

Wildfire emergency response has remained rooted in relatively low-tech solutions for coordination between ground and aerial assets. These low-tech solutions are robust for the remote environments in which wildfires are usually fought, but limit strategic cross-organizational support and the ability to deploy and effectively utilize aerial assets. As aircraft become more advanced and new technology, including drones, become available to firefighters, a new, more modern method of asset coordination is needed. NASA is working on a project called ‘Scalable Traffic Management for Emergency Response Operations’ (STEReO) to integrate unmanned aerial systems (UAS)and UAS traffic management (UTM)into wildfire response. STEReO’s goals include simplifying the coordination of aerial assets, improving the existing UAS framework, and increasing the role of additional autonomous systems to reduce human risk and to increase system resilience. This paper describes the development of the ‘System Modeling and Analysis of Resiliency in STEReO’ (SMARt-STEReO) project, which aims to model wildfire response and to quantify the additional system resilience that STEReO technology provides firefighters. This paper verifies SMARt-STEReO and defines its scope; it includes experimental and statistical analysis of the impact that the addition of UAS has on both performance metrics and also on performance resiliency response to a given fault. SMARt-STEReO is a grid-based model of fire propagation that incorporates varying crew responses. Through the use of a Python package called ‘fmdtools’, the model easily allows for the addition of faults to the system. These faults allow analysts to investigate various response parameters. Factors including terrain, fuel type and wind speed can be modified to affect the fire propagation; additionally, the number of ground crews, engines, fixed wing aircraft, helicopters, and UAS can be changed to affect the crew response. The communication lines between actors mimic those used in real life situations. This paper explains the development of SMARt-STEReO including background research, verification and validation, and preliminary experimental analysis of system resilience to both a minor and major fault in systems with and without UAS.

Resiliency↗

Integrated Optimization and Control of a Hybrid Gas Turbine/sCO 2 Power System

During phase-I, the project team led by Echogen Power Systems (EPS) had two primary objectives based on investigating the application of gas turbines with supercritical carbon dioxide (sCO 2 ) power cycles. The first objective was to improve the overall efficiency and performance of a hybrid gas turbine/sCO 2 power system through a joint optimization of the two subsystems (gas turbine and sCO 2 power cycle) using non-linear optimization techniques that simultaneously evaluate thermal performance of the combined cycle. The hybrid power system included several points of interaction, including (but not limited to) gas turbine exhaust, fuel heating, inlet chilling and turbine cooling. The second objective was to establish a baseline transient response model of the hybrid power system and a notional microgrid and begin steps to integrate the control systems of the three major elements (gas turbine, sCO 2 cycle and grid controller). The project team established a baseline performance for a combined cycle power plant using a production gas turbine and scaled sCO 2 power cycle only utilizing exhaust heat recovery. Echogen’s non-linear techno-economic optimization code was extended by adding gas turbine component models derived from a in-house developed gas turbine design code. With the two cycles coupled by the gas turbine exhaust, design parameters of both cycles were allowed to vary simultaneously to determine performance opportunity versus isolated designs. Returning to the baseline gas turbine/sCO 2 power cycle transient models: Echogen had in-house developed sCO 2 cycle transient model in GT-Suite system simulation software, and had partnered with Siemens Finspång for gas turbine transient model, and Siemens PTI group to provide micro-grid load profile as well as hybrid power cycle generated load (power and frequency) analysis. The transient model for the SGT-750 Siemens gas turbine was a “black-box” functional mock-up interface (FMI) model developed by Siemens Industrial Turbomachinery in Finspång, Sweden. The SGT-750 is a twin-shaft gas turbine that produces 40 MW electricity with an efficiency of about 40% at ISO conditions. At 100% gas turbine throttle (load), the SGT-750 has average exhaust conditions of 114.6 kg/s and 469.8°C. The transient model for sCO 2 power cycle was developed by Echogen in GT-SUITE 1D system simulation software platform. The basic CO 2 flow circuit has single-shaft turbomachinery with net 11.5 MW electrical power output at design conditions. The power turbine has a double-ended shaft with one end connected to synchronous generator through a fixed-ratio gearbox. The other end of power turbine is connected to the compressor through a continuously variable transmission. The major components of the sCO 2 power cycle modeled include air cooled condenser/cooler, CO 2 compressor, recuperator, two waste heat exchanger coils, power turbine, continuous variable transmission, gearbox and generator. Integration of SGT-750 transient model and sCO 2 power cycle transient model was done in Matlab Simulink. In the integrated model, the gas turbine and sCO 2 power cycle interacted at two points, first one being the gas turbine exhaust gas flow rate and temperature, which were inputs to sCO 2 power cycle model. The second point was the distribution of micro-grid load demand signal between the SGT-750 generator and sCO 2 cycle generator. For a given combined-cycle load demand, the gas turbine load demand was equal to the total demand minus the sCO 2 cycle power generated. In the present study the integrated model was simulated for two cases of grid load demand: (i) for a step change, both positive-step and negative-step, in grid load demand (ii) for a micro-grid load demand curve provided by Siemens PTI group. Finally, the time series plots representing load demand versus integrated system response were presented including the sCO 2 power cycle control system performance plots. The actual generated power and frequency of both the generators, gas turbine and sCO 2 power cycle, was supplied to Siemens PTI group for dynamic grid assessment, results of which are provided in appendices.

03 NATURAL GAS↗

Coarse grained simulation of convectively driven turbulent mixing, transition, and turbulence decay

Accurate predictions with quantifiable uncertainties are essential to many practical turbulent flow applications exhibiting extreme geometrical complexity and broad ranges of length and time scales. Under-resolved computer simulations are typically unavoidable in such applications, and implicit large-eddy simulation (ILES) often becomes the effective strategy. In this work, we focus on assessing ILES initialized with well-characterized 25 6 3 homogeneous isotropic turbulence datasets generated with direct numerical simulation (DNS). ILES solutions based on the LANL xRAGE code are studied as function of resolution for 6 4 3 , 12 8 3 , 25 6 3 , and 51 2 3 grids. ILES performance of new directionally-unsplit high-order numerical hydrodynamics algorithms in xRAGE is examined in this context. Compared to the initial 25 6 3 DNS, we find longer inertial subranges and higher turbulence Reynolds number (Re) for 25 6 3 and 51 2 3 xRAGE — attributed to having linked DNS (Navier–Stokes based) solutions to nominally inviscid (higher Re) Euler based ILES solutions. For fixed 25 6 3 resolution, we find that significantly larger simulated turbulence Re can be achieved with the higher-order unsplit (vs. split) discretizations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Overcoming obstacles to IPv6 on WLCG

The transition of the Worldwide Large Hadron Collider Computing Grid (WLCG) storage services to dual-stack IPv6/IPv4 is almost complete; all Tier-1 and 94% of Tier-2 storage are IPv6 enabled. While most data transfers now use IPv6, a significant number of IPv4 transfers still occur even when both endpoints support IPv6. This paper presents the ongoing efforts of the HEPiX IPv6 working group to steer WLCG toward IPv6-only services by investigating and fixing the obstacles to the use of IPv6 and identifying cases where IPv4 is used when IPv6 is available. Removing IPv4 use is essential for the long-term agreed goal of IPv6-only access to resources within WLCG, thus eliminating the complexity and security concerns associated with dual-stack services. We present our achievements and ongoing challenges as we navigate the final stages of the transition from IPv4 to IPv6 within WLCG.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Long-Duration High-Resolution Large-Eddy Simulations of Hurricane Laura (2020) for Infrastructure Design

This dataset provides long-duration large-eddy simulations (LES) of Hurricane Laura (2020), capturing the turbulent boundary-layer wind field during the storm's passage at horizontal grid spacings of 55.55 m and 10 m. Hurricane Laura made landfall as a Category 4 storm in southwestern Louisiana at 06:00 UTC on 27 August 2020, producing widespread damage to coastal infrastructure. The simulations characterize the spatial and temporal variability of the turbulent wind at heights spanning the lowest 300 m of the boundary layer, throughout the approach and passage of the storm's eyewall over a fixed location. To resolve the spatial heterogeneity of wind and turbulence conditions across the storm, seven independent refined LES runs are performed at radial locations spanning the storm relative to its direction of motion. The refinement positions are defined on a normalized radial coordinate r ̂=r/R, where R≈21 km is Laura's radius of maximum wind, and lie between r ̂=-1.5 and r ̂=+1.5 in ∆r ̂=0.5 increments along a line perpendicular to the storm's track at the midpoint of the simulation. Negative r ̂ corresponds to locations south-southwest of the storm center and positive r ̂ to locations north-northeast. The dataset is segmented into seven radial refinement groups.

17 WIND ENERGY↗

Computational investigation of slot blowing for fuselage forebody flow control

This paper presents a computational investigation of a tangential slot blowing concept for generating lateral control forces on an aircraft fuselage forebody. The effects of varying both the jet width and jet exit velocity for a fixed location slot are analyzed. This work is aimed at aiding researchers in designing future experimental and computational models of tangential slot blowing. The primary influence on the resulting side force of the forebody is seen to be the jet mass flow rate. This influence is sensitive to different combinations of slot widths and jet velocities over the range of variables considered. Both an actuator plane and an overset grid technique are used to model the tangential slot. The overset method successfully resolves the details of the actual slot geometry, extending the generality of the numerical method. The actuator plane concept predicts side forces similar to those produced by resolving the actual slot geometry.

Murman, Scott M.↗

Temporal Coarse Graining for Classical Stochastic Noise in Quantum Systems

Simulations of quantum systems with Hamiltonian classical stochastic noise can be challenging when the noise exhibits temporal correlations over a multitude of time scales, such as for 1/f noise in solid-state quantum information processors. Here we present an approach for simulating Hamiltonian classical stochastic noise that performs temporal coarse-graining by effectively integrating out the high-frequency components of the noise. We focus on the case where the stochastic noise can be expressed as a sum of Ornstein-Uhlenbeck processes. Temporal coarse-graining is then achieved by conditioning the stochastic process on a coarse realization of the noise, expressing the conditioned stochastic process in terms of a sum of smooth, deterministic functions and bridge processes with boundaries fixed at zero, and performing the ensemble average over the bridge processes. For Ornstein-Uhlenbeck processes, the deterministic components capture all dependence on the coarse realization, and the stochastic bridge processes are not only independent but taken from the same distribution with correlators that can be expressed analytically, allowing the associated noise propagators to be precomputed once for all simulations. This combination of noise trajectories on a coarse time grid and ensemble averaging over bridge processes has practical advantages, such as a simple concatenation rule, that we highlight with numerical examples.

Albash, Tameem [Sandia National Lab. (SNL-NM), Alb↗

Innovating the next generation of commercial smart building software

Nearly 30% of commercial building energy use is wasted due to equipment faults and HVAC controls problems. The result is increased emissions, compromised comfort and productivity, and less reliable coordination of building power needs with a clean grid. The energy impact alone represents $17 billion in potential savings. Today’s smart building software provides a robust solution to address these operational deficiencies. Energy management and information systems (EMIS) are saving up to 9% on average, with two-year paybacks. They are being incorporated into energy management processes, commissioning services, and utility programs. As effective as they are, two barriers prevent even deeper benefits; limited personnel to fix problems once they are identified, and the expense and time to manually implement changes in control systems. In partnership with the research community, the EMIS industry is developing new capabilities to overcome these barriers. Moving beyond siloed products for either fault detection and diagnostics, or optimal control, these new capabilities empower users to not only automatically identify faults, but also to push corrective action, and control improvements to their buildings. In this paper, several areas for enhancements are documented: ‘one-time’ correction of faults such as setpoints, schedules, and economizer lockouts; short-term active testing for automated proportional integral derivative (PID) loop tuning and functional testing; and continuous supervisory control for demand flexibility and year-round efficiency. Results are presented from a pair of partner implementations out of a dozen providers integrating these enhancements into their products, including field tests from across the country, and insights into operator acceptance and integration into operations and maintenance practices.

Casillas, Armando↗

Climate change-resilient snowpack estimation in the Western United States

Abstract In the 21st century, warmer temperatures and changing atmospheric circulation will likely produce unprecedented changes in Western United States snowfall 1–3 , with impacts on the timing, amount, and spatial patterns of snowpack 4–7 . The ~900 snow pillow stations are indispensable to water resource management by measuring snow-water equivalent (SWE) 8,9 in strategic but fixed locations 10,11 . However, this network may not be impacted by climate change in the same way as the surrounding area 12 and thus fail to accurately represent unmeasured locations; climate change thereby threatens our ability to measure the effects of climate change on snow. In this work, we show that maintaining the current peak SWE estimation skill is nonetheless possible. We find that explicitly including spatial correlations—either from gridded observations or learned by the model—improves skill at predicting distributed snowpack from sparse observations by 184%. Existing artificial intelligence methods can be useful tools to harness the many available sources of snowpack information to estimate snowpack in a nonstationary climate.

54 ENVIRONMENTAL SCIENCES↗

Communication training for aircrews: A review of theoretical and pragmatic aspects of training program design

This study is the final report of a project studying methods of communications training applicable to both civilian and military aviation personnel, including multiperson teams or single pilot fixed wing or rotary wing aircraft. A review is provided of a number of theories proposed as relevant for producing training materials for improved communications. Criteria are given for evaluating the applicability of training programs to the aviation environment, and these criteria are applied to United Airlines' Resources Management Training, as well as to a number of commercially available general purpose training programs. The report considers in detail assertiveness training and grid management training, examining their theoretical background and attempts made to validate their effectiveness. It was found that there are substantive difficulties in assessing the effectiveness of both training programs, as well as problems with the theories underlying them. However, because the aviation environment offers unique advantages for studying the effectiveness of communications training, recommendations are made on the design of appropriate training programs and on procedures that might be used to validate them.

Linde, Charlotte↗

Proceedings of the 2004 NASA/ONR Circulation Control Workshop, Part 2

This conference proceeding is comprised of papers that were presented at the NASA/ONR Circulation Control Workshop held 16-17 March 2004 at the Radisson-Hampton in Hampton, VA. Over two full days, 30 papers and 4 posters were presented with 110 scientists and engineers in attendance, representing 3 countries. As technological advances influence the efficiency and effectiveness of aerodynamic and hydrodynamic applications, designs, and operations, this workshop was intended to address the technologies, systems, challenges and successes specific to Coanda driven circulation control in aerodynamics and hydrodynamics. A major goal of this workshop was to determine the state-of-the-art in circulation control and to assess the future directions and applications for circulation control. The 2004 workshop addressed applications, experiments, computations, and theories related to circulation control, emphasizing fundamental physics, systems analysis, and applied research. The workshop consisted of single session oral presentations, posters, and written papers that are documented in this unclassified conference proceeding. The format of this written proceeding follows the agenda of the workshop. Each paper is followed with the presentation given at the workshop. the editors compiled brief summaries for each effort that is at the end of this proceeding. These summaries include the paper, oral presentation, and questions or comments that occurred during the workshop. The 2004 Circulation Control Workshop focused on applications including Naval vehicles (Surface and Underwater vehicles), Fixed Wing Aviation (general aviation, commercial, cargo, and business aircraft); V/STOL platforms (helicopters, military aircraft, tilt rotors); propulsion systems (propellers, jet engines, gas turbines), and ground vehicles (automotive, trucks, and other); wind turbines, and other nontraditional applications (e.g., vacuum cleaner, ceiling fan). As part of the CFD focus area of the 2004 CC Workshop, CFD practitioners were invited to compute a two-dimensional benchmark problem for which geometry, flow conditions, grids, and experimental data were available before the workshop. The purpose was to accumulate a database of simulations for a single problem using a range of CFD codes, turbulence models, and grid strategies so as to expand knowledge of model performance/requirements and guide simulation of practical CC configurations.

Jones, Gregory S.↗

The GGCMI Phase 2 emulators: global gridded crop model responses to changes in CO 2 , temperature, water, and nitrogen (version 1.0)

Statistical emulation allows combining advantageous features of statistical and process-based crop models for understanding the effects of future climate changes on crop yields. We describe here the development of emulators for nine process-based crop models and five crops using output from the Global Gridded Model Intercomparison Project (GGCMI) Phase 2. The GGCMI Phase 2 experiment is designed with the explicit goal of producing a structured training dataset for emulator development that samples across four dimensions relevant to crop yields: atmospheric carbon dioxide (CO2) concentrations, temperature, water supply, and nitrogen inputs (CTWN). Simulations are run under two different adaptation assumptions: that growing seasons shorten in warmer climates, and that cultivar choice allows growing seasons to remain fixed. The dataset allows emulating the climatological-mean yield response of all models with a simple polynomial in mean growing-season values. Climatological-mean yields are a central metric in climate change impact analysis; we show here that they can be captured without relying on interannual variations. In general, emulation errors are negligible relative to differences across crop models or even across climate model scenarios; errors become significant only in some marginal lands where crops are not currently grown. We demonstrate that the resulting GGCMI emulators can reproduce yields under realistic future climate simulations, even though the GGCMI Phase 2 dataset is constructed with uniform CTWN offsets, suggesting that the effects of changes in temperature and precipitation distributions are small relative to those of changing means. The resulting emulators therefore capture relevant crop model responses in a lightweight, computationally tractable form, providing a tool that can facilitate model comparison, diagnosis of interacting factors affecting yields, and integrated assessment of climate impacts.

54 ENVIRONMENTAL SCIENCES↗

The GGCMI Phase 2 emulators: global gridded crop model responses to changes in CO2, temperature, water, and nitrogen (version 1.0)

Statistical emulation allows combining advantageous features of statistical and process-based crop models for understanding the effects of future climate changes on crop yields. We describe here the development of emulators for nine process-based crop models and five crops using output from the Global Gridded Model Intercomparison Project (GGCMI) Phase 2. The GGCMI Phase 2 experiment is designed with the explicit goal of producing a structured training dataset for emulator development that samples across four dimensions relevant to crop yields: atmospheric carbon dioxide (CO2) concentrations, temperature, water supply, and nitrogen inputs (CTWN). Simulations are run under two different adaptation assumptions: that growing seasons shorten in warmer climates, and that cultivar choice allows growing seasons to remain fixed. The dataset allows emulating the climatological-mean yield response of all models with a simple polynomial in mean growing-season values. Climatological-mean yields are a central metric in climate change impact analysis; we show here that they can be captured without relying on interannual variations. In general, emulation errors are negligible relative to differences across crop models or even across climate model scenarios; errors become significant only in some marginal lands where crops are not currently grown. We demonstrate that the resulting GGCMI emulators can reproduce yields under realistic future climate simulations, even though the GGCMI Phase 2 dataset is constructed with uniform CTWN offsets, suggesting that the effects of changes in temperature and precipitation distributions are small relative to those of changing means. The resulting emulators therefore capture relevant crop model responses in a lightweight, computationally tractable form, providing a tool that can facilitate model comparison, diagnosis of interacting factors affecting yields, and integrated assessment of climate impacts.

James A Franke↗