PDF Publication Title:
Text from PDF Page: 108
Module Development Konstantinos G. Kyprianidis 2. The next simulation point(s) reuse the inverted Jacobian from the last, successfully converged, simulation point. 3. During the simulation of a given point, a Broyden update is performed on the inverted Jacobian after every iteration step as described in [158,159]. 4. The quality/accuracy of the inverted Jacobian deteriorates with every new simulation point; if the convergence rate drops below a certain thresh- old, the Jacobian matrix needs to be re-determined using a differentiation method in order to restore the convergence rate. 5. For consecutive simulation points whose solutions are too far from each other (i.e. for large jumps), the reused inverted Jacobian may no longer be sufficiently representative of the system. This can be detected by a slow convergence rate, numerical instabilities, and the function (model) report- ing calculation errors. In such a case, the iteration for the new simulation point is restarted from the original guess of the solution vector; the Jaco- bian matrix is re-determined on that particular solution vector guess using a differentiation method. A similar algorithm was investigated for steady state simulations during the development of the GeSTPAn code [23] but was never fully implemented because of convergence problems encountered when jumping between simulation points whose solutions are too far away from each other [156]. This important issue has been successfully resolved in the proposed algorithm through step 5. Although quasi-Newton methods and the modified algorithm proposed offer im- proved computational speed, it should be kept in mind that cheap approxima- tions to the inverted Jacobian may sometimes introduce deteriorated numerical stability as a trade-off. As a countermeasure, backtracking needs also be em- ployed (i.e. line search) to improve convergence (as discussed in [23,152]) when either: • The function residual did not actually decrease when the full Newton step was taken. • And/or the function (i.e. one of the engine component models) reported calculation errors. 68PDF Image | Multi-disciplinary conceptual design of future jet engine systems
PDF Search Title:
Multi-disciplinary conceptual design of future jet engine systemsOriginal File Name Searched:
thesis-future-jet-engines.pdfDIY PDF Search: Google It | Yahoo | Bing
NFT (Non Fungible Token): Buy our tech, design, development or system NFT and become part of our tech NFT network... More Info
IT XR Project Redstone NFT Available for Sale: NFT for high tech turbine design with one part 3D printed counter-rotating energy turbine. Be part of the future with this NFT. Can be bought and sold but only one design NFT exists. Royalties go to the developer (Infinity) to keep enhancing design and applications... More Info
Infinity Turbine IT XR Project Redstone Design: NFT for sale... NFT for high tech turbine design with one part 3D printed counter-rotating energy turbine. Includes all rights to this turbine design, including license for Fluid Handling Block I and II for the turbine assembly and housing. The NFT includes the blueprints (cad/cam), revenue streams, and all future development of the IT XR Project Redstone... More Info
Infinity Turbine ROT Radial Outflow Turbine 24 Design and Worldwide Rights: NFT for sale... NFT for the ROT 24 energy turbine. Be part of the future with this NFT. This design can be bought and sold but only one design NFT exists. You may manufacture the unit, or get the revenues from its sale from Infinity Turbine. Royalties go to the developer (Infinity) to keep enhancing design and applications... More Info
Infinity Supercritical CO2 10 Liter Extractor Design and Worldwide Rights: The Infinity Supercritical 10L CO2 extractor is for botanical oil extraction, which is rich in terpenes and can produce shelf ready full spectrum oil. With over 5 years of development, this industry leader mature extractor machine has been sold since 2015 and is part of many profitable businesses. The process can also be used for electrowinning, e-waste recycling, and lithium battery recycling, gold mining electronic wastes, precious metals. CO2 can also be used in a reverse fuel cell with nafion to make a gas-to-liquids fuel, such as methanol, ethanol and butanol or ethylene. Supercritical CO2 has also been used for treating nafion to make it more effective catalyst. This NFT is for the purchase of worldwide rights which includes the design. More Info
NFT (Non Fungible Token): Buy our tech, design, development or system NFT and become part of our tech NFT network... More Info
Infinity Turbine Products: Special for this month, any plans are $10,000 for complete Cad/Cam blueprints. License is for one build. Try before you buy a production license. May pay by Bitcoin or other Crypto. Products Page... More Info
| CONTACT TEL: 608-238-6001 Email: greg@infinityturbine.com | RSS | AMP |