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UNVEILING THE CRUCIAL ROLE OF IMPACT ENERGY LOSS FOR SO-CALLED INCOMPRESSIBLE FLUID FLOWS
impact energy loss
ABSTRACT Experiments show that pipe flows with large expansion angle and area ratio always accompany with significant amount of energy loss, actually energy loss ratios over 70﹪of incoming flow kinetic energy are commonplace. It is generally believed that all the energy loss is entirely due to viscous dissipation effect. In this dissertation, several interesting demonstrations have been given to prove the existence and import- ance of impact energy loss. In fact, the pipe expansion flow can be configured as high -speed flow ramming into low-speed flow and then moving together, this situation is similar to rope-lifting problem in system dynamics as illustrated herein as continuous inelastic impact process with unavoidable impact energy loss. Actually, in many cases impact energy loss plays a crucial role for so-called incompressible fluid flow, and viscosity is only playing the scapegoat for answering many absurdities. Virtually the intrinsic negligence of impact energy loss is the original major cause for many weird paradoxes and disaster solutions in fluid dynamics. Whereas, Euler equations derived in 1755 are among the most important equa- tions for general fluid dynamics analysis, in spite of their sparkling beauty, elegance, and sacrosanctity, it is well-known that fluid dynamics is a weird academic area full of peculiarities. In fact, the chastity of Euler and sibling Navier-Stokes equations has long been contaminated; for CFDers, ‘babysitting’ these governing equations by various ad hoc artificial measures has emerged as a fact of life for the state-of-the-art in an attempt to somehow manipulate a certain amount of disguised energy dissipation that is largely due to impact. In this sense, CFD is still very much an art than a science. Although Euler and associated equations are derived by momentum principle, yet no matter how surprisingly and sarcastically, they are not genuine momentum equations. Since a genuine momentum equation should be able to accommodate both cases either with or without energy loss, but Euler equations can only accommodate no-energy- loss cases. Pathologically, we have found that the intrinsic negligence of impact energy loss in deriving process renders the Euler equation as a non-genuine momen- tum equation which is hardly solvable. And, in turn it unveils the even more stunning role of impact energy loss as the triggering concept for a full-scale historical revolu- tion in FD/CFD as represented by Euler, Bernoulli, and Navier-Stokes equations. Then, should we blindly keep worshipping these non-genuine momentum equations forever? Insightfully, the culprit for this fatal non-genuineness as momentum equation is a seemingly innocent ‘artificial’ equalization of crosswise and streamwise fluid pressures by disregarding any possible energy loss in deriving processes. Sarcastically, while similar absurdities are not alone outside FD, this fatal error has survived the searching scrutiny of innumerable scholars for 249 years, this very fact sufficiently proves how slippery it is. Ironically, most dark-age endless troubles of ‘artificial’ viscosity/upwinding, and other ‘artificial’ measures in CFD can be originated from this catastrophic ‘artificial’ equalization in deriving Euler equation. Although this study induces a historical concept-revolution with tremendous and panoramic impact on past/future FD/CFD academia; yet its back-to-nature surgery of no surgery at all for curing the fatal Eulerian error by just relaxing the ‘artificial’ equalization and its associated judicious discussion on solution existence/uniqueness; are virtually sounding sort of ”空山松子落” 的 ”幽幽禪意”.
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