Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/2574
標題: 揭開衝擊能損對不可壓縮流場之重大效應
UNVEILING THE CRUCIAL ROLE OF IMPACT ENERGY LOSS FOR SO-CALLED INCOMPRESSIBLE FLUID FLOWS
作者: 江俊顯
Chiang, Jiunn-Shean
關鍵字: incompressible flow
不可壓流
impact energy loss
FD/CFD
衝擊能損
流體力學/計算流體力學
出版社: 機械工程學系
摘要: 摘要 實驗結果明白顯示管路流在大擴張角度與大擴面積比時總是伴隨著大量的能量損失,損失量大於入口動能的70﹪也是常見的現象。一般皆認為管路流能損皆是黏滯效應所造成的,然而本論文提出諸多例證說明衝擊能損存在的事實及重要性。事實上,擴管流可視為高速流追撞低速流而後一起運動,此種情況類似系統動力學的拉繩問題,可用完全非彈碰撞模型加以說明,其中必存在著重要而不可避免的能量損失。在許多實際狀況下衝擊能損於所謂不可壓縮流場中佔有著相當關鍵的地位,而流體黏滯性僅是扮演一個代罪羔羊的角色以勉強解釋許多流體力學中怪異而矛盾的現象。簡言之,不經意地忽略衝擊能損將造成許多流體力學中的悖論及奇特且不合理的解。 尤拉方程於1755年經尤拉導出之後,一直是流體力學分析中最重要的方程式之一,然而不論它如何廣受推崇及神聖不可侵犯,我們知道流體力學是一門奇特怪異的領域,存在著許許多多的悖論。實際上,尤拉方程及納維爾方程的完整性已經被質疑,對計算流體力學的學者而言,以各種特殊人為方法處理統御方程式成了一種先進的流行趨勢,而不知其結果多僅只是掩飾衝擊能損所造成的影響。此亦顯示計算流體力學本身仍有濃郁的藝術氣息而並非純科學。雖然尤拉及其相關公式是由牛頓運動定律推演而來,但是它並不是一個能包含能損情況的廣義的動量方程式,因為廣義的動量方程式必須同時可涵蓋有能損及無能損的情況。若深入觀察可知,傳統不經意地忽略衝擊能損的結果將導致並產生難以求解的非廣義的尤拉方程,因此衝擊能損的觀念將對流體力學及計算流體力學產生歷史性的重大影響。由更進一步探究發現,此一長年難以偵破之癥結是在於推導過程中不經意地做了看似合理 的人為等化假設,進而忽略了衝擊能損的效應,且於系統動力學中也曾出現類似的荒謬錯誤。 頗為諷刺地,計算流體力學中令人困擾的人工黏滯、上風法及許多人工方法皆起因於推導尤拉方程中做了看似合理的人為等化假設,導致得到非廣義的尤拉方程;其解決之道為清除此人為等化假設,並推得考慮衝擊能損效應,影響深遠且真正廣義的流體力學動量公式。本文對流力歷史性的重大理論問題近乎“無為”的解決之道與解的存在/唯一之機鋒論訴,也隱約散發出些許“空山松子落”的“幽幽禪意”。
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”.
URI: http://hdl.handle.net/11455/2574
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