本篇論文探討震波與爆震波在小尺寸導管內的傳播。數值上用具有三階及五階準確度的加權基本無振盪法的尤拉及涅維爾-史托克斯(Navier-Stokes equations) 解子來探討這個問題。文中所使用的解子經由震波管、范諾線流（Fanno-line flow）和雷利線流（Rayleigh-line flow）等問題驗證了正確性。為了要了解爆震波在多介質中的傳播，本研究分為三個部分。第一部分：關心震波及爆震波在微小尺寸導管內以空氣及水為工作介質時如何傳播、以及衰減的問題。研究之內容則以四種一維流動模式來探討。模式一：模擬絕熱壁的一維無黏性 (inviscid-flow) 導管流，用來當作其它模式流動比較的參考基準。模式二：模擬有磨擦壁面效應(frictional effect) 的一維導管流，用來當作模式三的檢驗參考。模式三：導管壁面無擴散效應的可壓縮性的涅維爾-史托克斯方程式 (Navier-Stokes equations) 來模擬一維導管流。模式四：導管壁面有擴散效應的可壓縮性的涅維爾-史托克斯方程式來模擬一維導管流。以上結果發現：在小尺寸的空氣流管內，黏性與擴散效應對震波或爆震波前的速度有相當大的影響。小尺寸的水流管內，黏性與擴散效應對弱震波或爆震波前的速度亦有不可忽略的影響。
部分二探討在兩種介質中，爆震波經過不同介質介面時、介面產生反射波的現象。本文選用的四種模擬介質，依序為類似人體組織的肌肉、腎、骨髓及脂肪。由於進入介質的爆震波強度非常弱，用聲波反射原理來驗證計算的反射波之物理性質，吾人發現結果非常吻合。
部分三探討了在帶有血塊小尺寸管之中，爆震波在考慮有黏性及壁擴散效應下，通過此種介質時，它的傳播、衰減及反射現象。結果發現，當起始爆震波位置固定，黏性與擴散效應對爆震波前的峰值壓力影響，與小管中血塊位置確切有關；也就是說，當血塊距離起始爆震波越遠，其峰值壓力就越弱。此外，本研究亦計算出爆震波通過血塊的峰值壓力與引發的脈衝。

In this study, a small multiple-medium duct with shock- or blast-wave propagation is considered and is numerically investigated by the Euler/Navier-Stokes solver with a 5th-order weighted essential non-oscillation scheme (WENO) except for special mention. Blast waves are generated by the rupture of two diaphragms of a high-pressure region located near the duct entrance. One blast wave produced will propagate downstream the duct. The developed solver is verified on a shock tube problem, a Fanno-line flow, and a Rayleigh-line flow.
In order to understand the blast-wave propagation through multiple media, the dissertation content is divided into three parts. The first part concerns with the propagation and attenuation of shock or blast waves in the small duct. The flow problem of interest is primarily modeled by four one-dimensional flow models. Model 1 is to simulate the duct flow using an inviscid-flow model with an adiabatic wall, which is used to a baseline. Model 2 is the simulation of the duct flow with frictional-wall effects, which is used for a check point for model 3. Model 3 simulates the duct flow using the compressible Navier-Stokes equations without the mass-diffusion effect. Model 4 simulates the duct flow using the compressible Navier-Stokes equations with the mass-diffusion effect. It is found in a small-scale airflow duct that the combination of viscous dissipation and mass diffusion has a significant effect on the shock-or blast-wave front velocity. In a small-scale water-flow duct, the combination of viscous dissipation and mass diffusion also has a non-negligible effect on weak shock-or blast-wave front velocity.
The reflection and transmission of blast wave through the interface of the media is investigated by using a 3rd-order WENO scheme in order to avoid numerical spurious oscillations for very weak shock waves. Part two is concerned with the physical phenomena of underwater blast wave propagating through two media without viscous and mass-diffusion effects for comparing with the acoustic principle of reflection and transmission. In addition to water, four kinds of material that have analogy to different tissues of human body are considered as a second medium and embedded in the water duct. Because the incident underwater blast wave is very weak, close to an acoustic wave, the computed peak pressures of transmitted blast wave front for four kinds of simulated tissues are in good agreements with those obtained by the acoustic principle.
In part three, we consider the propagation of blast-wave in a small-scale multiple-medium duct with a simulated clot under the condition of viscous and mass diffusion effects. The propagation, attenuation and reflection of the blast wave in inviscid- and viscous-flow models with mass diffusion effect are compared. It is found that the differences of the computed flow properties between these two flow models are considerably moderate. In addition, the pressure forces and the induced impulses by a moving blast wave at the clot interface are computed, which may be helpful for medical application.

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