低雷諾數近牆之等速度、等加速度固體球其流體力邊界效應之即時量測

Abstract

本論文以系統性實驗探討沉浸球體以等速及等加速運動垂直靠近牆面時所受之流體力，球體運動的雷諾數範圍介於0.21至3.33之間。將實驗球體連接小負載荷重元，球體運動以精密伺服馬達驅動，達成同步力量測。 我們首先驅動球體以等速度運動於水缸槽中心，完成擬穩態阻力(Quasi-Steady Drag)即時量測之校正工作。爾後將球體以相同的運動方式靠近下游水缸牆，水缸牆的存在將會改變流場的邊界條件，進而影響流體運動，使得球體所受流體總動力將有別於無牆時所受之流體總力，流體總力之差異即為牆面效應，以一修正係數表示。 針對擬穩態阻力量測所得之牆面修正係數介於兩種理論預測結果之間，其結果都將隨著球體與牆面間隙減少而單調遞增。當球體以等加速運動近牆時，牆面對於流體附加質量作用力(Added Mass Force)也將造成影響，其牆面修正係數可由勢流理論(Potential Flow Theory)推導而得，將流體總力扣除牆面修正後之擬穩態阻力以及修正流體附加質量作用力之結果，即為牆面修正流體歷史力(Basset History Force)。針對流體歷史力之牆面修正係數，我們擬合實驗結果可得到實驗公式，其結果隨間隙距離減小而單調遞增，隨加速度增加有飽和趨勢。

This thesis studies the hydrodynamic force on an immersed sphere approaching in normal direction toward a wall in constant velocity or constant acceleration motion by systematic experiments. The range of Reynolds number covers 0.21 to 3.33. A test sphere connected to a small capacity load cell was driven by a precision servo motor to achieve direct synchronized force measurement with sphere motion.

We firstly drove the sphere at constant velocities and accelerations near the center of a large tank for in-situ calibration and then drove the sphere at identical motion towards the wall. The downstream wall modifies flow boundary condition to result in hydrodynamic force different from the value found in infinite domain. The ratio between the forces with and without downstream wall quantifies the wall effect which is referred as the wall factor. The wall factor measured for quasi-steady force falls between the predictions from two theoretical models and grows monotonically with diminishing gap. Besides of this calibrated quasi-steady drag, wall effect on amplifying the added mass force when the sphere in constant acceleration towards wall was modeled by potential flow theory. These two force components, with respective wall factors, are then subtracted from the total unsteady hydrodynamic force to extrapolate wall-modified history force. An empirical formula was then fitted for the wall factor for history force, which shows dependences on gap and acceleration.