壁面蠕動具相位差之管道流場數值分析

Abstract

本研究利用非結構性移動網格和有限體積法去求解二維蠕動式管道流場，之後探討上/下管壁進行一蠕動波以不同相位差、雷諾數、振幅比、波數與背壓造成流場中平均流量的影響。再將數值方法結果與潤滑模型中理論解比較，即得知在小波數模擬計算之結果與理論解差異甚小。根據數值結果得知隨著相位差增加則平均流量會遞減，且在相位差為零有最大平均流量。在逆壓與順壓的情況下，由數值結果得知提高振幅比與波數皆可提高平均流量的輸出。再經數值結果發現在較小波數與背壓為零情況下，雷諾數對平均流量的影響幾乎無關，然而高波數的情形下平均流量隨著雷諾數增加；另外在固定背壓與振幅比的情形下，發現波數與平均流量之間有遞增的關係。並且從數值結果得知隨著背壓增加則平均流量減少，兩者之間呈線性遞減的關係。最後運用徑線圖配合著流線與速度分佈，觀察管道中流體的瞬時流場與質點運動情況，使本研究更加清楚蠕動式管道內流體運動的情形。

In this study, the two-dimensional peristaltic channel flow is solved by using the unstructured moving grid and the Finite Volume method. We then investigate the influence on the mean flow rate caused by the peristaltic waves in the upper/lower wall under different phase shift, Reynolds number, wave number, amplitude ratio and backpressure.Furthermore, when comparing the numerical results with the theory result of the lubrication model, we know their difference is very few when with smaller wave numbers. Based on the numerical results, we found that the average flow rate will decrease when the phase shift increasing, while the mean flow is maximized when the phase shift is at zero.Under the condition of adverse pressure and positive pressure, we can get the conclusion from the calculated results that the output of mean flow rate can be enhanced by increasing the amplitude ratio and the wave number. Furthermore, the Reynold number has little effect on mean flow rate under the low wave number and zero back pressure condition, but the mean flow rate will increase in line with Reynold number under high wave number condition.When fixing the backpressure and the amplitude ratio, the wave number has liner-increasing relation with the mean flow rate.Based on the numerical result, we further know that the mean flow rate has linear- decreasing relation with backpressure: mean flow rate will decrease when the backpressure increasing.Finally, by using streamline chart as well as pathline and velocity profile, we can observe the transient flow and particle motion in the channel and get a clearer picture of how fluid moves in the peristaltic channel.