本文的目的在以數值方法探討黏性及葉頂間隙效應對聲波激擾穿音速壓縮機轉子(NASA Rotor 67)流場之影響。首先，發展一個可以解析震波及聲波特性之高準確度氣動聲學Navier-Stokes 解子，使用的方法為改良式Osher-Chakravarthy MUSCL形式高解析度總變量縮減(Total Variation Diminishing)算則，時間積分則採用隱式ALU (Approximate Lower/Upper Factorization)，並採用高斯積分法計算黏性速度梯度及代數式紊流模型。本文同時以數值模擬理想化的非黏性無葉頂間隙及實際的黏性有葉頂間隙的轉子流場並比較之，兩者在震波位置及氣動力參數表現上皆相異。葉頂間隙的存在將導致洩漏渦流和逆流的發生，使有效流道縮減，洩漏渦流和流道中震波的交互作用致使震波發生偏折的現象，並在兩者交互作用區後產生一相對低速區。比較非黏性擬定常流及非定常流模擬結果發現，在低頻聲源激擾的狀況下，兩者結果相近，因此為節省計算時間，本文以擬定常流假設模擬黏性聲波激擾流場。比較非黏性無葉頂間隙及黏性有葉頂間隙的聲波激擾結果發現，後者的聲波激擾氣動力改變效率遠高於前者；探究流場內部變化發現，氣動力的改變主要是源於震波因聲波激擾而發生的移動現象。黏性流場因邊界層的存在，震波根部強度不如非黏性流場，較易受聲波激擾而移動，產生較大的空氣動力改變。比較不同激擾位置的結果發現，流場改變的趨勢定性上是相同的，在吹出相位(Blowing Phase)均造成震波和主要洩漏渦流前移，逆流區域增加；吸入相位(Suction Phase)則造成震波和主要洩漏渦流後移，逆流區域減少。本研究證實聲波激擾法在實際的穿音速壓縮機轉子流場上的應用，其結果比理想化的情況更為可行。

The purpose of the present study is to investigate the viscous and tip clearance effects on the transonic rotor 67 under acoustic excitations. A high-resolution aeroacoustic Navier-Stokes flow solver that can capture shock wave and resolve acoustic waves was first developed and validated. This numerical procedure employs the modified Osher-Chakravarthy upwind MUSCL type Total Variation Diminishing (TVD) scheme for acoustic and discontinuity capturing. Time-accuracy is accomplished by using implicit Approximate Lower/Upper Factorization (ALU) together with Newton subiterations. Sound source modeling, characteristic farfiled and inflow/outflow boundary condition treatments were carefully implemented to result in an accurate aeroacoustic solver. Algebraic turbulent model was employed. Comparing the results of Euler simulation without tip clearance and Navier-Stokes simulation with tip clearance, significant discrepancy in shock position and airloads was observed. The viscous simulation results indicate that the tip leakage flow forms a well-defined vortex emanating from the blade tip leading edge, which moves toward the pressure side of the blade passage. A distortion of the passage shock was seen arising from the interaction between leakage vortex and shock. Large pressure rise behind the shock causes a substantial diffusion of the vortex, resulting in a region of low speed zone occurring behind the interaction spot as well as a high blockage found in the blade passage. For low-frequency acoustic excitation, the results of inviscid quasi-steady and inviscid unsteady simulations are similar. In order to render the viscous simulation be realized within a tolerable time frame, quasi-steady approximation for the Navier-Stokes simulations was adopted. It was found in the acoustically excited flows that the change of airloads of the Navier-Stokes simulation, which is caused mainly by the shock excursion, is greater than that of the Euler simulation. Shock root structure is in general weaker in viscous flow owing to the presence of boundary layers, which causes shock in viscous flow be easier to move by acoustic excitation. The present excited flow field is not sensitive to the forcing locations. In general, both shock and primary vortex move upstream in the blowing phase and move downstream in suction phase. The effectiveness of acoustic excitation was shown to be more prominent in the viscous simulation, implying that the feasibility of acoustic excitation is much more possible than that was predicted in the inviscid analysis.

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