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At first, the paper presents the formulation for computing numerically the linear unsteady aerodynamic forces on the vibrating annular cascade blades. The formulation is based on the finite volume method, the Riemann solver, and the TVD scheme, following UPACS code developed by NAL, Japan. By applying the TVD scheme to the linear unsteady calculations, the precise calculation of the peak of unsteady aerodynamic forces at the steady shock wave location without empirical constants becomes possible. The comparison of numerical results of the present numerical calculation is made with those of the double linearization theory, which is valid under the assumption of small unsteady disturbances and small steady disturbances but the steady disturbances are still larger than the unsteady disturbances, and requires far less computational resources than the present numerical calculation. Under the conditions of small steady disturbances, a good agreement between these two methods is observed, so that the two codes are cross-validated. Also the comparison reveals the limit of the double linearization theory., 資料番号: AA0032819016, レポート番号: NAL SP-53

航空宇宙技術研究所 24-26 Jun. 1998 東京 日本, National Aerospace Laboratory 24-26 Jun. 1998 Tokyo Japan, 振動する翼列の線形非定常空気力計算は、計算機資源をあまり使用しないことと、非線形で時間の厳密な計算に比較して実用的に有用なフラッタ解析であるために重要性が大きい。本論文では、空間的な数値的振動がない振動する翼列の線形非定常流れ場を解くために開発された、有限差分法と組み合わせたTVD(全変動減少)スキームを振動する超音速通過流ファン翼列翼に応用して成功した。例とした数値計算は、様々なパラメータに対する非定常空気力の依存性の一般的傾向を、数値解の発振がほとんど無く、効果的に予測することが示された。Lax-Wendroffと有限体積法で予測した空間的数値振動に伴う流れ場の急激な変化は、本計算においては急激でない変化として捕らえられた。, Linear unsteady aerodynamic calculation of vibrating cascade blades has a great importance due to the small usage of the computer resources and its utility in practical flutter analysis compared with the nonlinear and time accurate calculations. In the present paper, the TVD (Total Variation Diminishing) scheme combined with the finite difference method, which has been developed to solve the linear unsteady flow field of vibrating cascade blades without the spatial numerical oscillation, has been applied successfully to the vibrating supersonic through flow fan cascade blades. Numerical example calculations indicate that the present calculation well predicts the general trend of dependencies of the unsteady aerodynamic forces on various parameters, with little numerical oscillation in solutions. The steep changes in the flow field accompanied by the spatial numerical oscillation predicted by the Lax-Wendroff and the finite volume method are captured as less steep change in the present calculation., 資料番号: AA0001958023, レポート番号: NAL SP-41