When a rocket launches, it exhausts a plume (rocket plume) which is of the supersonic jet condition. A rocket plume emits very strong acoustic waves, especially low frequency ones, which may critically damage the pay-loads of the rocket such as artificial satellites because they are very light and fragile. Thus accurate prediction and reduction of the sound pressure level (SPL) of acoustic waves, especially low frequency ones, are important. In order to predict acoustic waves from the rocket plumes, a semi-empirical method based on experimental and launch data was proposed. However, it is known that there is a difference between an actual SPL and a predicted one. In addition, though these semi-empirical methods are based on many past data, mechanisms such as noise-emission, noise-directivity and noise-source have not been well-discussed due to the difficulties of handling the experimental or launch data.

Thus a new prediction method based on a more accurate model for the jet acoustic waves is needed. In order to build a new engineering model based on physics, it is necessary to obtain detailed information of the flow fields and acoustics fields. Therefore, the analyses on the acoustic waves, mainly Mach waves, which is dominant acoustics from the rocket plume, from a simple single supersonic free jets are needed for improving the prediction method. In this study, especially following three engineering issues are investigated. First, the verification of this non-dimensionalization for high Mach number supersonic jets is conducted. The effective non-dimensionalization for the prediction of the acoustic waves enables us to reduce the parameters. However, this normalization for the high Mach number supersonic jet is not verified. Second, the Mach number and the temperature effects are investigated. The past studies did not include fluid parameters strongly such as the Mach number and the temperature. However these parameters seem to have very strong effects on the acoustic characteristics. Third, the source characteristics of Mach waves are investigated, taking an advantage of a computational approach. The past studies were not able to clarify the source characteristics of Mach waves because of difficulty of experiment.

With regard to the numerical methods, in this study, the monotonically integrated large eddy simulation approach is conducted with the seventh order WCNS, the tenth order compact scheme and the third order TVD-RK schemes under the 10 million computational grid system.

For the prediction of acoustic waves from the rocket plume, the verification of the effective normalization which bases the ideally expanded Mach number and the design Mach number is conducted. In this study, this normalization is verified for three supersonic jets whose ideally expanded Mach number are 3.0 where the designed Mach number is set to be 3.0, 3.5 and 4.0. The SPL distribution and the spectrum of several points of these three cases show good agreements within the error of 2-3dB, especially two cases, design Mach number 3.0 and 3.5, shows an excellent agreement, while there are some differences probably due to the shock associated noises in the upstream side. Present results show that the fact reported by Tam for the relatively low Mach number supersonic jet is applicable to the higher Mach number supersonic jet. For the prediction of acoustic waves from the rocket plume, namely one of the purposes of this research, this result implies that rocket parameters can be reduced.

Then, the other parameters, (ideally expanded) Mach number effects and temperature effects are investigated. A Mach number effect on flow fields is found to be potential core becomes longer with increasing Mach number. Mach number effects on acoustics fields are as follows. As Mach number increases, 1) SPL becomes higher, 2) the near field directivity of the jet becomes wider, 3) the direction of maximum acoustic emissions becomes larger and 4) the peak Strouhal number slightly becomes lower. On the other hand, a temperature effect on flow-fields is found to be that potential core becomes shorter with increasing temperature. Temperature effects on acoustics fields are as follows. As temperature increases, 1) SPL becomes slightly higher, 2) the width of directivity do not seem to change so much in spite of the change of potential core-length, 3) the direction of maximum acoustic emission becomes larger and 4) the peak Strouhal number becomes lower.

Temperature effects on potential core length noted above, namely it becomes shorter with increasing temperature, is very strong. Resulting potential core length of hot jets corresponds to that guessed by the study in the past. In order to predict flow-fields of rocket plume, this point seems to be very important. In addition, with increasing Mach number and temperature, SPL becomes higher, while peak Strouhal number becomes lower. Specifically Mach number rather affects SPL than the peak Strouhal number whereas temperature rather affects the peak Strouhal number than SPL.

With regard to the analysis of source characteristics, focused array methods, correlation of velocity fluctuations and normalization of source spectrum are conducted.

First, the focused array method which is one of microphone array methods is applied to the computational flow-fields and the resulting source position of Mach waves are discussed.

In the result, Mach wave source region is inside of the environmental supersonic region which is defined the local velocity and the ambient sonic speed.

In addition, the lower frequency source is located at the downstream side and spreading compared with the higher frequency ones. Second, the supersonically convective velocities of the disturbances assumed as the Mach wave sources are computed. These convective velocities of disturbances are visualized with the vector whose direction denotes expected as the angle of Mach wave radiation and the absolute value denotes the strength of correlations. These vectors exist at the almost similar region which is calculated as the source region with the focused array methods. In addition, the direction of the vector seems to be the almost same as that of the strong acoustic wave emission observed in the overall or octave band SPL distributions. Third, normalization of the source frequency is discussed. This idea originates the study in the past. The original model shows the good collapse, but has no physical background. To construct a more reliable model, the simple physical model is proposed. As a result, the normalization seems to work well except for the temperature effect on the shear layer fluctuation. Finally, using the above normalization, it is shown that the lowest frequency of Mach waves probably is decreasing with increasing the ratio of environmental supersonic region to the potential core length.

These knowledge and data obtained in this study are very useful ones for improving the prediction model of acoustic from a rocket plume.

修士(工学)野々村拓提出の論文は、「Characteristics of Acoustic Waves Generated by Flow Instability of Supersonic Jets」(和訳:「超音速ジェットの変動が生み出す音響場特性に関する研究」)と題し、本文8章から構成されている.

ロケットプルームから放射される強い音響波(プルーム音響)はペイロードである衛星等に悪影響を及ぼすことから、その予測法構築や低減化が重要になる.プルーム音響の予測には、現在でも実測に基づいた半経験的手法が利用されているが、経験要素の影響が大きく、物理現象に基づいた予測モデルの構築が期待されている.

ロケットプルームから出る音響波のうち、最も問題になるのは下流方向に放射される低周波のマッハ波である.特定の周波数でピークを持つような音響波に比して、このようなマッハ波に対する研究は限定的であり、一部に実験的、数値解析的な既存研究が存在するが、その議論は十分とはいえない.

このような観点から、筆者はロケットプルームを超音速ジェットとしてモデル化し、そこから放射されるマッハ波の解析を行った.特に音響予測に置ける有効となる無次元化の妥当性、マッハ波の放射に対するマッハ数および温度の影響、マッハ波の音源特性などを明らかにすることを目的として研究を行った.従来の定常解析と異なり、超音速ジェットから発生する音響波を捉えるには、高い空間解像度を必要とする非定常な乱流現象を解析しなければならず、計算コストが課題となる.筆者は、2種類の高解像度スキームを組み合わせた手法を新たに用いることでこの課題を解決し、目的となるマッハ波の解析を進めた.

第1章は序論で、過去のロケット音響予測に関する研究、超音速ジェットから発生する音響波に関する研究を概観し、本論文における研究対象を述べた後、本論文の目的と意義を明確にしている.

第2章では、問題設定が述べられている.ジェット状態を決めるパラメタを4つ定義し、それらの値の決定方法を議論している.加えてジェットプロファイルを決定し、数値シミュレーションの対象となるケースを定義している.

第3章では、数値解析手法を記述している.流体場および近傍音響場では、乱流の大規模構造を解析するため3次元圧縮性Navier-Stokes方程式を支配方程式にし、前述した高解像度な手法を用いた大規模解析を行ったことを述べている.またキルヒホフ法を用いた遠方での音響評価法やFFT処理といった後処理に関する手順を示している.

第4章では、数値解析手法の検証を行っている.信頼性の議論に供するため既存の実験、数値解析データが豊富な条件を選び,その解析を行っている.最初に、流れ場、近傍音響場が過去の知見と定性的に一致することおよび外部境界条件の与え方に問題がないことを確認している.続いて過去の研究で得られた結果と流体変動や音響場のデータを定量的に比較し、以下の議論で問題がないことを明らかにしている.また信頼できる周波数帯を議論、さらに格子収束性、境界条件の影響を評価している.

第5章では、音響予測に有効な無次元化の妥当性を確認している.これは過去の研究から示唆された考え方で、適正膨張を仮定した解析により過膨張状態のジェットから出る音響波を予測するものである.適正膨張状態が等しい3つの異なるジェットの流れ場、近傍音響場の比較を行い、これらがほぼ等しい変動場特性を持つことを示している.この結果はジェットの状態を決めるパラメタを1つ減じてよいことを示唆しており、以降の研究結果の礎となっている.

第6章では、ジェットマッハ数およびジェットと外部環境の温度比の効果を、流れ場、音響場の違いという観点で議論している.マッハ数の増加に伴いジェットの乱れのない領域(ポテンシャルコア)が長くなること、温度比の増加に伴いポテンシャルコアが短くなることなどを明らかにしている.

第7章では、マッハ波の音源に関する解析結果を述べている.マイクロフォンアレイ法により、マッハ波の音源が雰囲気音速からみた超音速領域に存在していることをまず明らかにしている.続いて超音速擾乱の速度から予測されるマッハ波の放射角度を可視化し、定性的な音源位置の評価法として妥当であることを明らかにしている.さらに、ジェットせん断層内での軸方向各位置での音源スペクトルがせん断層厚さと中心軸平均速度で正規化できることを示している.最後に、以上の知見を利用し、マッハ数や温度が上昇すると低周波のマッハ波が放出されるという現象のメカニズムを明らかにしている.

以上要するに、本論文は、先端的な数値シミュレーション技術を駆使することで、これまで明らかでなかった超音速ジェットから放射されるマッハ波の特性を明らかにしたものである.得られた結果は、ロケットプルームから発生する音響波の予測に有用な知見を与えることはもちろん、超音速機、極超音速機のジェットから発生する音響の予測にも役立つものであり、今後の航空宇宙工学に貢献するところが大きい。

よって、本論文は博士(工学)の学位請求論文として合格と認められる.