Improved energy normalization function in rocket motor stability calculations |
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| Institution: | 1. Institute of Advanced Materials, Nanjing University of Posts & Telecommunications, Nanjing 210046, China;2. Institute of Advanced Materials, Nanjing University of Technology, Nanjing 210009, China;3. Institute of Materials Research and Engineering, 3 Research Link 117602, Singapore, Singapore;4. School of Materials Science & Engineering, Nanjing University of Posts & Telecommunications, Nanjing 210046, China;5. Department of Mechanical and Aerospace Engineering, University of Central Florida, 4000 Central Florida Blvd, Orlando, FL 32816, USA;1. Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India;2. Department of Physics, Zakir Husain Delhi College, University of Delhi, Delhi 110002, India;3. Department of Physics, Ramjas College, University of Delhi, Delhi 110007, India;1. Institute of Atomic and Molecular Sciences, Academia Sinica, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan;2. Department of Engineering and System Science, National Tsing Hua University, No. 101, Sec 2, Kuang-Fu Road, Hsinchu 30013, Taiwan;3. Center for Condensed Matter Sciences, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan;4. Department of Molecular Science and Engineering, National Taipei University of Technology, Taipei 10617, Taiwan |
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| Abstract: | This work details the derivation of the energy normalization function which arises in motor stability calculations. It starts by identifying the flow parameters that appear in Kirchoff's expression defining the acoustic energy density in a given enclosure. Special care is taken to account for the rotational contributions due to unsteady chamber vorticity. Subsequently, these flow parameters are inserted into the energy normalization function and perturbed to the leading order. The resulting expressions are simplified and asymptotically integrated to obtain the average value of the energy normalization function. This procedure is repeated for two basic geometries pertaining to the circular-port and slab rocket motors, respectively. Our results demonstrate that inclusion of unsteady rotational flow components is critically important for the accurate assessment of energy. We also find that the conventional one-dimensional approach is lacking because it omits unsteady rotational contributions. It under-predicts the energy normalization function by 25% in each of the circular and slab motor cases. |
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