{"title":"Survey of Calculation Methods for Polytropic Efficiencies","authors":"Hans E. Wettstein","doi":"10.1115/gt2021-59967","DOIUrl":null,"url":null,"abstract":"\n Calculating polytropic efficiencies is a basic task used for quantifying performance of power cycles involving compression and/or expansion. The incremental definition of a “polytropic curve” of gases by Gustav Zeuner in 1905 may be the oldest mention of the word “polytropic” in a thermodynamic context [1].\n In Turbomachinery blading, the typical changes of state are nearly adiabatic and polytropic. L. S. Dzung was probably the first defining an incremental polytropic efficiency in 1944 [3]. Recursive integration of this has become the best thermodynamic quality measure of a blading.\n Both Zeuner and Dzung started their consideration with an incremental definition. However, they integrated analytically assuming ideal gas data. This resulted in the well-known formula (1) p v n = constant Most thermodynamic textbooks declare this the definition of a polytropic change of state. However, the incremental definition survived too. Stodola [2], Dzung and later scientists established it as another definition of a polytropic change of state.\n Thus, we face now two definitions of a polytropic change of state, which are theoretically identical for ideal gases but different for real gases and vapors. In educational context, this is disturbing and forcing to a logical detour. We trace the historic roots and show that the initial incremental definition is the physically healthier one. Recursive integration allows direct application to turbomachinery with any finite pressure ratio and to any real fluid.","PeriodicalId":169840,"journal":{"name":"Volume 4: Controls, Diagnostics, and Instrumentation; Cycle Innovations; Cycle Innovations: Energy Storage; Education; Electric Power","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Volume 4: Controls, Diagnostics, and Instrumentation; Cycle Innovations; Cycle Innovations: Energy Storage; Education; Electric Power","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1115/gt2021-59967","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Calculating polytropic efficiencies is a basic task used for quantifying performance of power cycles involving compression and/or expansion. The incremental definition of a “polytropic curve” of gases by Gustav Zeuner in 1905 may be the oldest mention of the word “polytropic” in a thermodynamic context [1].
In Turbomachinery blading, the typical changes of state are nearly adiabatic and polytropic. L. S. Dzung was probably the first defining an incremental polytropic efficiency in 1944 [3]. Recursive integration of this has become the best thermodynamic quality measure of a blading.
Both Zeuner and Dzung started their consideration with an incremental definition. However, they integrated analytically assuming ideal gas data. This resulted in the well-known formula (1) p v n = constant Most thermodynamic textbooks declare this the definition of a polytropic change of state. However, the incremental definition survived too. Stodola [2], Dzung and later scientists established it as another definition of a polytropic change of state.
Thus, we face now two definitions of a polytropic change of state, which are theoretically identical for ideal gases but different for real gases and vapors. In educational context, this is disturbing and forcing to a logical detour. We trace the historic roots and show that the initial incremental definition is the physically healthier one. Recursive integration allows direct application to turbomachinery with any finite pressure ratio and to any real fluid.
计算多向效率是用于量化涉及压缩和/或膨胀的功率循环性能的基本任务。1905年古斯塔夫·齐纳(Gustav Zeuner)对气体“多向性曲线”的增量定义,可能是在热力学背景下最早提到“多向性”一词的人。在涡轮机械叶片中,典型的状态变化几乎是绝热的和多向性的。1944年,L. S. Dzung可能是第一个定义增量多向效率的人。递归积分已成为衡量叶片热力学质量的最佳方法。Zeuner和Dzung都是从增量定义开始考虑的。然而,他们整合了分析假设的理想气体数据。这就得到了著名的公式(1)p v n =常数,大多数热力学教科书都称这是多向态变化的定义。然而,增量定义也保留了下来。Stodola b[2], jung和后来的科学家建立了它作为多向性状态变化的另一个定义。因此,我们现在面临着多向态变化的两种定义,这两种定义在理论上对理想气体是相同的,但对实际气体和蒸汽却不同。在教育背景下,这是令人不安的,并迫使一个合乎逻辑的弯路。我们追溯历史根源,并表明最初的增量定义是身体更健康的定义。递归积分允许直接应用于任何有限压力比的涡轮机械和任何实际流体。