Thermal Stress Analysis of Annular Fin Subject To Varying Contact Pressure and Heat Conduction

環形鰭片在不同接觸壓力與熱導下之熱應力分析

賴新一(Hsin-Yi Lai) ； 魏任宏(Jen-Hung Wei) ； 陳朝光(Chao-Kuang Chen) ； 張桂豪(Kuei-Hao Chang)

《中國機械工程學刊》 41卷5期 (2020/10) Pp. 539-550

摘要

The purpose of this paper is to investigate the heat transfer and thermal stress of a variable temperature inner tube for transporting saturated water vapor and its external interference annular fin under different contact pressures. The related variables include interference between the fin and the inner tube, the fin material and fin radius ratio, to obtain temperature and thermal stress distribution under different variables, as well as possible damage beyond the design limit, to confirm that the system can operate within the scope of safety design. First, the contact pressure between the two interfaces is obtained by considering the temperature boundary condition of the inner tube wall varying with time and the saturated vapor pressure at that temperature. Subsequently, contact thermal conductivity is calculated by Yovanovich's empirical formula, and then the thermal contact conductivity is used as the boundary condition of the fin to solve the temperature distribution curve. The distribution curve of thermal stress, including radial stress and tangential stress, is obtained from the temperature field. In this paper, the effects of various interferences and different ratios of fin diameters on temperature distribution, temperature difference at the interface, and thermal stress distribution of fins are discussed, as is the relationship between heat transfer efficiency and heat transfer capacity of fins in a steady state. conductivity, while contact thermal conductivity affects the heat transfer efficiency of fins. The temperature disparity on the contact surface decreases with the increase in contact pressure. The interference can effectively narrow the temperature gap, and the stress field varies with the interference, the ratio of inner to outer radius, and the thermal expansion rate of the material itself. The greater the interference, the greater the radial stress near the contact surface, and the circumferential stress distribution is transformed from the pressure on the fin base to the tensile force at the fin tail end. This is because, when the effect of temperature change is less than that of displacement, the circumferential stress will present compressive force and vice versa; it will present tensile force. The greater the ratio of inner to outer diameter, the greater the stress in the circumference and radial direction.

關鍵字

Thermal contact conductivity ； contact pressure ； heat transfer ； thermal stress ； annular fin

並列摘要

本文旨在探討傳送飽和水蒸汽之變溫內管與其外在具干涉之環型鰭片在不同接觸壓力下之熱傳遞與熱應力問題。主要相關變量包括鰭片、內管表面干涉量、鰭片材質與內外徑比，上述可用來求取不同變量下之溫度與熱應力分布；及考量超出設計上限所帶來之可能破壞，以確認系統能在安全設計內範疇下運作。首先考慮無熱阻情形下並給予內管壁一隨時間變化之溫度邊界條件與該溫度下之飽和水蒸汽壓，求解得兩介面之接觸壓力， 接者利用Yovanovich經驗式換算出接觸熱導，再以接觸熱導作為鰭片之邊界條件求解其溫度分布曲線，並利用溫度場求得熱應力分布曲線，包含徑向應力與切向應力。文中探討不同干涉量及不同內外徑比對於鰭片之溫度分布、介面溫差、熱應力分布之影響，以及穩態時之鰭片熱傳效率與熱傳量之關係。研究結果得知，接觸壓力影響接觸熱導，而接觸熱導影響鰭片熱傳效率。又接觸面上之溫差會隨著接觸壓增大而變小，干涉量可有效地縮小溫度差距且應力場大小會隨著干涉量、內外徑比與其本身材料熱膨脹率而變化。干涉量越大接觸面附近徑向應力越大，而周向應力分布為鰭片基底之壓所力轉換成鰭片尾端之拉伸力，這是由於當溫度變化所造成的效應小於位移所造成的效應時，周向應力會呈現壓縮力，反之則會呈現拉伸力。又內外徑比越大對於周向與徑向之應力都會越大。