英文原文 Screw Compressors N. Stosic I. Smith A. Kovacevic Screw Compressors Mathematical Modelling and Performance Calculation With 99 Figures ABC Prof. Nikola Stosic Prof. Ian K. Smith Dr. Ahmed Kovacevic City University School of Engineering and Mathematical Sciences Northampton Square London EC1V 0HB U.K. e-mail: n.stosiccity.ac.uk i.k.smithcity.ac.uk a.kovaceviccity.ac.uk Library of Congress Control Number: 2004117305 ISBN-10 3-540-24275-9 Springer Berlin Heidelberg New York ISBN-13 978-3-540-24275-8 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. 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Typesetting: by the authors and TechBooks using a Springer LATEX macro package Cover design: medio, Berlin Printed on acid-free paper SPIN: 11306856 62/3141/jl 5 4 3 2 1 0 Preface Although the principles of operation of helical screw machines, as compressors or expanders, have been well known for more than 100 years, it is only during the past 30 years that these machines have become widely used. The main reasons for the long period before they were adopted were their relatively poor efficiency and the high cost of manufacturing their rotors. Two main developments led to a solution to these difficulties. The first of these was the introduction of the asymmetric rotor profile in 1973. This reduced the blowhole area, which was the main source of internal leakage by approximately 90%, and thereby raised the thermodynamic efficiency of these machines, to roughly the same level as that of traditional reciprocating compressors. The second was the introduction of precise thread milling machine tools at approximately the same time. This made it possible to manufacture items of complex shape, such as the rotors, both accurately and cheaply. From then on, as a result of their ever improving efficiencies, high reliability and compact form, screw compressors have taken an increasing share of the compressor market, especially in the fields of compressed air production, and refrigeration and air conditioning, and today, a substantial proportion of compressors manufactured for industry are of this type. Despite, the now wide usage of screw compressors and the publication of many scientific papers on their development, only a handful of textbooks have been published to date, which give a rigorous exposition of the principles of their operation and none of these are in English. The publication of this volume coincides with the tenth anniversary of the establishment of the Centre for Positive Displacement Compressor Technology at City University, London, where much, if not all, of the material it contains was developed. Its aim is to give an up to date summary of the state of the art. Its availability in a single volume should then help engineers in industry to replace design procedures based on the simple assumptions of the compression of a fixed mass of ideal gas, by more up to date methods. These are based on computer models, which simulate real compression and expansion processes more reliably, by allowing for leakage, inlet and outlet flow and other losses, VI Preface and the assumption of real fluid properties in the working process. Also, methods are given for developing rotor profiles, based on the mathematical theory of gearing, rather than empirical curve fitting. In addition, some description is included of procedures for the three dimensional modelling of heat and fluid flow through these machines and how interaction between the rotors and the casing produces performance changes, which hitherto could not be calculated. It is shown that only a relatively small number of input parameters is required to describe both the geometry and performance of screw compressors. This makes it easy to control the design process so that modifications can be cross referenced through design software programs, thus saving both computer resources and design time, when compared with traditional design procedures. All the analytical procedures described, have been tried and proven on machines currently in industrial production and have led to improvements in performance and reductions in size and cost, which were hardly considered possible ten years ago. Moreover, in all cases where these were applied, the improved accuracy of the analytical models has led to close agreement between predicted and measured performance which greatly reduced development time and cost. Additionally, the better understanding of the principles of operation brought about by such studies has led to an extension of the areas of application of screw compressors and expanders. It is hoped that this work will stimulate further interest in an area, where, though much progress has been made, significant advances are still possible. London, Nikola Stosic February 2005 Ian Smith Ahmed Kovacevic Notation A Area of passage cross section, oil droplet total surface a Speed of sound C Rotor centre distance, specific heat capacity, turbulence model constants d Oil droplet Sauter mean diameter e Internal energy f Body force h Specific enthalpy h = h(), convective heat transfer coefficient between oil and gas i Unit vector I Unit tensor k Conductivity, kinetic energy of turbulence, time constant m Mass m Inlet or exit mass flow rate m = m () p Rotor lead, pressure in the working chamber p = p() P Production of kinetic energy of turbulence q Source term Q Heat transfer rate between the fluid and the compressor surroundingsQ= Q() r Rotor radius s Distance between the pole and rotor contact points, control volume surface t Time T Torque, Temperature u Displacement of solid U Internal energy W Work output v Velocity w Fluid velocity V Local volume of the compressor working chamber V = V () V Volume flow VIII Notation x Rotor coordinate, dryness fraction, spatial coordinate y Rotor coordinate z Axial coordinate Greek Letters Temperature dilatation coefficient Diffusion coefficient Dissipation of kinetic energy of turbulence i Adiabatic efficiency t Isothermal efficiency v Volumetric efficiency Specific variable Variable Lame coefficient Viscosity Density Prandtl number Rotor angle of rotation Compound, local and point resistance coefficient Angular speed of rotation Prefixes d differential Increment Subscripts eff Effective g Gas in Inflow f Saturated liquid g Saturated vapour ind Indicator l Leakage oil Oil out Outflow p Previous step in iterative calculation s Solid T Turbulent w pitch circle 1 main rotor, upstream condition 2 gate rotor, downstream condition Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Types of Screw Compressors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.1 The Oil Injected Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.2 The Oil Free Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Screw Machine Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Screw Compressor Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.5RecentDevelopments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.5.1RotorProfiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.5.2CompressorDesign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2ScrewCompressorGeometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.1 The Envelope Method as a Basis for the Profiling of Screw Compressor Rotors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2 Screw Compressor Rotor Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3 Rotor Profile Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.4 Review of Most Popular Rotor Profiles . . . . . . . . . . . . . . . . . . . . . 23 2.4.1 Demonstrator Rotor Profile (“N” Rotor Generated) . . . . 24 2.4.2 SKBK Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.4.3 Fu Sheng Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.4.4 “Hyper” Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.4.5 “Sigma” Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.4.6 “Cyclon” Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.4.7 Symmetric Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4.8 SRM “A” Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.4.9 SRM “D” Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.4.10 SRM “G” Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.4.11 City “N” Rack Generated Rotor Profile . . . . . . . . . . . . . 32 2.4.12 Characteristics of “N” Profile . . . . . . . . . . . . . . . . . . . . . . . 34 2.4.13 Blower Rotor Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 X Contents 2.5 Identification of Rotor Position in Compressor Bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.6 Tools for Rotor Manufacture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.6.1 Hobbing Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.6.2 Milling and Grinding Tools . . . . . . . . . . . . . . . . . . . . . . . . 48 2.6.3 Quantification of Manufacturing Imperfections . . . . . . . . 48 3 Calculation of Screw Compressor Performance . . . . . . . . . . . . . 49 3.1 One Dimensional Mathematical Model . . . . . . . . . . . . . . . . . . . . . 49 3.1.1 Conservation Equations for Control Volume and Auxiliary Relationships . . . . . . . 50 3.1.2 Suction and Discharge Ports . . . . . . . . . . . . . . . . . . . . . . . . 53 3.1.3 Gas Leakages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.1.4 Oil or Liquid Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.1.5 Computation of Fluid Properties . . . . . . . . . . . . . . . . . . . . 57 3.1.6 Solution Procedure for Compressor Thermodynamics . . 58 3.2 Compressor Integral Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.3 Pressure Forces Acting on Screw Compressor Rotors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.3.1 Calculation of Pressure Radial Forces and Torque . . . . . 61 3.3.2 Rotor Bending Deflections . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.4 Optimisation of the Screw Compressor Rotor Profile, Compressor Design and Operating Parameters . . . . . . . . . . . . . . 65 3.4.1 Optimisation Rationale . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.4.2 Minimisation Method Used in Screw Compressor Optimisation . . . . . . . . . . . . . . . . . 67 3.5 Three Dimensional CFD and Structure Analysis of a Screw Compressor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4 Principles of Screw Compressor Design . . . . . . . . . . . . . . . . . . . 77 4.1 Clearance Management. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.1.1 Load Sustainability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.1.2 Compressor Size and Scale . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.1.3 Rotor Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.2 Calculation Example: 5-6-128mm Oil-Flooded Air Compressor . . . . . . . . . . . . . . . . . . . 82 4.2.1 Experimental Verification of the Model . . . . . . . . . . . . . . . 84 5 Examples of Modern Screw Compressor Designs . . . . . . . . . . 89 5.1 Design of an Oil-Free Screw Compressor Based on 3-5 “N” Rotors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.2 The Design of Family of Oil-Flooded Screw Compressors Based on 4-5 “N” Rotors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 Contents XI. 5.3 Design of Replacement Rotors for Oil-Flooded Compressors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 5.4 Design of Refrigeration Compressors . . . . . . . . . . . . . . . . . . . . . 100 5.4.1 Optimisation of Screw Compressors for Refrigeration . . . 102 5.4.2 Use of New Rotor Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . .103 5.4.3 Rotor Retrofits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.4.4 Motor Cooling Through the Superfeed Port in Semihermetic Compressors . . . . . . . . . . . . . . . . . . . . . . 103 5.4.5 Multirotor Screw Compressors . . . . . . . . . . . . . . . . . . . . . . 104 5.5 Multifunctional Screw Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 5.5.1 Simultaneous Compression and Expansion on One Pair of Rotors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 5.5.2 Design Characteristics of Multifunctional Screw Rotors .109 5.5.3 Balancing Forces on Compressor-Expander Rotors . . . . . 110 5.5.4 Examples of Multifunctional Screw Machines . . . . . . . . . 111 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 A Envelope Method of Gearing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 B Reynolds Transport Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 C Estimation of Working Fluid Properties . . . . . . . . . . . . . . . . . . . 127 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133中文譯文 螺桿壓縮機(jī) N.斯托西奇史密斯先生 A 科瓦切維奇 螺桿壓縮機(jī) 計(jì)算的數(shù)學(xué)模型和性能 尼古拉教授 斯托西奇教授 伊恩史密斯博士 艾哈邁德科瓦切維奇 工程科學(xué)和數(shù)學(xué) 北安普敦 廣場倫敦城市大學(xué) 英國 電子郵件： n.stosiccity.ac.uk i.k.smithcity.ac.uk a.kovaceviccity.ac.uk 國會(huì)圖書館控制號(hào)： 2004117305 isbn-10 3-540-24275-9 紐 約施普林格柏林海德堡 isbn-13 978-3-540-24275-8 紐約施普林格柏林海德堡 這項(xiàng)工作是受版權(quán)保護(hù) ,我們 保留所有權(quán)利 。 無論材料的全部或部分關(guān)注的是特定的權(quán)利，尤其是 翻譯，轉(zhuǎn)載，插圖，朗誦，廣播復(fù)用或以任何其他方式復(fù)制，并在銀行數(shù)據(jù)存儲(chǔ) 的權(quán)利 。本出版物或其部分僅僅是在 1965 年 9 月 9 日的德國版權(quán)法規(guī)定允許復(fù)制，目前的版本，并允許使用必須得到施普林格 的允許 。違法行為 將會(huì)遭受 德國版權(quán)法的起訴。 施普林格是施普林格科學(xué) +商業(yè)媒體的一部分 施普林格出版社柏林印 刷在荷蘭海德堡 2005 一般描述性名稱，注冊域名，商標(biāo)的使用，本出版物中做等。 排版：由作者使用 施普林格 乳膠宏包封面設(shè)計(jì)：中部，柏林 打印在無酸紙旋轉(zhuǎn)： 11306856 62 3141 JL 543210 雖然螺旋機(jī)的工作原理，壓縮機(jī)或膨脹機(jī)，已超過 100 年，這是在過去的 30 年里，這些機(jī)器已 經(jīng)被 廣泛使用。主要 因?yàn)橐郧?他們采取了相對貧窮的效率和制造成本高的轉(zhuǎn)子。兩個(gè)主要的 技術(shù)革新 解決 了 這些 困難 。 第一個(gè)出現(xiàn) 在 1973 年的 不對稱轉(zhuǎn)子。這減少了打擊孔的 面積，這是內(nèi)部泄漏的主要來源，約 90%，從而提高了熱力學(xué)效 率， 這些機(jī)器 大約是傳統(tǒng)的往復(fù)式壓縮機(jī)的同一水平。第二個(gè)是精密螺紋銑削機(jī)床。這使它能夠制造形狀復(fù)雜的物品，如 轉(zhuǎn) 子，既準(zhǔn)確又便宜。 從那以后，由于他們不斷改進(jìn)，可靠性高性 能 和緊湊的形式，螺桿壓縮機(jī)已越來越多的占領(lǐng) 壓縮機(jī)市場，尤其是在壓縮空氣生產(chǎn)的領(lǐng)域，制冷和空調(diào)，而今天，制造工業(yè)壓縮機(jī)占相當(dāng)大的比例是 也 這種類型的。 盡管，現(xiàn)在廣泛使用的螺桿壓縮機(jī)和許多科學(xué)發(fā)展論文出版，只有一小部分教科書已經(jīng)出版，使其操作和沒有這些原則的論述嚴(yán)謹(jǐn)是英文的。 本書的出版恰逢城市大學(xué)第十周年的設(shè)立 。它 為正位移壓縮機(jī)技術(shù) 突 出貢獻(xiàn)，位于倫敦，如果不是 他，這 所有的材料 就不會(huì)被發(fā)明。 它的目的是給了藝術(shù)的狀態(tài)的數(shù)據(jù)匯總。在一個(gè)單一的體積的可用性將幫助工程師在工業(yè)取代基于一個(gè)簡單的假設(shè)壓縮程序設(shè)計(jì)固定的理想氣體的質(zhì)量，通過更多的最新方法。這些都是基于計(jì)算機(jī)模型，模擬實(shí)際的壓縮和膨脹過程更可靠，通過允許泄漏，入口和出口和其他損失，和工作過程中的實(shí)際性質(zhì)的假設(shè)。同時(shí)，方法提出了發(fā)展轉(zhuǎn)子，基于齒輪嚙合的數(shù)學(xué)理論，而不是經(jīng)驗(yàn)曲線擬合。 此外，一些描述包括通過這些機(jī)器的熱三維建模程序和如何相互作用的轉(zhuǎn)子和殼體之間產(chǎn)生性能的變化，至今無 法計(jì)算。結(jié)果表明，只有一小數(shù)量的輸入?yún)?shù)來描述的幾何形狀和螺桿壓縮機(jī)的性能。這使得它很容易控制的設(shè)計(jì)過程，修改陽離子可以交叉引用通過設(shè)計(jì)軟件程序，從而節(jié)省計(jì)算機(jī)重新來源和設(shè)計(jì)時(shí)間，與傳統(tǒng)的設(shè)計(jì)方法相比。 所有所描述的分析程序，已經(jīng)過驗(yàn)證的機(jī)器目前在工業(yè)生產(chǎn)中，已經(jīng)導(dǎo)致在性能和尺寸和降低成本的改進(jìn)，它幾乎沒有考慮可能十年前就。此外，在所有情況下，這些應(yīng)用，分析模型的精度提高了預(yù)測值與實(shí)測性能大大減少開發(fā)時(shí)間和成本彪密切之間的協(xié)議。此外，的操作原則所帶來的這些研究更好的理解導(dǎo)致螺桿壓縮機(jī)和膨脹機(jī)的應(yīng)用領(lǐng)域的擴(kuò) 展。人們希望這項(xiàng)工作將刺激在一個(gè)地區(qū)，那里的進(jìn)一步的興趣，雖然已經(jīng)取得了很大進(jìn)展，顯斜面的進(jìn)步仍然是可能的。 倫敦，二月 2005 伊恩史密斯艾哈邁德尼古拉斯托西奇科瓦切維奇 符號(hào) A 通道橫截面，油滴表面總面積 a 聲音的速度 C 轉(zhuǎn)子中心的距離，比熱容，湍流模型常數(shù) d 油滴的平均直徑 e 內(nèi)部能量 f 體力 h 比焓 h= H（） ,，對流換熱系數(shù)石油和天然氣之間的系數(shù) i 單位向量 I 單位張量 k 電導(dǎo)率，湍流動(dòng)能，時(shí)間常數(shù) m 質(zhì)量 .m 入口或出口質(zhì)量 的 流量 .m =.m （ ） p 轉(zhuǎn)子引線，在工作腔壓力（ P = P ） P 湍流動(dòng)能