2007年--外文翻譯--注油式回轉(zhuǎn)雙螺桿壓縮機工作循環(huán)數(shù)學(xué)模型的建立（節(jié)選）

1、<p>　　3360漢字，2236單詞，11500英文字符</p><p>　　出處：Seshaiah N, Ghosh S K, Sahoo R K, et al. Mathematical modeling of the working cycle of oil injected rotary twin screw compressor[J]. Applied Thermal Engineering

2、, 2007, 27(1): 145-155.</p><p><b>　　英文附錄</b></p><p>　　Mathematical modeling of the working cycle of oil injected rotary twin screw compressor</p><p>　　N. Seshaiah *, Sub

3、rata Kr. Ghosh, R.K. Sahoo, Sunil Kr. Sarangi</p><p>　　Cryogenics and Gas dynamics Laboratory, Department of Mechanical Engineering, National Institute of Technology, Sector-2, NIT Campus, Rourkela 769008, O

4、rissa, India</p><p>　　Received 12 July 2005; accepted 8 May 2006 ；Available online 7 July 2006</p><p><b>　　Abstract</b></p><p>　　Oil injected twin-screw air and gas comp

5、ressors are widely used for medium pressure applications in many industries. Low cost air compressors can be adopted for compression of helium and special gases, leading to signi?cant cost saving. Mathematical analysis o

6、f oil injected twin-screw compressor is carried out on the basis of the laws of perfect gas and standard thermodynamic relations. Heat transfer coe?cient required for computer simulation is experimentally obtained and us

7、ed in performance pr</p><p>　　Keywords: Screw compressor; Oil injection; Heat transfer coe?cient; Leakage; Flow coe?cients</p><p>　　Introduction</p><p>　　The screw compressor is a p

8、ositive displacement machine that uses a pair of intermeshing rotors housed in a suitable casing to produce compression. Screw compressors are capable of high-speed operation over a wide range of operating pressures. In

9、a screw machines, oil is deliberately injected into the compression chamber to improve and to provide sealing, lubrication, corrosion resistance and cooling e?ect. Rotary dual screw compressors are widely used in industr

10、y for air and gas compression and</p><p>　　able for compression of air and helium used in small and intermediate size cryogenic refrigerators and lique?ers. A computerized method for generation of rotor pro?

11、les and analysis and performance has been suggested by Singh et al. [1,2]. Due to the high cost of energy, particularly in India, it is necessary that all machines operate e?ciently. This can be achieved only when machin

12、e performance is well understood and is predictable. Unlike other compressors, the mechanism of gas compression in a</p><p>　　2. Modeling of compressor cycle</p><p>　　Analysis of volumetric and

13、power e?ciencies is essential to estimate the suitability of a compressor for a particular application. The main objective of the present performance analysis is to develop a numerical model to ascertain the suitability

14、of a commercially available air compressor for di?erent gas compression applications. E?ciency of any compressor depends on the processes involved in the working cycle. Major processes of screw compressor are suction, co

15、mpression and discharge. Analysis</p><p>　　2.1. Suction process</p><p>　　Volumetric e?ciency of the compressor greatly depends on the amount of gas mass inducted into the suction cavity during s

16、uction process. This, in turn, depends on the temperature of the cavity walls at steady state. Analysis of the suction process gives the average temperature of the gas in the suction cavity at the end of suction process.

17、 Model of the working chamber during suction process is shown in Fig. 1. Since the pressure and temperature ?uctuations during suction process are generally sm</p><p>　　? Inlet velocities of gas and oil.<

18、/p><p>　　? Inlet temperature of gas and oil.</p><p>　　? Pressure drop across the inlet port.</p><p>　　? Rate of heat ?ow from gas to oil (or from oil to gas).</p><p>　　Th

19、e quantity of gas mass inducted into the suction cavities depends on the temperatures of inlet gas and the cavity walls. During the suction process the cavity wall temperature is higher than the inducted gas temperature

20、because of the heat ?ow from the compressed gas during the compression process. The cavity wall is covered with a ?lm of lubricating oil which leaks from the adjoining compression space when the oil is injected. The amou

21、nt of heat transferred from the hot suction cavity wall (l</p><p>　　If the temperature rise of the inducted gas is small compared to the temperature di?erence between the lubricating oil ?lm and the inducted

22、 gas, the heat transfer between the leaked oil and inducted gas may be written as below:</p><p>　　Under ideal conditions, the heat lost by the oil ?lm must be equal to heat gained by the fresh gas mass. From

23、 Eqs. (1) and (2), the mean temperature of inducted gas at the end of suction process can be obtained as</p><p>　　The amount of gas mass inducted into the geometrical volume at suction condition (Ps,Ts)is<

24、;/p><p>　　, the geometrical volume of a pair of male and female rotor cavities is de?ned [3] as below:</p><p>　　, and being the cross sectional areas of the male and female cavities respectively an

25、d L the rotor length.</p><p>　　The gas mass in the suction cavity at condition (Ps,T1) can be estimated by the expression</p><p>　　This gas mass is the sum of fresh charge inducted (M1) and the

26、mass leaked through interlobe clearance ()</p><p>　　Eliminating the total mass between Eqs. (5) and (6), the fresh gas mass inducted during suction process is obtained as below:</p><p>　　Substi

27、tuting this value of value in Eq. (3), the following quadratic equation is obtained in terms of the gas temperature :</p><p>　　2.2. Compression and discharge process</p><p>　　Both the compressi

28、on and the discharge processes are unsteady processes. Thermodynamic properties of the gas and oil vary continuously during compression process. The gas in the working chamber is compressed to a high pressure by the rota

29、tional movement of the rotors. To simplify the analysis, it is assumed that the oil and gas are separate ?uids, and only heat is exchanged between them. The discharge port is so located that the cavities connect to the d

30、ischarge port when the pressure in the wor</p><p>　　The following factors are taken into account in the model:</p><p>　　1. volume change due to rotor rotation,</p><p>　　2. mass and

31、enthalpy ?ows of gas， entering or leaving the working space through discharge port and leakage paths,</p><p>　　3. mass and enthalpy ?ows of oil, entering or leaving the working space through discharge port a

32、nd leakage　paths,</p><p>　　4. heat exchange between gas and oil.</p><p>　　To simplify the calculations, the following assumptions are made:</p><p>　　? Gas and oil temperatures are h

33、omogeneous at any instant in the working space.</p><p>　　? Gas and oil never change phase.</p><p>　　? Pressure is uniform throughout the working space at any stage.</p><p>　　? The w

34、orking gas is an ideal gas.</p><p>　　? Oil is an incompressible ?uid.</p><p>　　? Heat exchange between gas and oil is in proportion to the temperature di?erence between them.</p><p>

35、;　　? A pressure ?uctuation across the discharge port is negligible.</p><p>　　Fujiwara and Osada [4] derived the fundamental equations based on standard thermodynamic laws and the laws of perfect gas. The fol

36、lowing equations are derived with some modi?cations and other details are introduced as needed.</p><p>　　The ?rst law of thermodynamics for unsteady ?ow of gas through the working chamber can be expressed as

37、</p><p>　　is the sum of internal, potential and kinetic energies. Assuming the potential and kinetic energies of gas to be negligible, from the above equation the change in internal energy in time dt can be

38、computed as</p><p>　　Change in internal energy can also be expressed as a function of mass and temperature change and de?ned as below:</p><p>　　The change of enthalpy due to leakage can be expre

39、ssed as</p><p>　　The gas work may be expressed in terms of geometrical volume change, and oil volume change due to leakage. Since the oil is an incompressible ?uid, the gas work is expressed as</p>&l

40、t;p>　　Heat exchange between the gas and the oil in time is assumed to follow the Newton’s law of cooling and is expressed as</p><p>　　Substituting (11)–(14) in (10), and rearranging, the rate of change o

41、f working gas temperature is obtained</p><p>　　The ?rst term on the right-hand side of the above equation relates to the change in volume including the leakage rate of oil. The second and third terms represe

42、nt the e?ect of gas leakage into and out of the compressor cavity respectively. The last term is derived from the heat transfer from gas to the oil.</p><p>　　The rate of change of net gas volume of the worki

43、ng chamber [4] can be written as below:</p><p>　　The rate of change of gas mass due to internal leakage is given by the expression</p><p>　　The equation of state of perfect gas may be written as

44、 follows:</p><p>　　The di?erential form of the above equation can be written as follows:</p><p>　　Substituting Eqs. (15)–(17) in Eq. (18), the rate of change of pressure is obtained as follows:&

45、lt;/p><p>　　The rate of change of oil temperature is obtained from energy balance in terms of leakage oil temperature and heat transferred from the gas. The increase of oil temperature in the working chambers i

46、s due to heat gained from the leakage oil (which is at higher temperature) and the heat gained from the gas under compression.</p><p>　　Assuming the potential and kinetic energies to be negligible, the entha

47、lpy change of oil in the working chamber can be expressed as follows:</p><p>　　where is the heat lost by the leaked oil.</p><p>　　The enthalpy change of oil in time dt may be expressed as</p

48、><p>　　The work done by the oil is zero (i.e dW = 0), since oil is an incompressible ?uid.</p><p>　　The heat gained by the oil in time dt is given by the expression</p><p>　　The oil le

49、akage in to the working chamber is at higher temperature than the oil in the cavity. The energy lost by leaked oil is given by the expression</p><p>　　Substituting Eqs. (21)–(23) in Eq. (20), the rate of cha

50、nge of oil temperature is obtained as follows:</p><p>　　The rate of change of oil mass in the working chamber due to leakage as follows:</p><p>　　2.3. Leakage calculation of gas and oil</p>

51、;<p>　　Leakage is a major concern in screw compressors. The major leakage paths identi?ed during compression process are leakage through interlobe clearance, through blowhole, rotor tip-housing clearance and clear

52、ance between rotor discharge end and casing wall [5–7]. Leakage mass through interlobe clearance will go directly into the suction chambers. Except at the lobe tip clearance, leakage gas and oil are uniformly mixed and t

53、he ?ow is isolated from any heat exchange with their surroundings while ma</p><p>　　where and being upstream and down stream pressures respectively.</p><p>　　Due to the presence of oil, exact

54、properties of oil–gas mixture are not known. However, the properties are calculated based on well justi?able assumptions and compared with experimental data. By comparison with laboratory tests, the following assumptions

55、 for di?erent types of leakage paths have been shown to be the most appropriate [5]</p><p>　　(1) The gas/oil mixture in all leakage paths is homogeneous.</p><p>　　(2) The gas/oil mixture ratio i

56、s same in all leakage paths except at the lobe tip clearance and equal to the mixture ratio passing through discharge port.</p><p>　　The apparent ratio of speci?c heats of oil and gas mixture is calculated f

57、rom Ref. [4]</p><p>　　The modi?ed gas constant of the mixture is also calculated using Ref. [4]</p><p>　　The mass ratio of oil to gas in the working chambers as well as through all leakage paths

58、 is homogeneous and equal to the mixture ratio in the working volume [5] and is expressed as below:</p><p>　　The average leakage area is determined by multiplying sealing line length with an average gap (cle

59、arance) for each type of leakage. Normally, the average gap/clearance is determined from the actual clearance measurements in the compressor. The discharge or ?ow coe?cients are empirically selected to account in the pre

60、sence of oil. At the lobe tip, it is assumed that the clearance ?lls with the oil due to the action of centrifugal force, and the oil leakage ?ow is in single phase. The leakage ?ow </p><p>　　The leakage gas

61、 mass rate into the working chambers is through leading blowhole, and through clearance between discharge end of rotors and casing wall from male and female rotor leading cavities. It can be calculated using the below ex

62、pression:</p><p>　　The leakage gas mass going out of the working chambers is through trailing blowhole, interlobe clearance, and through the clearance between lagging cavity end and casing wall, of male and

63、female rotors at discharge end and is expressed</p><p><b>　　as</b></p><p>　　Similarly, the leakage rate of oil mass into and out of the working chambers is given by the relations：<

64、;/p><p>　　Eqs. (26)–(34) are adequate to calculate the rate of change of gas and oil mass during compression and discharge process.</p><p>　　3. Conclusions</p><p>　　A numerical model o

65、f the oil injected dual screw compressor has been developed covering both suction and compression-discharge steps to study the in?uence of design and operating parameters on the compressor volumetric and adiabatic e?cien

66、cies. Heat transfer coe?cient between gas and oil has been determined from experimental observations in which volumetric e?ciency decreases with decrease of inlet temperature. Flow coe?cients have also been determined fr

67、om experimentally obtained compressor e?c</p><p>　　References</p><p>　　[1] Pawan J. Singh, A.D. Onuschak, A comprehensive, computerized method for twin screw rotor pro?le generation and analysis

68、, in: Proceedings of the Purdue Compressor Technology Conference, Purdue, USA, 1984, pp. 519–527.</p><p>　　[2] Pawan J. Singh, G.C. Patel, A generalized performance computer program for oil ?ooded twin-screw

69、 compressors, in: Proceedings of the Purdue Compressor Technology Conference, Purdue, USA, 1984, pp. 544–553.</p><p>　　[3] P. Koelet, Industrial Refrigeration Principle Design and Applications, McGraw Hill,

70、1992.</p><p>　　[4] M. Fujiwara, Y. Osada, Performance analysis of oil injected screw compressor and its application, International Journal of Refrigeration 18 (4) (1995) 220–227.</p><p>　　[5] B.

71、 Sangfors, Computer simulation of oil injected twin-screw compressor, in: Proceedings of the Purdue Compressor Technology Conference, Purdue, USA, 1984, pp. 528–535.</p><p>　　[6] A. Pietsch, S. Nowotny, Ther

72、modynamic calculation of a duel screw compressor based on experimentally measured values taking supercharge into account, in: International Compressor Engineering Conference, Purdue, USA, 1990, vol-I, pp. 44–50.</p>

73、;<p>　　[7] Huagen Wu, Ziwen Xing, Pengcheng Shu, Theoretical and experimental study on Indicator diagram of twin screw refrigeration compressor, International Journal of Refrigeration 27 (4) (2004) 331–338, June.&

74、lt;/p><p>　　[8] M. Fujiwara, K. Kasuya, T. Matsunaga, W. Makoto, Computer modeling for performance analysis of rotary screw compressor, in: Proceedings of the Purdue Compressor Technology Conference, Purdue, US

75、A, 1984, pp. 536–543.</p><p>　　[9] M. Fujiwara, H. Mori, T. Suwama, Prediction of the oil free screw compressor performance using digital computers, in: Proceedings of the Purdue Compressor Technology Confer

76、ence, Purdue, USA, 1974, pp. 186–189.</p><p>　　[10] Robert W. Fox, Alan T. McDonald, Introduction to Fluid Mechanics, second ed., John Wiley & Sons, 1973.</p><p>　　[11] N. Stosic, I.K. Smith

77、, A. Kovacevic, Retro?t ‘N’ Rotors for e?cient oil ?ooded screw compressors, in: International Compressor Conference, Purdue, USA, 2000, pp. 917–924.</p><p>　　[12] K. Ueno, K.S. Hunter, Compressor e?ciency d

78、e?nitions. Available from: <www.vairex.com> May 12, 2003.</p><p>　　[13] Huagen Wu, Xueyuan Peng, Ziwen Xing, Pengcheng Shu, Experimental study on P–V Indicator diagrams of twin screw refrigeration comp

79、ressor with economizer, Applied Thermal Engineering 24 (10) (2004) 1491–1500.</p><p>　　[14] R.P. Taylor, B.K. Hodge, C.A. James, Estimating uncertainty in thermal systems analysis and design, Applied Thermal

80、 Engineering 1 (1) (1999) 3–17.</p><p>　　注油式回轉(zhuǎn)雙螺桿壓縮機工作循環(huán)數(shù)學(xué)模型的建立</p><p>　　N. Seshaiah *, Subrata Kr. Ghosh, R.K. Sahoo, Sunil Kr. Sarangi印度奧里薩，魯爾克拉，尼特校園第2部門，國家技術(shù)學(xué)院，機械工程系，低溫與氣體動力學(xué)實驗室，郵編769008200

81、5年7月12收到；2006年5月8日接受；2006年7月7日網(wǎng)上提供</p><p><b>　　摘要 </b></p><p>　　在許多行業(yè)中，注油式雙螺桿空氣和氣體壓縮機被廣泛用于中壓。成本低的空氣壓縮機能夠適合壓縮氦和特殊氣體，可以大量節(jié)省成本。注油式雙螺桿壓縮機的數(shù)學(xué)分析是建立在理想氣體和標(biāo)準(zhǔn)熱力關(guān)系規(guī)則的基礎(chǔ)上的。當(dāng)工作介質(zhì)為空氣或氦氣時，傳熱系數(shù)需要

82、通過計算機模擬實驗獲取并且用于性能預(yù)測。數(shù)學(xué)模型在計算壓縮機的性能和用實驗數(shù)據(jù)來驗證結(jié)果方面得到了發(fā)展。從效率曲線上獲得流量系數(shù)來進(jìn)行數(shù)值模擬，計算泄漏率。在功率和容積效率方面，對一些影響壓縮機運行和設(shè)計參數(shù)進(jìn)行了分析和介紹。</p><p>　　關(guān)鍵詞：螺桿壓縮機 注油式 傳熱系數(shù) 泄漏 流量系數(shù)</p><p><b>　　1 導(dǎo)言 </b></p&

83、gt;<p>　　螺桿式壓縮機是一種正位移機器，采用一對嚙合轉(zhuǎn)子安置在一個合適的套管里從而壓縮氣體的。各種操作壓力下，螺桿壓縮機具有高速運行的特性。螺桿機械中，油是有意注入壓縮腔室，以改善和提供密封，潤滑，耐腐蝕和冷卻效果。旋轉(zhuǎn)式雙螺桿壓縮機，在空氣和氣體壓縮和制冷領(lǐng)域有著廣泛的應(yīng)用。它們尤其適合小型和中型尺寸低溫冰箱、液化器的空氣和氦氣的壓縮。一般轉(zhuǎn)子的概況、分析、性能的計算方法已經(jīng)由Singh等人給出[ 1,2 ]。由

84、于高能源成本，尤其是在印度，保證所有的機器有效運作是必要的。要做到這一點，只有當(dāng)機器的性能被很好的理解和預(yù)測。不像其他的壓縮機，注油式螺桿壓縮機的氣體壓縮結(jié)構(gòu)是極其復(fù)雜的。很難用分析的方法來估計壓縮機性能。另一方面，實驗研究是昂貴的，因為任何改變轉(zhuǎn)子的幾何形狀的新轉(zhuǎn)子的加工需要采用昂貴的加工技術(shù)。</p><p>　　2 壓縮機循環(huán)的模型建立 </p><p>　　對特定應(yīng)用下估算壓縮機是

85、否合適，容積效率和功率的分析是至關(guān)重要的。本性能分析的主要目的是建立一個數(shù)學(xué)模型，以確定不同壓縮氣體是否適合商用空氣壓縮機。任何壓縮機的效率取決于工作循環(huán)這個過程。螺桿壓縮機的主要過程為吸氣，壓縮和排氣。要建立壓縮機性能模型，這些單個過程的分析是至關(guān)重要的。</p><p><b>　　2.1 吸氣過程 </b></p><p>　　壓縮機的容積效率很大程度上取決于吸

86、氣過程引入吸氣腔的氣體質(zhì)量的多少。反過來，這取決于吸氣腔溫度場的穩(wěn)定。分析吸氣過程時給出吸氣腔的平均氣溫是吸氣終了時的溫度。吸氣工作腔的模型如圖1所示。吸氣過程中由于壓力和溫度的波動一般很小，因此吸氣過程的下面幾個物理量可認(rèn)為是常量：</p><p>　　?潤滑油和氣體的入口速度。 ?潤滑油和氣體入口溫度。 ?入口壓降。 ?從氣體到潤滑油（或從潤滑油到氣體）的熱流率。</p><p>

87、;　　吸入氣腔氣體的質(zhì)量取決于入口氣體和氣腔壁的溫度。在吸氣過程中，氣腔壁溫度高于氣體溫度，因為壓縮過程中壓縮氣體的熱流動。腔壁面覆蓋著一層潤滑油膜，當(dāng)油被注入時，油膜從相鄰的壓縮空間中泄露。該熱量從熱吸氣腔壁（潤滑油膜）轉(zhuǎn)移到吸入氣體中，這個過程可估算為如下表達(dá)式表示：</p><p>　　如果吸入氣體溫度升高相對于潤滑油膜與吸入氣體的溫差很小時，噴入的潤滑油和氣體之間的熱傳遞表達(dá)如下：</p>

88、<p>　　在理想條件下，油膜熱損失必須等于新氣體獲得的熱量。從方程（1）和（2）得 ，吸氣過程終了時的吸入氣體溫度為</p><p>　　吸氣條件下，吸入幾何體積中的氣體質(zhì)量為</p><p>　　是一對陰陽轉(zhuǎn)子氣腔的幾何體積，由參考文獻(xiàn)[3]給出如下：</p><p>　　和為陰陽氣腔的橫截面積，L為轉(zhuǎn)子長度。</p><p>

89、　　在吸入氣腔的氣體在條件下的質(zhì)量可由如下表達(dá)式估算：</p><p>　　氣體質(zhì)量是新吸入氣體質(zhì)量()和葉間容積的泄露質(zhì)量()之和</p><p>　　等式（5）和（6）減去總質(zhì)量 ，在吸氣過程中吸入氣體質(zhì)量如下：</p><p>　　帶入的值到等式（3）中，氣體溫度就可獲得下面的二次方程：</p><p>　　2.2 壓縮和排氣過程 &l

90、t;/p><p>　　壓縮和排氣過程都是不穩(wěn)定過程。潤滑油和氣體的熱力學(xué)性質(zhì)在壓縮過程中不斷變化。工作腔中的氣體被旋轉(zhuǎn)的轉(zhuǎn)子壓縮到高壓狀態(tài)。為了簡化分析，假定潤滑油和氣體是孤立的流體，它們之間只有熱交換關(guān)系。排氣出口是如此的近以至于氣腔和出口相連，工作腔里的壓力達(dá)到設(shè)計的排氣壓力，而且連續(xù)排氣直到陽轉(zhuǎn)子的凸起部分完全脫離陰轉(zhuǎn)子凹下去部分。</p><p>　　模型中，下列因素被考慮到：<

91、/p><p>　　1.由于轉(zhuǎn)子旋轉(zhuǎn)導(dǎo)致的容積變化；2.通過排氣出口和滲漏路徑，氣體進(jìn)入和排出工作腔時的質(zhì)量和焓流動；3.通過排氣出口和滲漏路徑，潤滑油進(jìn)入和排出工作腔時的質(zhì)量和焓流動； 4.潤滑油和氣體之間的熱交換。</p><p>　　為了簡化計算，做如下假設(shè)：</p><p>　　?潤滑油和氣體溫度均勻分布于工作腔。 ?潤滑油和氣體狀態(tài)永遠(yuǎn)不改變。 ?任何

92、階段的整個工作腔的壓力是統(tǒng)一的。 ?工作氣體為理想氣體。 ?潤滑油為不可壓縮流體。 ?氣體和潤滑油的熱交換與溫差成比例。 ?忽略排氣通道的壓力波動。</p><p>　　基于標(biāo)準(zhǔn)的熱力學(xué)定律和理想氣體定律，F(xiàn)ujiwara和Osada [ 4 ]推導(dǎo)了基本方程。下面推導(dǎo)出的方程做了進(jìn)一步的修改和其它必要細(xì)節(jié)的介紹。</p><p>　　工作腔中，不穩(wěn)定流動氣體的熱力學(xué)第一定律表示為

93、：</p><p>　　是內(nèi)能，勢能和動能的總和。假設(shè)忽略氣體的勢能和動能，上面的方程中內(nèi)能在時間內(nèi)的變化量由下式計算：</p><p>　　內(nèi)能的改變量同樣可以由質(zhì)量和溫度變化方程表示，如下：</p><p>　　由于泄漏而改變的焓表示為</p><p>　　氣體做功可由能幾何體積的變化來表示，潤滑油體積變化是由于泄漏。由于潤滑油是一種不可

94、壓縮液體，氣體做功表示為</p><p>　　氣體和潤滑油在時間內(nèi)的熱交換，我們假設(shè)服從冷卻的牛頓定律，表達(dá)如下：</p><p>　　將(11)–(14)帶入(10)，整理有做功氣體的溫度變化率為：</p><p>　　右邊等式的第一項與體積的變化有關(guān)，包括潤滑油的泄漏率。第二項和第三項表示壓縮腔氣體泄漏進(jìn)和漏出的影響。最后一項由氣體到潤滑油的熱傳導(dǎo)推導(dǎo)而來。&l

95、t;/p><p>　　工作腔凈氣體體積變化率[4]如下：</p><p>　　由于內(nèi)部泄漏而產(chǎn)生的質(zhì)量變化率表達(dá)如下：</p><p>　　理想氣體狀態(tài)方程如下：</p><p>　　上式有不同表達(dá)形式，如：</p><p>　　將等式（15）—（17）帶入等式（18），得到壓力變化率的式子如下：</p>&

96、lt;p>　　在泄漏潤滑油溫度和氣體熱交換方面，潤滑油溫度變化率可由能量守恒推導(dǎo)而得。工作腔中潤滑油溫度的升高是由于從泄漏的油（它的溫度較高）和壓縮狀態(tài)下的氣體中獲得了能量。</p><p>　　假設(shè)忽略勢能和動能，在工作腔中的潤滑油焓的變化可由下式確定：</p><p>　　式中為泄漏潤滑油的熱損失。</p><p>　　潤滑油在時間內(nèi)焓的變化量為：<

97、/p><p>　　潤滑油做功為零（如）,因為潤滑油為不可壓縮流體。在時間內(nèi)潤滑油獲得的能量為：</p><p>　　工作腔的潤滑油溫度高于儲油罐里的油溫。漏油導(dǎo)致的能量損失由下式給出：</p><p>　　將等式（21）—（23）帶入等式（20），則潤滑油的溫度變化率如下：</p><p>　　由泄漏導(dǎo)致工作腔中潤滑油得質(zhì)量改變率的計算公式如下：

98、</p><p>　　2.3 氣體和潤滑油的泄漏計算</p><p>　　螺桿壓縮機主要關(guān)心的是泄漏。泄漏的主要途徑為壓縮過程通過葉間間隙、通過氣孔、轉(zhuǎn)子葉尖間隙和轉(zhuǎn)子排氣末端與氣腔壁的間隙泄漏[ 5-7 ] 。通過葉間間隙的泄漏質(zhì)量將直接進(jìn)入吸氣腔中。除在凸齒間隙外，泄漏的氣體和油會均勻混合，并且流體是孤立于任何周圍環(huán)境的熱交換，同時保持熱平衡。在這項研究中，假設(shè)泄漏率服從廣為人知的噴嘴

99、流動方程[ 8,9 ]</p><p>　　式中，和分別表示上游和下游的壓力。</p><p>　　因潤滑油的存在，油氣混合物的確切性質(zhì)不知道。然而，基于合理的假設(shè)和實驗數(shù)據(jù)，油氣混合物的性質(zhì)是可以計算的。通過實驗測試比較，下面的假設(shè)是不同類型的泄漏途徑，已經(jīng)被證明為最合適的[ 5 ]</p><p>　　（1）所有泄漏途徑中氣/油混合是一致的。 （2）除了凸起頂

100、部的間隙外，所有的泄漏途徑中氣/油混合比例是相同的，且等于排氣通道的混合比例。 油和氣的比熱可由參考文獻(xiàn)[ 4 ]計算：</p><p>　　修改后的混合氣體常數(shù)同樣可由參考文獻(xiàn)[4]計算得：</p><p>　　工作腔潤滑油相對于氣體的質(zhì)量比例以及通過所有滲漏路徑是一致的，且等于工作容積比例[ 5 ] ，并表示如下：</p><p>　　平均滲漏面積由密

101、封線長度乘以每種泄漏類型平均寬度（間隙）決定的。通常情況下，從壓縮機實際測量間隙來確定平均寬度/間隙。排氣或流量系數(shù)，在潤滑油的計算中完全由經(jīng)驗選定。在葉間頂部，由于離心力作用，假定間隙填充潤滑油，且潤滑油泄漏流體是單相。潤滑油的泄漏率可以由不可壓縮粘性流體流過窄縫的方程[10]計算得到如下：</p><p>　　工作腔中泄漏氣體質(zhì)量率通過氣孔，通過轉(zhuǎn)子排氣終了和陰陽轉(zhuǎn)子的氣腔壁間隙。它可以由以下表達(dá)式計算出：&

102、lt;/p><p>　　氣體泄漏質(zhì)量通過后孔、葉間間隙、通過絕熱腔尾部和腔壁的間隙、最后流出工作腔，排氣終了時陰陽轉(zhuǎn)子可表示為：</p><p>　　相似地，進(jìn)入和排出工作腔的潤滑油質(zhì)量泄漏率由下式給出：</p><p>　　關(guān)于壓縮和排氣過程，等式（26）—（34）用來計算氣體和潤滑油的質(zhì)量變化率已經(jīng)足夠了。</p><p><b>