螺桿壓縮機(jī)性能的計算吸入室中占主導(dǎo)地位外文文獻(xiàn)翻譯@中英文翻譯@外文翻譯

英文原文 3.1 One Dimensional Mathematical Model 51 The Conservation of Internal Energy . ddvpQhmhmdQdu outoutinin += （ 3.1） where is angle of rotation of the main rotor, h = h( ) is specific enthalpy, m = m ( ) is mass flow rate p = p( ), fluid pressure in the working chamber control volume, Q = Q( ), heat transfer between the fluid and the compressor surrounding, V = V ( ) local volume of the compressor working chamber. In the above equation the subscripts in and out denote the fluid inflow and outflow. The fluid total enthalpy inflow consists of the following components: o ilo ilglgls u cs u vinin hmhmhmh .,.m += (3.2) where subscripts l, g denote leakage gain suc, suction conditions, and oil denotes oil. The fluid total outflow enthalpy consists of: lllld isd isouout hmhmhm ,. += (3.3) where indices l, l denote leakage loss and dis denotes the discharge conditions with m dis denoting the discharge mass flow rate of the gas contaminated with the oil or other liquid injected. The right hand side of the energy equation consists of the following terms which are model The heat exchange between the fluid and the compressor screw rotors and casing and through them to the surrounding, due to the difference in temperatures of gas and the casing and rotor surfaces is accounted for by the heat transfer coefficient evaluated from the expression Nu = 0.023 Re0.8. For the characteristic length in the Reynolds and Nusselt number the difference between the outer and inner diameters of the main rotor was adopted. This may not be the most appropriate dimension for this purpose, but the characteristic length appears in the expression for the heat transfer coefficient with the exponent of 0.2 and therefore has little influence as long as it remains within the same order of magnitude as other characteristic dimensions of the machine and as long as it characterizes the compressor size. The characteristic velocity for the Re number is computed from the local mass flow and the cross-sectional area. Here the surface over which the heat is exchanged, as well as the wall temperature, depend on the rotation angle of the main rotor. The energy gain due to the gas inflow into the working volume is represented by the product of the mass intake and its averaged enthalpy. As such, the energy inflow varies with the rotational angle. During the suction period, gas enters the working volume bringing the averaged gas enthalpy, 52 3 Calculation of Screw Compressor Performance which dominates in the suction chamber. However, during the time when the suction port is closed, a certain amount of the compressed gas leaks into the compressor working chamber through the clearances. The mass of this gas, as well as its enthalpy are determined on the basis of the gas leakage equations. The working volume is filled with gas due to leakage only when the gas pressure in the space around the working volume is higher, otherwise there is no leakage, or it is in the opposite direction, i.e. from the working chamber towards other plenums. The total inflow enthalpy is further corrected by the amount of enthalpy brought into the working chamber by the injected oil. The energy loss due to the gas outflow from the working volume is defined by the product of the mass outflow and its averaged gas enthalpy. During delivery, this is the compressed gas entering the discharge plenum, while, in the case of expansion due to inappropriate discharge pressure, this is the gas which leaks through the clearances from the working volume into the neighbouring space at a lower pressure. If the pressure in the working chamber is lower than that in the discharge chamber and if the discharge port is open, the flow will be in the reverse direction, i.e. from the discharge plenum into the working chamber. The change of mass has a negative sign and its assumed enthalpy is equal to the averaged gas enthalpy in the pressure chamber. The thermodynamic work supplied to the gas during the compression process is represented by the term pdV d . This term is evaluated from the local pressure and local volume change rate. The latter is obtained from the relationships defining the screw kinematics which yield the instantaneous working volume and its change with rotation angle. In fact the term dV/d can be identified with the instantaneous interlobe area, corrected for the captured and overlapping areas. If oil or other fluid is injected into the working chamber of the compressor, the oil mass inflow and its enthalpy should be included in the inflow terms. In spite of the fact that the oil mass fraction in the mixture is significant, its effect upon the volume flow rate is only marginal because the oil volume fraction is usually very small. The total fluid mass outflow also includes the injected oil, the greater part of which remains mixed with the working fluid. Heat transfer between the gas and oil droplets is described by a first order differential equation. The Mass Continuity Equation o u to u tinin hmhmd md. = （ 3.4） The mass inflow rate consists of: o ilgls u cinin mmmhm .,. （ 3.5） 3.1 One Dimensional Mathematical Model 53 The mass outflow rate consists of: . ,. lldisout mmm (3.6) Each of the mass flow rate satisfies the continuity equation Am . (3.7) where wm/s denotes fluid velocity, fluid density and A the flow crosssection area. The instantaneous density = ( ) is obtained from the instantaneous mass m trapped in the control volume and the size of the corresponding instantaneous volume V , as = m/V . 3.1.2 Suction and Discharge Ports The cross-section area A is obtained from the compressor geometry and it may be considered as a periodic function of the angle of rotation . The suction port area is defined by: su cosu cAA sin,su c (3.8) where suc means the starting value of at the moment of the suction port opening, and Asuc, 0 denotes the maximum value of the suction port crosssection area. The reference value of the rotation angle is assumed at the suction port closing so that suction ends at = 0, if not specified differently. The discharge port area is likewise defined by: se cod isAA s in,d is (3.9) where subscript e denotes the end of discharge, c denotes the end of compression and Adis, 0 stands for the maximum value of the discharge port crosssectional area. Suction and Discharge Port Fluid Velocities )(2 12 hh (3.10) where is the suction/discharge orifice flow coefficient, while subscripts 1 and 2 denote the conditions downstream and upstream of the considered port. The provision supplied in the computer code will calculate for a reverse flow if h2 h1. 54 3 Calculation of Screw Compressor Performance 3.1.3 Gas Leakages Leakages in a screw machine amount to a substantial part of the total flow rate and therefore play an important role because they influence the process both by affecting the compressor mass flow rate or compressor delivery, i.e. volumetric efficiency and the thermodynamic efficiency of the compression work. For practical computation of the effects of leakage upon the compressor process, it is convenient to distinguish two types of leakages, according to their direction with regard to the working chamber: gain and loss leakages. The gain leakages come from the discharge plenum and from the neighbouring working chamber which has a higher pressure. The loss leakages leave the chamber towards the suction plenum and to the neighbouring chamber with a lower pressure. Computation of the leakage velocity follows from consideration of the fluid flow through the clearance. The process is essentially adiabatic Fanno-flow. In order to simplify the computation, the flow is is sometimes assumed to be at constant temperature rather than at constant enthalpy. This departure from the prevailing adiabatic conditions has only a marginal influence if the analysis is carried out in differential form, i.e. for the small changes of the rotational angle, as followed in the present model. The present model treats only gas leakage. No attempt is made to account for leakage of a gas-liquid mixture, while the effect of the oil film can be incorporated by an appropriate reduction of the clearance gaps. An idealized clearance gap is assumed to have a rectangular shape and the mass flow of leaking fluid is expressed by the continuity equation: glll Am . (3.11) where r and w are density and velocity of the leaking gas, Ag = lg g the clearance gap cross-sectional area, lg leakage clearance length, sealing line, g leakage clearance width or gap, = (Re, Ma) the leakage flow discharge coefficient. Four different sealing lines are distinguished in a screw compressor: the leading tip sealing line formed between the main and gate rotor forward tip and casing, the trailing tip sealing line formed between the main and gate reverse tip and casing, the front sealing line between the discharge rotor front and the housing and the interlobe sealing line between the rotors. All sealing lines have clearance gaps which form leakage areas. Addit ionally, the tip leakage areas are accompanied by blow-hole areas. According to the type and position of leakage clearances, five different leakages can be identified, namely: losses through the trailing tip sealing and front sealing and gains through the leading and front sealing. The fifth, “ throughleakage” does not directly affect the process in the working chamber, but it passes through it from the discharge plenum towards the suction port. The leaking gas velocity is derived from the momentum equation, which accounts for the fluid-wall friction: 3.1 One Dimensional Mathematical Model 55 02211 Dgdxfdpd l (3.12) where f(Re, Ma) is the friction coefficient which is dependent on the Reynolds and Mach numbers, Dg is the effective diameter of the clearance gap, Dg 2 g and dx is the length increment. From the continuity equation and assuming that T const to eliminate gas density in terms of pressure, the equation can be integrated in terms of pressure from the high pressure side at position 2 to the low pressure side at position 1 of the gap to yield: 1222122.ln2mppaA gll (3.13) where = fLg/Dg + characterizes the leakage flow resistance, with Lg clearance length in the leaking flow direction, f friction factor and local resistance coefficient. can be evaluated for each clearance gap as a function of its dimensions and shape and flow characteristics. a is the speed of sound. The full procedure requires the model to include the friction and drag coefficients in terms of Reynolds and Mach numbers for each type of clearance. Likewise, the working fluid friction losses can also be defined in terms of the local friction factor and fluid veloc ity related to the tip speed, density, and elementary friction area. At present the model employs the value of in terms of a simple function for each particular compressor type and use. It is determined as an input parameter. These equations are incorporated into the model of the compressor and employed to compute the leakage flow rate for each clearance gap at the local rotation angle . 3.1.4 Oil or Liquid Injection Injection of oil or other liquids for lubrication, cooling or sealing purposes, modifies the thermodynamic process in a screw compressor substantially. The following paragraph outlines a procedure for accounting for the effects of oil injection. The same procedure can be applied to treat the injection of any other liquid. Special effects, such as gas or its condensate mixing and dissolving in the injected fluid or vice versa should be accounted for separately if they are expected to affect the process. A procedure for incorporating these phenomena into the model will be outlined later. A convenient parameter to define the injected oil mass flow is the oil-to-gas mass ratio, moil/mgas, from which the oil inflow through the open oil port, which is assumed to be uniformly distributed, can be evaluated as 2 1. zmmmmgaso ilo il (3.14) where the oil-to-gas mass ratio is specified in advance as an input parameter 56 3 Calculation of Screw Compressor Performance In addition to lubrication, the major purpose for injecting oil into a compressor is to cool the gas. To enhance the cooling efficiency the oil is atomized into a spray of fine droplets by means of which the contact surface between the gas and the oil is increased. The atomization is performed by using specially designed nozzles or by simple high-pressure injection. The distribution of droplet sizes can be defined in terms of oil-gas mass flow and velocity ratio for a given oil-injection system. Further, the destination of each distinct size of oil droplets can be followed until it hits the rotor or casing wall by solving the dynamic equation for each droplet size in a Lagrangian frame, accounting for inertia gravity, drag, and other forces. The solution of the droplet energy equation in parallel with the momentum equation should yield the amount of heat exchange with the surrounding gas. In the present model, a simpler procedure is adopted in which the heat exchange with the gas is determined from the differential equation for the instantaneous heat transfer between the surrounding gas and an oil droplet. Assuming that the droplets retain a spherical form, with a prescribed Sauter mean droplet diameter dS, the heat exchange between the droplet and the gas can be expressed in terms of a simple cooling law Qo = hoAo(Tgas Toil), where Ao is the droplet surface, Ao = d2 S , dS is the Sauter mean diameter of the droplet and ho is the heat transfer coefficient on the droplet surface, determined from an empirical expression. The exchanged heat must balance the rate of change of heat taken or given away by the droplet per unit time, Qo = mocoildTo/dt = mocoil dTo/d , where coil is the oil specific heat and the subscript o denotes oil droplet. The rate of change of oil droplet temperature can now be expressed as: o iloog a so cm TTAhddT 00 (3.15) The heat transfer coefficient ho is obtained from: 33.06.0 PrRe6.02u N (3.16) Integration of the equation in two time/angle steps yields the new oil droplet temperature at each new time/angle step: kkTTT pogaso 1 , (3.17) where To,p is the oil droplet temperature at the previous time step and k is the non-dimensional time constant of the droplet, k = / t = / , with = mocoil/hoAo being the real time constant of the droplet. For the given Sauter mean diameter, dS, the non-dimensional time constant takes the form o o ilSOo o ilo h cdAh cmk 6 (3.18) The derived droplet temperature is further assumed to represent the average temperature of the oil, i.e. Toil To, which is further used to compute the enthalpy of the gas-oil mixture. 3.1 One Dimensional Mathematical Model 57 The above approach is based on the assumption that the oil-droplet time constant is smaller than the droplet travelling time through the gas before it hits the rotor or casing wall, or reaches the compressor discharge port. This means that heat exchange is completed within the droplet travelling time through the gas during compression. This prerequisite is fulfilled by atomization of the injected oil. This produces sufficiently small droplet sizes to gives a small droplet time constant by choosing an adequate nozzle angle, and, to some extent, the initial oil spray velocity. The droplet trajectory computed independently on the basis of the solution of droplet momentum equation for different droplet mean diameters and initial velocities. Indications are that for most screw compressors currently in use, except, perhaps for the smallest ones, with typical tip speeds of between 20 and 50m/s, this condition is well satisfied for oil droplets with diameters below 50 m. For more details refer to Stosic et al., 1992. Because the inclusion of a complete model of droplet dynamics would complicate the computer code and the outcome would always be dependant on the design and angle of the oil injection nozzle, the present computation code uses the above described simplified approach. This was found to be fully satisfactory for a range of different compressors. The input parameter is only the mean Sauter diameter of the oil droplets, dS and the oil properties density, viscosity and specific heat. 3.1.5 Computation of Fluid Properties In an ideal gas, the internal thermal energy of the gas-oil mixture is given by: o ilo ilgaso ilgas m c TpVm c Tm R TmumuT 11 (3.19) where R is the gas constant and is adiabatic exponent Hence, the pressure or temperature of the fluid in the compressor working chamber can be explicitly calculated by input of the equation for the oil temperature Toil: o ilO I LmcmRk m c TUkT 111 (3.20) If k tends 0, i.e. for high heat transfer coefficients or small oil droplet size, the oil temperature fast approaches the gas temperature. In the case of a real gas the situation is more complex, because the temperature and pressure can not be calculated explicitly. However, since the internal energy can be expressed as a function of the temperature and specific volume only, the calculation procedure can be simplified by employing the internal energy as a dependent variable instead of enthalpy, as often is the practice. The equation of state p = f1(T,V ) and the equation for specific internal energy u = f2(T,V ) are usually decoupled. Hence, the temperature can be calculated from the known specific internal energy and the specific volume obtained from the solution of differential equations, whereas the pressure 中文譯文 33.1 一維數(shù)學(xué)模型 51 內(nèi)部能量守恒 . ddvpQhmhmdQdu outoutinin += (3.1) 其中 是角度的旋轉(zhuǎn)的主旋翼 h =h（ ）的比焓， m =m （ ）是質(zhì)量流率 p = （ ） ，工作腔的控制體積中的流體壓力， Q = Q（ ）的流體之間的熱傳遞和壓縮機(jī)周圍， V = V （ ） ，壓縮機(jī)工作腔中的本地卷。 在上述方程中，輸入和輸出的下標(biāo)表示的流體流入及流出。 流體的總焓流入由以下組件： o i lo i lglgls u cs u vinin hmhmhmh .,.m (3.2) 其中，下標(biāo) L， G 表示泄漏增益 SUC ，抽吸條件，和油為石油。 流體總流出焓包括： lllld isd isouo u t hmhmhm ,. (3.3) 指數(shù)升， l 表示泄漏損耗和 dis 表示放電條件與 m顯示表示放電注入的油或其它液體污染的氣體的質(zhì)量流率 右手 法 側(cè)的能量方程由模型的下列術(shù)語 流體和壓縮機(jī)的螺桿轉(zhuǎn)子和殼體，并通過它們的周邊，由于氣體的溫度 的 差異， 上 述殼體和轉(zhuǎn)子的表面之間的熱交換的傳熱系數(shù)求值表達(dá)式 = 0.023， RE0 占 .8 。通過主轉(zhuǎn)子的外徑和內(nèi)徑之間 的差異為特征長度的雷諾數(shù)和努塞爾數(shù)。這可能不是用于此目的的最合適的尺寸，但出現(xiàn)的特征長度在 0.2 的指數(shù)部分的傳熱系數(shù)的表達(dá)式，因此，只要它表征壓縮機(jī)的體積 ， 它仍然在同一個數(shù)量級，作為其他特征尺寸的影響不大的機(jī)器。特征速度為 Re 數(shù)的計算從本機(jī)的質(zhì)量流量和橫截面面積。這里的表面，在其上進(jìn)行熱交換，以及壁溫，依靠的主旋翼的旋轉(zhuǎn)角度 。 上述 所表示的商品的大量攝入量和其平均焓由于工作體積的氣體流入的能量增益 決定 。因此，能量的流入的旋轉(zhuǎn)角變化。在吸入期間， 等于 氣體進(jìn)入工作容積帶來的平均氣體焓 。 52 3 螺桿壓縮機(jī)性 能的計算吸入室中占主導(dǎo)地位。 然而，在吸入口關(guān)閉時，一定量的壓縮氣體通過間隙泄漏到壓縮機(jī)工作腔 。該氣體的質(zhì)量，以及其焓 在 氣體泄漏方程的基礎(chǔ)上確定。工作體積充滿了氣體，由于泄漏，只有當(dāng)工作體積周圍的空間中的氣體壓力較高，否則無泄漏，或它是在相反的方向，即從對其他壓力通風(fēng)系統(tǒng)的工作腔。 總流入焓進(jìn)一步校正的焓的量帶入工作腔注入的油。 由于從工作體積的氣體流出的能量損失是指由商品質(zhì)量的流出和平均氣體焓。在 工作過程中，這是進(jìn)入排放氣室，被壓縮的氣體的同時，在擴(kuò)展的情況下，由于不適當(dāng)?shù)呐懦鰤毫?，這是通過在較低壓力下 工作體積到鄰近的空間的間隙泄漏的氣體。如果工作腔中的壓力低于在排出室，排放口是打開的，該流程將在相反的方向，即從排出氣室進(jìn)入工作腔。質(zhì)量的變化，有一個負(fù)號 其假定的焓等于壓力腔中的平均氣體焓。 供給的工作氣體在壓縮過程中的熱力學(xué)表示由術(shù)語 PdV d 。這個術(shù)語是從本地的壓力和體積變化率進(jìn)行評估。后者被定義產(chǎn)生瞬時工作體積和其旋轉(zhuǎn)角度的變化的螺桿運(yùn)動學(xué)的關(guān)系得到的。事實(shí)上，術(shù)語的 dV /差 d可確定瞬時 interlobe 區(qū)，捕獲和重疊區(qū)域校正。 如果油或其它流體注入 上 述壓縮機(jī)的工作腔，油質(zhì)量的流入和 其焓應(yīng)包括在流入條款 而 事實(shí)，盡管在混合物中的油的質(zhì)量分?jǐn)?shù)顯著的體積流率時，其效果是 不明顯的 ，因?yàn)橛偷捏w積分?jǐn)?shù)通常是非常小的?？偭鞒龅牧黧w的質(zhì)量，還包括注入的油，其中的較大部分仍然與工作流體混合。氣體之間的熱傳遞和油滴描述由一個一階微分方程 確定 。 質(zhì)量連續(xù)性方程 outoutinin hmhmddm (3.4) 質(zhì)量連續(xù)性方程 o ilgle u cinin mmmhm , (3.5) 3.1 一維數(shù)學(xué)模型 53 質(zhì)量的流出率包括： lldisout mmm , (3.6) 質(zhì)量流率的每一個 方程 滿足連續(xù)性方程 Am . (3.7) 其中 W m/s表示流體速度， - 流體密度和 A - 流 體 截面區(qū)域。得到的瞬 時密度 = （ ）被困在控制量與相應(yīng)的瞬時體積 V 的大小從瞬時的質(zhì)量為 m ， 密度 為 =m/ V 。 3.1.2 吸氣和排氣口 從壓縮機(jī)的幾何形狀的橫截面面積 A 得到的旋轉(zhuǎn)角度 ， 它可以被認(rèn)為是周期函數(shù)。吸氣口區(qū)域被定義為： s u cos u cAA s in,s u c (3.8) SUC 裝置上面的吸氣口開口，并且 ASUC 的時刻開始的 值， 0 表示為在吸入口的橫截面面積的最大值。 如果未指定不同的旋轉(zhuǎn)角度 的基準(zhǔn)值，吸入口關(guān)閉 時， 假設(shè) 在 吸管 末端 = 0。 排放口區(qū)同樣被定義為： ce cod i sd i s AA s in, （ 3.9） 其中下標(biāo) e 表示放電結(jié)束， c 表示排出口的橫截面面積的最大值壓縮和 ADIS ， 0 表示結(jié)束。 吸入和排出端口流體速度 ）（ 12 h-h2 （ 3.10） 其中， 為吸入 /排放孔的流量系數(shù)，而下標(biāo) 1 和 2 表示所考慮的端口的上游和下游 ， 在計算機(jī)代碼 中 提供計算，如 果 H2 H1 反向流動。 54 3 螺桿壓縮機(jī)性能的計算 3.1.3 氣體泄漏 泄漏量的主要部分 是 總流速的螺紋機(jī)，因此發(fā)揮了重要作用，因?yàn)樗鼈冇绊懙倪^程都影響了壓縮機(jī)的質(zhì)量流率或壓縮機(jī)送貨，即容積效率和壓縮工作的熱力學(xué)效率。對于實(shí)際計算時壓縮機(jī)的過程中泄漏的影響，這是方便區(qū)分 的 兩種類型泄漏，根據(jù)他們的方向方面的工作室：增益和損失的泄漏。增益來自排放氣室，并從相鄰的工作腔室 獲得 ，其中有一個較高的壓力泄漏。虧損泄漏離開吸氣室和鄰近腔室向具有較低的壓力 的腔室流動 。 泄漏速度 的 計算如下考慮的流體流過的間隙。 該過程本質(zhì)上是絕熱 的 Fanno 流。為了簡化計算，該流程是有時被假設(shè)為在恒定的溫度 條件下 ，而不是在等焓。此 處 出發(fā)從當(dāng)時的絕熱條件下進(jìn)行分析以差的形式，小的旋轉(zhuǎn)角的變化 來表示 ，即在本模型中， 泄漏 只有很輕微的影響。本模型只 考慮 氣體泄漏 ， 沒有嘗試考慮到泄漏的氣 - 液混合物中，可摻入適當(dāng)減少間隙的間隙油膜的 影響 效果。 一個理想化的間隙被假定為具有矩形形狀，并漏出的液體的質(zhì)量流量的連續(xù)性方程所表達(dá)： glll Am . (3.11) = （ Re,Ma） ，其中 r 和 w 是泄漏氣體的密度和速度， Ag= lgg 表示 間隙的橫截面面積， lg 代表 泄漏間隙的長度，封口線， g表示 泄漏間隙的寬度或間隙，泄漏流排放系數(shù)。 在螺桿式壓縮機(jī)：領(lǐng)先的尖端密封線之間形成的主柵極的轉(zhuǎn)子 指 向尖端和套管， 落 后的頂端密封線主柵極反向尖端和套管之間形成四個不同的密封線來區(qū)分，前部之間的密封線排出轉(zhuǎn)子正面殼體和轉(zhuǎn)子之間的密封線 interlobe 。所有密封線有間隙差距形成泄漏區(qū)域。此外，葉頂間隙泄漏區(qū)域伴隨著通過吹孔區(qū)。 據(jù)的類型和位置的泄漏間隙， 5 個不同的泄漏可以被識別，即：通過后前端密封和通過領(lǐng)先和前密封的密封和收益損失。第五，的 “ throughleakage ”不直接影響在工作腔內(nèi)的過程，而是通過從排放氣室向吸入口。 泄漏的氣體速度是來自動量方程， 粘 液壁的摩擦 3.1 一維數(shù)學(xué)模型 55 02211 Dgdxfdpd l （ 3.12） 其中 f （ Re， Ma）的摩擦系數(shù)，這是依賴于雷諾數(shù)和馬赫數(shù)， Dg 是間隙的有效直徑， Dg 2g 和 dx 的長度增量。 從連續(xù)性方程，并假設(shè) T常量來消除壓力的氣體密度，該方程可以被集成在壓力從位置 2 處的高壓側(cè)到低壓側(cè)的間隙，得到 1 位： 1222122ln2 ppaAm gll (3.13) 其中， = fLg / Dg+ 泄漏流電阻的特點(diǎn)， Lg 表示 間隙泄漏流方向， f 表示 摩擦系數(shù)和局部阻力系數(shù) ， 代表間隙 長度。 可以評價為每個間隙為一個函數(shù)，它的尺寸和形狀和流動特