螺杆压缩机性能的计算吸入室中占主导地位外文文献翻译@中英文翻译@外文翻译

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 中文译文 33.1 一维数学模型 51 内部能量守恒 . ddvpQhmhmdQdu outoutinin += (3.1) 其中 是角度的旋转的主旋翼 h =h（ ）的比焓， m =m （ ）是质量流率 p = （ ） ，工作腔的控制体积中的流体压力， Q = Q（ ）的流体之间的热传递和压缩机周围， V = V （ ） ，压缩机工作腔中的本地卷。 在上述方程中，输入和输出的下标表示的流体流入及流出。 流体的总焓流入由以下组件： o i lo i lglgls u cs u vinin hmhmhmh .,.m (3.2) 其中，下标 L， G 表示泄漏增益 SUC ，抽吸条件，和油为石油。 流体总流出焓包括： lllld isd isouo u t hmhmhm ,. (3.3) 指数升， l 表示泄漏损耗和 dis 表示放电条件与 m显示表示放电注入的油或其它液体污染的气体的质量流率 右手 法 侧的能量方程由模型的下列术语 流体和压缩机的螺杆转子和壳体，并通过它们的周边，由于气体的温度 的 差异， 上 述壳体和转子的表面之间的热交换的传热系数求值表达式 = 0.023， RE0 占 .8 。通过主转子的外径和内径之间 的差异为特征长度的雷诺数和努塞尔数。这可能不是用于此目的的最合适的尺寸，但出现的特征长度在 0.2 的指数部分的传热系数的表达式，因此，只要它表征压缩机的体积 ， 它仍然在同一个数量级，作为其他特征尺寸的影响不大的机器。特征速度为 Re 数的计算从本机的质量流量和横截面面积。这里的表面，在其上进行热交换，以及壁温，依靠的主旋翼的旋转角度 。 上述 所表示的商品的大量摄入量和其平均焓由于工作体积的气体流入的能量增益 决定 。因此，能量的流入的旋转角变化。在吸入期间， 等于 气体进入工作容积带来的平均气体焓 。 52 3 螺杆压缩机性 能的计算吸入室中占主导地位。 然而，在吸入口关闭时，一定量的压缩气体通过间隙泄漏到压缩机工作腔 。该气体的质量，以及其焓 在 气体泄漏方程的基础上确定。工作体积充满了气体，由于泄漏，只有当工作体积周围的空间中的气体压力较高，否则无泄漏，或它是在相反的方向，即从对其他压力通风系统的工作腔。 总流入焓进一步校正的焓的量带入工作腔注入的油。 由于从工作体积的气体流出的能量损失是指由商品质量的流出和平均气体焓。在 工作过程中，这是进入排放气室，被压缩的气体的同时，在扩展的情况下，由于不适当的排出压力，这是通过在较低压力下 工作体积到邻近的空间的间隙泄漏的气体。如果工作腔中的压力低于在排出室，排放口是打开的，该流程将在相反的方向，即从排出气室进入工作腔。质量的变化，有一个负号 其假定的焓等于压力腔中的平均气体焓。 供给的工作气体在压缩过程中的热力学表示由术语 PdV d 。这个术语是从本地的压力和体积变化率进行评估。后者被定义产生瞬时工作体积和其旋转角度的变化的螺杆运动学的关系得到的。事实上，术语的 dV /差 d可确定瞬时 interlobe 区，捕获和重叠区域校正。 如果油或其它流体注入 上 述压缩机的工作腔，油质量的流入和 其焓应包括在流入条款 而 事实，尽管在混合物中的油的质量分数显着的体积流率时，其效果是 不明显的 ，因为油的体积分数通常是非常小的。总流出的流体的质量，还包括注入的油，其中的较大部分仍然与工作流体混合。气体之间的热传递和油滴描述由一个一阶微分方程 确定 。 质量连续性方程 outoutinin hmhmddm (3.4) 质量连续性方程 o ilgle u cinin mmmhm , (3.5) 3.1 一维数学模型 53 质量的流出率包括： lldisout mmm , (3.6) 质量流率的每一个 方程 满足连续性方程 Am . (3.7) 其中 W m/s表示流体速度， - 流体密度和 A - 流 体 截面区域。得到的瞬 时密度 = （ ）被困在控制量与相应的瞬时体积 V 的大小从瞬时的质量为 m ， 密度 为 =m/ V 。 3.1.2 吸气和排气口 从压缩机的几何形状的横截面面积 A 得到的旋转角度 ， 它可以被认为是周期函数。吸气口区域被定义为： s u cos u cAA s in,s u c (3.8) SUC 装置上面的吸气口开口，并且 ASUC 的时刻开始的 值， 0 表示为在吸入口的横截面面积的最大值。 如果未指定不同的旋转角度 的基准值，吸入口关闭 时， 假设 在 吸管 末端 = 0。 排放口区同样被定义为： ce cod i sd i s AA s in, （ 3.9） 其中下标 e 表示放电结束， c 表示排出口的横截面面积的最大值压缩和 ADIS ， 0 表示结束。 吸入和排出端口流体速度 ）（ 12 h-h2 （ 3.10） 其中， 为吸入 /排放孔的流量系数，而下标 1 和 2 表示所考虑的端口的上游和下游 ， 在计算机代码 中 提供计算，如 果 H2 H1 反向流动。 54 3 螺杆压缩机性能的计算 3.1.3 气体泄漏 泄漏量的主要部分 是 总流速的螺纹机，因此发挥了重要作用，因为它们影响的过程都影响了压缩机的质量流率或压缩机送货，即容积效率和压缩工作的热力学效率。对于实际计算时压缩机的过程中泄漏的影响，这是方便区分 的 两种类型泄漏，根据他们的方向方面的工作室：增益和损失的泄漏。增益来自排放气室，并从相邻的工作腔室 获得 ，其中有一个较高的压力泄漏。亏损泄漏离开吸气室和邻近腔室向具有较低的压力 的腔室流动 。 泄漏速度 的 计算如下考虑的流体流过的间隙。 该过程本质上是绝热 的 Fanno 流。为了简化计算，该流程是有时被假设为在恒定的温度 条件下 ，而不是在等焓。此 处 出发从当时的绝热条件下进行分析以差的形式，小的旋转角的变化 来表示 ，即在本模型中， 泄漏 只有很轻微的影响。本模型只 考虑 气体泄漏 ， 没有尝试考虑到泄漏的气 - 液混合物中，可掺入适当减少间隙的间隙油膜的 影响 效果。 一个理想化的间隙被假定为具有矩形形状，并漏出的液体的质量流量的连续性方程所表达： glll Am . (3.11) = （ Re,Ma） ，其中 r 和 w 是泄漏气体的密度和速度， Ag= lgg 表示 间隙的横截面面积， lg 代表 泄漏间隙的长度，封口线， g表示 泄漏间隙的宽度或间隙，泄漏流排放系数。 在螺杆式压缩机：领先的尖端密封线之间形成的主栅极的转子 指 向尖端和套管， 落 后的顶端密封线主栅极反向尖端和套管之间形成四个不同的密封线来区分，前部之间的密封线排出转子正面壳体和转子之间的密封线 interlobe 。所有密封线有间隙差距形成泄漏区域。此外，叶顶间隙泄漏区域伴随着通过吹孔区。 据的类型和位置的泄漏间隙， 5 个不同的泄漏可以被识别，即：通过后前端密封和通过领先和前密封的密封和收益损失。第五，的 “ throughleakage ”不直接影响在工作腔内的过程，而是通过从排放气室向吸入口。 泄漏的气体速度是来自动量方程， 粘 液壁的摩擦 3.1 一维数学模型 55 02211 Dgdxfdpd l （ 3.12） 其中 f （ Re， Ma）的摩擦系数，这是依赖于雷诺数和马赫数， Dg 是间隙的有效直径， Dg 2g 和 dx 的长度增量。 从连续性方程，并假设 T常量来消除压力的气体密度，该方程可以被集成在压力从位置 2 处的高压侧到低压侧的间隙，得到 1 位： 1222122ln2 ppaAm gll (3.13) 其中， = fLg / Dg+ 泄漏流电阻的特点， Lg 表示 间隙泄漏流方向， f 表示 摩擦系数和局部阻力系数 ， 代表间隙 长度。 可以评价为每个间隙为一个函数，它的尺寸和形状和流动特