【導(dǎo)讀】努塞爾數(shù)是流體的雷諾功能數(shù)和普朗特?cái)?shù)，以及流體與材料導(dǎo)熱系數(shù)比例三者。最后的結(jié)論認(rèn)為在熱源位于轉(zhuǎn)子和定子的接觸處，并取決于固體溫度分布。該冷卻油流似乎不影響塞爾系數(shù)。數(shù)值計(jì)算結(jié)果通過(guò)與采用紅外線照相機(jī)對(duì)實(shí)驗(yàn)密。封裝置測(cè)試的結(jié)果比較，得到驗(yàn)證。存在壓力，溫度和速度，因而不能使用彈性體密封。這些密封裝置通常是由安裝在。體上的靜止部分組成。液保持接觸（圖1）。形和可能的相變會(huì)使?jié)櫥瑺顩r發(fā)生改變。對(duì)這些變化的可能導(dǎo)致密封泄漏率增大或。然而，在密封裝置里產(chǎn)生熱量的重要組成部。中Bruiere進(jìn)行的數(shù)值研究使這一假設(shè)得到了證實(shí)。測(cè)量的努塞爾數(shù)接近Gazley[9]andBecker. 體流動(dòng)，尤其是密封中軸向冷卻流和由角運(yùn)動(dòng)誘發(fā)的環(huán)泰勒流的相互作用。較小程度上，進(jìn)行試驗(yàn)分析。時(shí)，密封受內(nèi)壓和運(yùn)用高粘度礦物油造成層流。此外，軸未通過(guò)封腔，導(dǎo)致類似轉(zhuǎn)。數(shù)值仿真允許作者提出對(duì)于旋轉(zhuǎn)和固定部位的雷諾數(shù)，努塞爾

　　

【正文】 he rotor by pressurized air acting on the top surface of the annular piston. The thermal properties of the materials of the seal ponents are given in Table 1. Hydraulic equipment provides oil at controlled pressure and temperature. The oil is a mineral ISO VG 46. Its characteristics are presented in Table 2. The typical operating conditions and the main dimensions of the mechanical face seal are detailed in Table 3. . Physical background The oil flow in the mechanical face seal is similar to the flow between a static and a rotating disk with a corotating shroud. Owen and Rogers [18] suggested employing the following Reynolds number to characterize the flow regime: 2e RR ???? （ 1） There is a superposed flow due to the oil circulation whose mass flow rate is m˙. We can introduce the nondimensional flow rate proposed by Owen and Rogers: W mC R?? (2) The flow is also a function of a geometric parameter, this being the gap ratio: HG R? (3) In the simulations presented here, the geometrical configuration remains constant with the axial clearance H.=. mm, R.=. mm leading to G.=. and the Reynolds is varied from about 600 to 8000 (see Table 4). In 1960, Daily and Neece [19] analyzed experimentally an enclosed rotating disc. They observed four different regimes varying with the value of the gap ratio the Reynolds number Re. According to their regime chart, the present seal operates in regime II, that is to say a laminar flow with two separated boundary layers, one on each disc Table 1. Material thermal characteristics and assignment Thermal conductivity k（ W/m ℃） Element Carbon 15 Rotor Stainless steel 46 Shaft,piston ,supports ,expander 英文文獻(xiàn)翻譯 Calcium fluoride Stator Elastomer seals Table 2 Fluid properties Density ρ（ Kg/m3） 850 Specific heat Cp（ J/Kg℃） 2020 Thermal conductivity k（ W/m℃） Dynamic viscosity μ（ Pas） (35℃ ) Table 3 Operating conditions and principal dimensions Angular velocity ω（ rpm） 3001500 Fluid pressure （ Pa） 50000 Inlet fluid temperature（℃） 35 Mass flow ratem? （ kg/s） Inner radius of the rotor R(m) Outer radius of the rotor R0（ m） Inner radius of the disk Ri（ m） Axial clearance H（ m） Disk thickness E（ m） The secondary cooling flow provides a circulation of oil from the rotating part to the stationary part. This is similar to the flow induced by the centrifugal effect. The nondimensional flow rate is varied from to 80. The heat transfer in the fluid is a function of the flow characteristics and thus depends on the Reynolds number, the flow rate and the gap ratio. However, there is a difference in thermal behaviour and mechanical behaviour that is quantified by the Prandtl number: r CpP k?? （ 4） This number more particularly controls the ratio of the thickness of the momentum boundary layer δm to that of the thermal boundary layer δt. According to Schlichting [20]: 英文文獻(xiàn)翻譯 m rt P?? ? （ 5） In the present case the Prandtl number of the oil is varied from 330 to 1330, leading to a ratio value for the thicknesses of the boundary layers of 18 to 36. In most cases described in the Owen and Rogers book [18], there is an analogy between the mechanical problem and the thermal problem because there is a uniform heat source on the rotating disc that is also obviously a uniform momentum source. In the present case, the heat source is located in the sealing interface. Thus the Nusselt number also depends on the temperature distribution in the seal rings, this being a function of the material properties. It is necessary to introduce another dimensionless parameter: rkk 或 skk （ 6） that is, the ratio of the fluid conductivity k to the conductivity of the solid under consideration (ks for the stator and kr for the rotor). The variation range of the dimensionless numbers are given in Table 4. Table 4 Range variation of the dimensionless numbers Reynolds number Re 6008000 Dimensionless mass flow Cw Gap ration G Prandtl number 3301330 Rotor conductivity ratio k/kr Stator conductivity ratio k/ks 3. Numerical model The simulations were performed by means of the putational fluid dynamic code (CFD) Fluent. The problem is assumed to be axisymmetric. The mesh and the boundary conditions used in the numerical analysis are presented in Fig. 3. The twodimensional axisymmetric Navier–Stokes equations, incorporating the 英文文獻(xiàn)翻譯 circumferential velocity term and continuity equation are solved in the fluid domain. Moreover a tangential momentum equation is also considered for the swirling ponent of the velocity. As previously said, the fluid flow is laminar. Since the pressure value is not of interest in our study, an inlet mass flow condition is applied at the oil inlet section. It provides a uniform fluid velocity distribution along the inlet section, its magnitude being calculated with respect to the specified mass flow. An outflow condition is used for the outlet section. This condition leads to a zero diffusion flux for all flow variables and ensures an overall mass balance. The zero diffusion flux is physically reached when the flow is fully developed, that is a reasonable assumption when considering the length of the outlet annular pipe (see Fig. 2). Finally, an angular velocity is applied to the rotating walls as indicated in Fig. 3. The energy equation is solved for the whole domain, including solids and fluid. Because of the high viscosity of the oil, the viscous dissipation is considered in the energy equation. The fluid entering the seal has a uniform temperature of 35 .C. Since it is not possible nor reasonable to solve the lubrication equations in the rotor stator contac