Analysis of Flux of Gas Passing Circle Lacuna

Journal of Marine Seience and Application, vol. I, No. 2, December 2002Analysis of Flux of Gas Passing Circle LacunaZHAO Shi-jun, SUN Ke-yu, YU Xiu-pingAutomation College, Harbin Engineering University, Harbin 150001, chinaAbstract: The rate of flow of the gas fowing through cirque chink often needs calculation in engineering. The characters of com-pressibility and thermodynamics have some effect on the gas nowing, so the analysis on the flow of gas is more complex than thatof liquid. But under different conditions and different requirements of precision the analysis can be simplified suitably, then makethe formulae given become simple subsequently. This paper analyzes various gas Alux based on basic characters and motion laws oflysis is just applied in an engineering project.Key words: circle lacuna; compressible fluid; incompressible fluid; density inertial forceCLC number: V211 Document code: A Article ID: 1671-9433(2002)02-0037-05such as compressibility. So we should consider the0 Introductioneffect when we calculate gas flux. For example forThe flow rate of the gas flowing through cirquechink often needs calculation in engineering. Forcirque chink ranges from 0. 025 mm to 0. 082 mmwith its length of 1200 mm and pressure dispatch of 1ample, to measure the leakage of oil pump in oil pro- MPa. As a result, the density and the flowing velocityduction, a cirque chink is just formed between thepillar and the inner wall of pump, and the effect ofat the entrance are distinctly different from those atthis cirque chink on productivity can be evaluated exit, and the volume flux in different positions is alsothrough measuring the leakage of oil pump. Diesel oil different distinctly in the direction of gas flow.Thechange must be considered in calculfluxway, but this way is not so convenient. In order todesign a measuring system with the measuring medium 1 Air flux formulae for the case ofof gas, the rate of gas flowing through this cirqueincompressible flowchink needs to be calculated. Theoretically speakingit's more complex to calculate gas flux than to do thatIn order to make the analysis convenient a threeof liquid, due to its nature, e. g. compressibility and dimensional coordinate system XYZ )is built asits thermodynamic behavior. In practice, complex for- shown in figurel(b). Among this coordinate, x de-mulae are often simplified to some degree according to notes the direction of gas flow, namely the direction ofthe circumstances and requirements of precision. The chinks length; Y denotes the direction of lacunasformulae about air flux given in many paImely the direction of lacunas thicknesstained by considering gas as incompressible, so these Z denotes the direction of lacunas width. The widthformulae are not suitable at some occasions where the is in fact the girth of cirque chink( the girth is dcompressibility factor cant be ignored. This can be where, d denotes the diameter of cirque chink ). Leseen in the cirque chink of oil pump shown above with the length, thickness, width to be denoted by 1, 6, 8e nature of little thickness, long length and big respectively. Po denotes absolute pressure in the frontpressure dispatch, so the gas flowing in this cirque of theute pressure in thechink must be affected by the gas intrinsic nature backH中国煤化工at the point(X,y)CNMHGReceived date: 2002-09-22Journal of Marine Science and Application, Vol. 1, No. 2, December 2002a control element exist, in front of which the pres-2{uY(Y-8),(6)sure is P+dP. and at its back the pressure is Pd P. The element length is dX, height is d Y, ande=budr=2u d XbY(Y-8dY=b is width. In steady follow condition the total forceb8 dPon the element is balanced, i. e. the pressures at12ud xfront and at the back of the element keep balancewhere Q is the volume flux at point(X, Y);with viscous forces at the top and at the bottom of theConsidering p of the gas is constant in the direcelementtion of flow, and if the pressure gradient along-axb[P-(P+dP)]dY=d PbLT-(T+ dr)]dX,(1)Isis a constant. l.e.constant as△Pd Xd yaps dxd(2)Pso we get the formulae for flux as fol-where T is shearing stress(3)b63△P12△P,where Q is themass fluxat point(X, Y). Eq(8)and eq.(9)are respectively thee formulaevolume flux and mass flux for an incompressible gasflow through a cirque chink, For eccentric cirque la-(a)configuration of cirque chinkcuna as shown in Figure 2. formula for mass flux ofan be expressedQ=1+1.5△P,(10)where e is eccentric quantum and 8=(D-d)/2 isaverrage thickness of the lacuna. When the lacuna islong, neither the axis nor the outer pipe is absolutely(b)force of control componentunbent. Partial touch of them is inevitable. So theresult of calculation can be corrected by a coefficientFig. 1 Principle ofk in practice(11)shearing stress in the laminar flow is as follows:Qn=k1△P,1