Numerical Analysis in the Flow Field of a Labyrinth Seal

This paper pRisents nwneric:a.l analysis of the incompressible turbulent flow field in a single cavity of the stepped multi-cavity seal. The dimensionless bulk pressure drop for the cavity with and without groove has been investigated for four different Reynolds numbers and three different shaft ro~ating speeds. SIMPLER algoritlun is applied to solve the NavierStokes equation and lowReynolds number ke equation which takes turbulent flow into account For the constant Reynolds number, it was found th3t the dimensionless pressure drop is proportional to shaft speed. Especially, the increment is higher at the low Reynolds number and lower at the high Reynolds nwnber. At no shaft ro~ation, the dimensionless bulk pressure drop is increased linearly with Reynolds number. When the axial speed is relatively high in comparision with the circumferential speed, the groove in a cavity creates high pressure drop giving low leakage. NOMENCLATURE c :annular clearance cl 'c2' <;: empiric:a.l tuzbulent model conslants k :turbulent kinetic energy K : dimensionless turbulence kinetic energy , klu!. p :pressure P :dimensionless pressure, plpu!, Re: Reynolds number, 2u mC I u, R,: turbulent Reynolds nwnber, k I'IJ1£ U :o (U, V, W) dimensionless timemean velocity , u/u m u = (u,v,w) time-mean velocity (in X, r, 8 direction) Urn : il.ltial entrance velocity u' : flucruation velocity X , r , 6 : axial, IlldiaJ and circumferential coordinates X,R : dimensionless axial and circumferential coordinates, x/c and r/c.respectivel y e : energy dissipation rare e· : dimensionless energy dissipation rate, e/ (u!. I c) u'; dimensionless dynamic viscosity ' 1l I u mC 1l • : effective dynan:Uc viscosity, 1l 1 + 1l , u,: dynamic viscosity 'll,: turbulent dynamic viscosity, c. k I e p: density l!k : Prandti-Schmidt number fork c,: Prandti-Scbmidt number fore