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Research Papers

# Prediction of Ingestion Through Turbine Rim Seals—Part II: Externally Induced and Combined Ingress

[+] Author and Article Information
J. Michael Owen

Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK

J. Turbomach 133(3), 031006 (Nov 12, 2010) (9 pages) doi:10.1115/1.4001178 History: Received July 23, 2009; Revised August 10, 2009; Published November 12, 2010; Online November 12, 2010

## Abstract

Ingress of hot gas through the rim seals of gas turbines can be modeled theoretically using the so-called orifice equations. In Part I of this two-part paper, the orifice equations were derived for compressible and incompressible swirling flows, and the incompressible equations were solved for axisymmetric rotationally induced (RI) ingress. In Part II, the incompressible equations are solved for nonaxisymmetric externally induced (EI) ingress and for combined EI and RI ingress. The solutions show how the nondimensional ingress and egress flow rates vary with $Θ0$, the ratio of the flow rate of sealing air to the flow rate necessary to prevent ingress. For EI ingress, a “saw-tooth model” is used for the circumferential variation of pressure in the external annulus, and it is shown that $ε$, the sealing effectiveness, depends principally on $Θ0$; the theoretical variation of $ε$ with $Θ0$ is similar to that found in Part I for RI ingress. For combined ingress, the solution of the orifice equations shows the transition from RI to EI ingress as the amplitude of the circumferential variation of pressure increases. The predicted values of $ε$ for EI ingress are in good agreement with the available experimental data, but there are insufficient published data to validate the theory for combined ingress.

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## Figures

Figure 1

Variation of Cw,min with Rew for axial-clearance seal, Gc=0.01(4). For Reϕ/106, ○:=0, ◻:=0.2; ▽:=0.4; △:=0.6; ×:=0.8; ▼:=1.0; ▲:=1.2.

Figure 8

Circumferential distribution of Cp,2: Solid line is for Conf 1a of Johnson (19) Dashed line is equivalent saw-tooth distribution

Figure 9

Variation of ε with Φ0 for Confs 1a and 1c. Rectangular blocks represent range of experimental data (15); dashed line represents orifice model of Johnson (19); solid line represents saw-tooth model with Γc=1.

Figure 10

Variation of ε with Φ0. Symbols represent experimental data of Johnson (21); solid line represents saw-tooth model with Γc=1.

Figure 11

Variation of Cw,min,com/Cw,min,RI with ΓΔp1/2 according to Eq. 57 with Cd,e/Cd,e′=1

Figure 2

Variation of Cw,min with Pmax(4) (symbols represent experimental data; line corresponds to Eq. 21)

Figure 3

Variation of Cw,min with Cp,max(14) (symbols represent experimental data; lines correspond to correlations)

Figure 4

Arbitrary circumferential variation of pressure and radial velocity in external annulus

Figure 5

Circumferential variation of pressure and radial velocity for saw-tooth model: (a) circumferential variation of p1 and p2; (b) circumferential variation of Vr

Figure 6

Variation of Cw,e,Cw,i and ε with Cw,0 for saw-tooth model (Cd,i=Cd,e)

Figure 7

Effect of Cd,i/Cd,e on variation of ε with Cw,o. Solid line, saw-tooth model; dashed line, RI ingress.

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