Inertial waves in turbine rim seal flows

Rotating fluids are well-known to be susceptible to waves. This has received much attention from the geophysics, oceanographic and atmospheric research communities. Inertial waves, which are driven by restoring forces, for example, the Coriolis force, have been detected in the research fields mentioned above. This paper investigates inertial waves in turbine rim seal flows in turbomachinery. These are associated with the large-scale unsteady flow structures having distinct frequencies, unrelated to the main annulus blading, identified in many experimental and numerical studies. These unsteady flow structures have been shown in some cases to reduce sealing effectiveness and are difficult to predict with conventional steady Reynolds-averaged Navier-Stokes (RANS) approaches. Improved understanding of the underlying flow mechanisms and how these could be controlled is needed to improve the efficiency and stability of gas turbines. This study presents large-eddy simulations for three rim seal configurations—chute, axial, and radial rim seals—representative of those used in gas turbines. Evidence of inertial waves is shown in the axial and chute seals, with characteristic wave frequencies limited within the threshold for inertial waves given by classic linear theory (i.e., $|f^{*}/f_{\mathrm{rel}}|\le 2$) and instantaneous flow fields showing helical characteristics. The radial seal, which limits the radial fluid motion with the seal geometry, restricts the Coriolis force and suppresses the inertial wave.

Figure 1

Illustration of a typical rim seal configuration in an axial turbine stage and principal flow mechanisms.

Figure 2

Schematics of three typical rim seal configurations. Geometrical parameters are in millimetres, and the surfaces of rotating components are highlighted with thick solid lines.

Figure 3

Meshes at the rim seal clearances. Dark lines correspond to elements. Gray lines represent polynomial submeshes. (a) Chute seal, (b) Axial seal, and (c) Radial seal.

Figure 4

Mesh resolutions at the seal clearances. Black: $\mathrm{\Delta }{y}^{+}$. Red: $\mathrm{\Delta }{s}^{+}$, i.e., the direction parallel to the seal geometry in the meridional plane. Blue: $\mathrm{\Delta }{\left(r\theta \right)}^{+}$. Solid curves: stationary component side. Dashed curves: rotating component side. Cav.: cavity. Ann.: annulus.

Figure 5

Mean pressure distribution. (a) Comparison of Semtex, previous LES solution [30], and experimental results [27] for the chute seal configuration. (b) Semtex solutions for the three seal types. $r$ is the local radius, and $x$ is the axial position.

Figure 6

Mean streamwise (in parallel with the seal geometry on a meridional plane) velocity profiles within the seal overlap. (a) Chute, (b) Axial, and (c) Radial.

Figure 7

FFT of unsteady pressure data. $f/f_d$ denotes the frequency normalized with the disk frequency. (a) Chute, (b) Axial, and (c) Radial.

Figure 8

Instantaneous flow fields illustrated with swirl ratio contours. The extraction planes are given by the left insets.

Figure 9

Instantaneous flow fields illustrated with the circumferential ($v_{\theta }$), streamwise ($v_s$, in parallel to the seal geometry) velocities and the pressure coefficient. Sampling planes are constructed by extruding the middle sampling lines shown in Fig. 6. R: rotating component wall. S: stationary component wall. The direction of rotation is from right to left. Velocity units are m/s. (a) Chute, (b) Axial, and (c) Radial.

Figure 10

Instantaneous velocity fields on cross sections at different circumferential positions. The time corresponds to that in Fig. 9. $v_x/\left(\mathrm{\Omega }b\right)$ and $v_r/\left(\mathrm{\Omega }b\right)$ represent nondimensional axial and radial velocities. (a) Contour of $v_x/\left(\mathrm{\Omega }b\right)$ at $\theta =5°$. Ingestion, (b) Contour of $v_x/\left(\mathrm{\Omega }b\right)$ at $\theta =15°$. Egestion, (c) Contour of $v_r/\left(\mathrm{\Omega }b\right)$ at $\theta =50°$. Ingestion, (d) Contour of $v_r/\left(\mathrm{\Omega }b\right)$ at $\theta =20°$. Egestion, and (e) Contour of $v_x/\left(\mathrm{\Omega }b\right)$ at $\theta =30°$.

Figure 11

Instantaneous helicity density $[\mathbf{u}·\mathit{\omega }/(\left|\mathbf{u}\right|\left|\mathit{\omega }\right|\left)\right]$ plots in the relative frame of reference rotating with the mean flow core. Contours are taken at two time instants differing by one rotor revolution time. The second plot of each seal is at the same time as results in Fig. 9. Sampling planes are constructed by extruding the middle sampling lines shown in Fig. 6. R: rotating component wall. S: stationary component wall. The direction of rotation is from right to left. (a) Chute, (b) Axial, and (c) Radial.

Figure 12

Instantaneous velocities in the relative frame of reference rotating with the mean flow core. Samples are taken at the center between the stationary and rotating components in Fig. 9. The direction of rotor's movement is from right to left.

Figure 13

Instantaneous relative tangential and radial velocities, and pressure for the axial seal. Zoomed view of data shown in Fig. 12 between $\theta ={50}^{\circ }$ and ${60}^{\circ }$. Flow moves from right to left.

Figure 14

Schematic of ingestion and egestion flow through rim seal affected by an inertial wave.