The flow structure of a rotating cavity with axial throughflow is reviewed, firstly the isothermal flow scenario is considered and then the buoyancy-induced flow of the non- isothermal case.
2.2.1 Isothermal Flow
FIGURE2.2: Schematic diagram of flow structure in an isothermal rotating
cavity with axial throughflow, r-z plane, from Owen and Long (2015)
Figure 2.2 shows a simplified diagram of the flow inside a rotating isothermal cavity, where the axial throughflow creates a toroidal vortex in the cavity. An increase in ro- tational speed has the effect of suppressing the toroidal vortex whilst an increase in the throughflow extends the radial extent of the vortex. Owen and Pincombe (1979) used
Laser-Doppler Anemometry (LDA) and flow visualisation on a simplified isothermal ro- tating cavity where G = 0.53 and a/b = 0.1 without a central shaft. Tests were conducted over 0.8 < Ro < ∞. The extent of the toroidal vortex was observed to decrease with Ro; radially outward of the vortex solid-body rotation occurred. Inside the toroidal vor- tex the tangential velocity to disc rotational speed or swirl ratio Vθ/Ωr was observed to
exceed 1.
Farthing et al. (1992b) used similar LDA and flow visualisation techniques in four different rotating cavities, where a/b ≈ 0.1 in all cases with gap ratios over the range 0.133 < G < 0.533 without a central shaft. The Rossby number was varied such that 1 <Ro < ∞ with constant axial Reynolds number Rez= 5000. A phenomena referred to
as vortex breakdown which has been observed as axisymmetric or non-axisymmetric was found. In the latter the central throughflow departs from the central axis and precesses around the cavity creating non-axisymmetric flow in the cavity. This was also observed by Owen and Pincombe (1979). The radial extent of the toroidal vortex was seen to de- crease with Ro and G.
2.2.2 Nonisothermal Flow
In the nonisothermal case buoyancy-induced flow becomes dominant. Farthing et al. (1992b) found that when the rotating cavity is heated, either symmetrically (both discs heated) or asymmetrically (only one disc heated) the flow develops into a non-axisymmetric system of cyclonic and anti-cyclonic circulations. The axial throughflow enters the cavity radially via a structure referred to as a radial arm, similar to a rising plume of smoke, and bifurcates into two circulation zones. A dead zone was found between the two zones, so- called as no smoke was seen to enter the core area. However a radial inflow was observed to occur in the Ekman layers (Figure 2.3). Three gap ratios, 0.12 < G < 0.27 were tested using smoke visualisation and found to exhibit highly unsteady 3D buoyancy-induced flow in all cases. The LDA measurements showed that the core of the cavity flow had a swirl ratio of slightly less than one, indicating it precessed slower than the discs. Though there was an effect of G, ∆T and Ro, typically it was found that 0.9 < Vθ/Ωr < 1.
FIGURE2.3: Schematic diagram of flow structure in a nonisothermal rotat- ing cavity with an axial throughflow r-θ plane, from Farthing et al. (1992b)
Bohn et al. (2000) used ammonium chloride smoke and laser sheet illumination on the cavity mid-axial plane, with symmetrically heated discs and axial throughflow. A co-rotating central shaft was used with a/b = 0.3, G = 0.2 and dh/b = 0.09. Though
the working parameters - 2 × 105 <Re
θ < 8 × 105 and 2 × 104 <Rez < 7 × 104 - were
markedly different, similar flow structures to those found by Farthing et al. (1992b) were observed. The visualisation results indicated laminar behaviour across all experimental conditions with a swirl ratio typically 0.88 < Vθ/Ωr < 0.9. Qualitative observations
were made of the cyclonic, anti-cyclonic, radial arm and dead zone, referred to as the centripetal zone. Figure 2.4 shows the mid-axial plane in the centripetal zone, where there is an indication of a radially inflowing structure (leftmost picture central dark zone) with smoke structures rolling up on either side indicating this may be a jet, moving faster than the surrounding flow.
Owen and Powell (2004) obtained LDA measurements in an axial throughflow rig with working parameters 4 × 105 <Reθ < 3.2 × 106and 0.05 < Ro < 14 for a/b = 0.4 and
G = 0.2. Only the downstream disc was heated and a central shaft was used. Spectral analysis of the velocity measurements indicated a multi-celled flow structure consisting of one, two or three pairs of cyclonic and anti-cyclonic circulations. The steady-state time- averaged LDA results indicated a swirl ratio 0.96 < Vθ/Ωr < 0.99for 0.67 < x < 0.97.
Long, Miche, and Childs (2007) presented LDA measurements from the University of Sussex Multiple Cavity Rig (MCR). This rig is a 70% replica of a HP compressor rotor
FIGURE2.4: Flow visualisation of centripetal zone by Bohn et al. (2000)
with a/b = 0.318 and G = 0.195. Similar to an engine, the shroud was heated directly via an external supply of pressurised hot air. The rig also featured an axial throughflow of cooling air and a central shaft that could co-rotate, counter-rotate or remain stationary. Figure 2.5 shows a schematic of the MCR used by Long, Miche, and Childs (2007), LDA measurements were taken from cavities 2 and 3.
FIGURE2.5: The Multiple Cavity Rig (MRC) from Long, Miche, and Childs (2007)
Figure 2.6 shows the values of swirl ratio Vθ/Ωr across a range of Rossby numbers
and two different values of dh/b, referred to as wide and narrow with dh/b = 0.164 and
dh/b = 0.092respectively. Although there is a tendency for increasing Ro to increase the
FIGURE 2.6: Radial distribution of swirl ratio, Vθ/Ωrin a rotating cavity with axial throughflow showing the effects of clearance ratio, dh/b and
Rossby number, Ro, from Long, Miche, and Childs (2007)
ratio. In all cases the value of Vθ/Ωrtends to one in the outer part of the cavity and the
toroidal vortex is thought suppressed at lower radius for all narrow cases as the swirl ratio is less than one. It was also shown that the axial velocities inside the cavity were essentially zero, consistent with the Taylor-Proudman theorem, and that radial velocities were comparable to relative tangential velocities.