Experimental and computational investigation of flow structure of buoyancy induced flow in heated rotating cavities

This paper presents Laser-Doppler Anemometry (LDA) measurements obtained from the Sussex Multiple Cavity test facility. This facility comprises a number of heated disc cavities with a cool bore flow and is intended to emulate the secondary air system flow in an H.P compressor. Measurements were made of the axial and tangential components of velocity over the respective range of Rossby, Rotational and Axial Reynolds numbers, (Ro, <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mtext>R</mml:mtext><mml:msub><mml:mtext>e</mml:mtext><mml:mi>θ</mml:mi></mml:msub></mml:math></inline-formula> and<inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mrow><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">R</mml:mi></mml:mrow><mml:msub><mml:mtext>e</mml:mtext><mml:mi>z</mml:mi></mml:msub></mml:math></inline-formula>),<inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mrow><mml:mspace width="0.25em"/></mml:mrow><mml:mn>0.32</mml:mn><mml:mo><</mml:mo><mml:mtext>Ro</mml:mtext><mml:mo><</mml:mo><mml:mn>1.28</mml:mn></mml:math></inline-formula>,<inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mrow><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">R</mml:mi></mml:mrow><mml:msub><mml:mtext>e</mml:mtext><mml:mi>θ</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>7.1</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>5</mml:mn></mml:msup></mml:math></inline-formula>, <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mn>1.2</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>4</mml:mn></mml:msup><mml:mo><</mml:mo><mml:mrow><mml:mspace width="0.25em"/><mml:mi mathvariant="normal">R</mml:mi></mml:mrow><mml:msub><mml:mtext>e</mml:mtext><mml:mi>z</mml:mi></mml:msub><mml:mo><</mml:mo><mml:mn>4.8</mml:mn><mml:mo>×</mml:mo><mml:msup><mml:mn>10</mml:mn><mml:mn>4</mml:mn></mml:msup></mml:math></inline-formula> and for the values of the buoyancy parameter <inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:mi>β</mml:mi><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi></mml:mrow><mml:mtext>T</mml:mtext></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:math></inline-formula> :<inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:mrow><mml:mspace width="0.25em"/></mml:mrow><mml:mn>0.50</mml:mn><mml:mo><</mml:mo><mml:mrow><mml:mspace width="0.25em"/><mml:mi>β</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">Δ</mml:mi></mml:mrow><mml:mtext>T</mml:mtext><mml:mo><</mml:mo><mml:mn>0.58</mml:mn></mml:math></inline-formula>. The frequency spectra analysis of the tangential velocity indicates the existence of pairs of vortices inside the cavities. The swirl number, <italic>X_k</italic>, calculated from these measurements show that the cavity fluid approaches solid body rotation near the shroud region. The paper also presents results from Unsteady Reynolds-Averaged Navier-Stokes (URANS) calculations for the test case where Ro = 0.64. The time-averaged LDA data and numerical results show encouraging agreement.

Inner rocky super-Earth formation: distinguishing the formation pathways in viscously heated and passive discs

Observations have revealed that super-Earths (planets up to 10 Earth masses) are the most abundant type of planets in the inner systems. Their formation is strongly linked to the structure of the protoplanetary disc, which determines growth and migration. In the pebble accretion scenario, planets grow to the pebble isolation mass, at which the planet carves a small gap in the gas disc halting the pebble flux and thus its growth. The pebble isolation mass scales with the disc’s aspect ratio, which directly depends on the heating source of the protoplanetary disc. I compare the growth of super-Earths in viscously heated discs, where viscous heating dissipates within the first million years, and discs purely heated by the central star with super-Earth observations from the Kepler mission. This allows two formation pathways of super-Earths to be distinguished in the inner systems within this framework. Planets growing within 1 Myr in the viscously heated inner disc reach pebble isolation masses that correspond directly to the inferred masses of the Kepler observations for systems that feature planets in resonance or not in resonance. However, to explain the period ratio distribution of Kepler planets – where most Kepler planet pairs are not in mean motion resonance configurations – a fraction of these resonant chains has to be broken. In case the planets are born early in a viscously heated disc, these resonant chains thus have to be broken without planetary mergers, for example through the magnetic rebound effect, and the final system architecture should feature low mutual inclinations. If super-Earths form either late or in purely passive discs, the pebble isolation mass is too small (around 2–3 Earth masses) to explain the Kepler observations, implying that planetary mergers have to play a significant role in determining the final system architecture. Resonant planetary systems thus have to experience mergers already during the gas disc phase, so the planets can get trapped in resonance after reaching 5–10 Earth masses. In case instabilities are dominating the system architecture, the systems should not be flat, but feature mutually inclined orbits. This implies that future observations of planetary systems with radial velocities (RV) and transits (for example through the Transiting Exoplanet Survey Satellite (TESS) and its follow up RV surveys) could distinguish between these two formation channels of super-Earth and thus constrain planet formation theories.

Buoyancy-Induced Flow in Open Rotating Cavities

Buoyancy-induced flow can occur in the cavity between the co-rotating compressor discs in gas-turbine engines, where the Rayleigh numbers can be in excess of 1012. In most cases the cavity is open at the centre, and an axial throughflow of cooling air can interact with the buoyancy-induced flow between the discs. Such flows can be modeled, computationally and experimentally, by a simple rotating cavity with an axial flow of air. This paper describes work conducted as part of ICAS-GT, a major European research project. Experimental measurements of velocity, temperature and heat transfer were obtained on a purpose-built experimental rig, and these results have been reported in an earlier paper. In addition, 3D unsteady CFD computations were carried out using a commercial code (Fluent) and an RNG k-ε turbulence model. The computed velocity vectors and contours of temperature reveal a flow structure in which, as seen by previous experimenters, ‘radial arms’ transport cold air from the centre to the periphery of the cavity, and regions of cyclonic and anti-cyclonic circulation are formed on either side of each arm. The computed radial distribution of the tangential velocity agrees reasonably well with the measurements in two of the three cases considered here. In the third case, the computations significantly over-predict the measurements; the reason for this is not understood. The computed and measured values of Nu for the heated disc show qualitatively similar radial distributions, with high values near the centre and the periphery. In two of the cases, the quantitative agreement is reasonably good; in the third case, the computations significantly under-predict the measured values.

Buoyancy-Induced Flow in a Heated Rotating Cavity

Experimental measurements were made in a rotating-cavity rig with an axial throughflow of cooling air at the centre of the cavity, simulating the conditions that occur between corotating compressor discs of a gas-turbine engine. One of the discs in the rig was heated, and the other rotating surfaces were quasi-adiabatic; the temperature difference, between the heated disc and the cooling air was between 40 and 100 °C. Tests were conducted for axial Reynolds numbers, Rez, of the cooling air between 1.4 × 103 and 5 × 104, and for rotational Reynolds numbers, Reφ, between 4 × 105 and 3.2 × 106. Velocity measurements inside the rotating cavity were made using LDA, and temperatures and heat flux measurements on the heated disc were made using thermocouples and fluxmeters. The velocity measurements were consistent with a 3D, unsteady, buoyancy-induced flow in which there was a multicell structure comprising one, two or three pairs of cyclonic and anti-cyclonic vortices. The core of fluid between the boundary layers on the discs rotated at a slower speed than the discs, as found by other experimenters. At the smaller values of Rez, the radial distribution and magnitude of the local Nusselt numbers, Nu, were consistent with buoyancy-induced flow. At the larger values of Rez, the distribution of Nu changed, and its magnitude increased, suggesting the dominance of the axial throughflow.