Experimental and computational investigation of flow structure of buoyancy induced flow in heated rotating cavities
Authors: Fazeli Seyed Mostafa , Kanjirakkad Vasudevan , Long Christopher 
Published: September 2021

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<sub>k</sub></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.