Prabu Balasubramanian
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Prabu Balasubramanian has a total of 2 co-authors. Here are the top co-authors by number of shared publications:
- Andrew Cowell
Department of Engineering, School of Science and Engineering, Glasgow Caledonian University, Cowcaddens Road, Glasgow G4 0BA, UK
1 shared publication - Don McGlinchey
School of Computing, Engineering and Built Environment, Glasgow Caledonian University, Glasgow G4 0BA, UK
1 shared publication
Latest Publications
- Open Access
- 25 November 2025
- Published by MDPI AG in Applied Sciences
- Vol. 15 (23) , 12503
A Phase Map for Vertical Upflow of Slightly Cohesive Geldart A Powders Focused on High Solids Mass Flux
Flow regimes of vertical upflow for slightly cohesive Geldart A powders at high solids mass flux ( 500 kg/m2s) are not fully resolved. In particular, Dense Suspension Upflow (DSU) as a distinct flow regime and its transition boundaries are not broadly accepted. Furthermore, the locus of the pressure gradient minimum, which is the broadly accepted dense–dilute transition at low requires validation at high . In our recent work, by adapting the phase map of Wirth and by Eulerian modeling, DSU was defined as a distinct flow regime with gross upflow of solids and with granular temperature at the wall greater than that in the bulk. This study has further validated the definition of DSU and its transition boundaries by extending the modeling to areas not fully explored in the earlier work. Furthermore, this study has identified (a) the possibility of a phase of DSU between fast fluidization and turbulent regime at all ; and (b) the need to review the suitability of the locus of the pressure gradient minimum as the dense–dilute transition at high . Additionally, our work has demonstrated (a) a new provisional correlation that the upper transport velocity for Geldart A powders is significantly greater than hitherto predicted; and (b) the slip velocity in the transport regimes increases with to peak within fast fluidization and falls thereafter to attain low multiples of the terminal settling velocity within DSU.- 25 November 2025
- Published by MDPI AG in Applied Sciences
- Vol. 15 (23) , 12503
Open AccessA Phase Map for Vertical Upflow of Slightly Cohesive Geldart A Powders Focused on High Solids Mass Flux
Flow regimes of vertical upflow for slightly cohesive Geldart A powders at high solids mass flux ( 500 kg/m2s) are not fully resolved. In particular, Dense Suspension Upflow (DSU) as a distinct flow regime and its transition boundaries are not broadly accepted. Furthermore, the locus of the pressure gradient minimum, which is the broadly accepted dense–dilute transition at low requires validation at high . In our recent work, by adapting the phase map of Wirth and by Eulerian modeling, DSU was defined as a distinct flow regime with gross upflow of solids and with granular temperature at the wall greater than that in the bulk. This study has further validated the definition of DSU and its transition boundaries by extending the modeling to areas not fully explored in the earlier work. Furthermore, this study has identified (a) the possibility of a phase of DSU between fast fluidization and turbulent regime at all ; and (b) the need to review the suitability of the locus of the pressure gradient minimum as the dense–dilute transition at high . Additionally, our work has demonstrated (a) a new provisional correlation that the upper transport velocity for Geldart A powders is significantly greater than hitherto predicted; and (b) the slip velocity in the transport regimes increases with to peak within fast fluidization and falls thereafter to attain low multiples of the terminal settling velocity within DSU. - 4 September 2025
- Published by Glasgow Caledonian University
Phase Maps for Fluidized Dense Phase Conveying and Validation by Eulerian Modelling
Design of Pneumatic Conveying (PC) systems for particulate solids remains largely empirical, requiring full-scale experiments with the product. The objective of this project is to facilitate numerical modelling of Fluidized Dense phase conveying (FDC) (1000 ≲ solids mass flux (Gs) ≲ 3000 kg/m2s), for slightly cohesive Geldart A powders (Hausner ratio < 1.25), by resolving their flow regimes and transitions of vertical upflow and horizontal flow. The vertical upflow phase map of Wirth (1988) and the horizontal flow phase map of Zenz (1949) were adapted to the powders, based on published experimental data, and uncertainties were validated by resolved Eulerian modelling with the MFiX-TFM code. The model covered the full spectrum of solids volume fraction (εS), as dense moving bed coexists with dilute phase during horizontal flow; the Simonin viscous stress model, which incorporates the turbulence model of Simonin for dilute flow conditions as well as the Granular Kinetic Theory for dense conditions, was complemented by the Princeton frictional stress model for near close packed conditions. Within the computing means, 2D long pipe models for vertical upflow, and a novel pseudo-3D disk model, with a single layer of 3D cells with axially periodic Boundary Conditions (BC), for horizontal flow were used. Key model limitations: (a) The horizontal flow model failed to predict the lateral displacement of solids, due to the lack of a slip shear lift force model and the apparent steady state caused by the Cartesian cut-cell coordinates with free-slip wall BC for solids phase; (b) The modelled powder is monodisperse with dominant gravity over van der Waals forces, atypical for FDC. Key findings for vertical upflow include: (a) FDC for finer Geldart A powders largely occurs under Dense Suspension Upflow (DSU) and for coarser powders under DSU and / or Fast Fluidization (FF); (b) Transition from FF to DSU, defined as the disappearance of the S-shaped axial εS profile, occurs at the GS at which the entire pipeline attains gross upflow with little backmixing; (c) DSU can be characterised as a transport regime with gross upflow of solids, with the granular temperature (Θ) in the bulk lower than that at the wall; (d) all the isofluxes (lines of constant GS) merge at the transition to turbulent fluidization, to follow the unique locus within captive beds; (d) Increasing the GS from a low value, the slip velocity increases to a maximum within FF and falls thereafter to low multiples of the terminal settling velocity within DSU; (e) Upper transport velocity for Geldart A powders is significantly greater than hitherto predicted; a new provisional correlation is proposed based on published direct measurements in circulating fluidized beds for typical Geldart A powders. Key findings for horizontal flow include: (a) A postulate that, for coarser powders, isofluxes may show a higher pressure gradient towards the feed zone (FZ), and a more pronounced pressure minimum earlier along the pipeline, than for finer powders. This is because coarser powders incur higher frictional losses towards the FZ due to higher εS ; along the pipeline, with increasing Vg , as frictional losses taper off with εS falling below the threshold of ~ 0.5, the viscous losses rise faster from being insignificant at the FZ to takeover; (b) Increase in pressure gradient towards the conveying limit for horizontal pipeline segments are nominal, suggesting that the minimum Vg limit for FDC powders is probably determined by the composite system characteristics including bends; (c) The > 2 orders of magnitude lower Θ in the dense moving bed, as predicted by numerical simulations, suggests that the transition from moving bed flow to dilute phase, defined as the point where the moving bed gets fully suspended, can be perceived from granular temperature (Θ).
- 4 September 2025
- Published by Glasgow Caledonian University
Phase Maps for Fluidized Dense Phase Conveying and Validation by Eulerian Modelling
Design of Pneumatic Conveying (PC) systems for particulate solids remains largely empirical, requiring full-scale experiments with the product. The objective of this project is to facilitate numerical modelling of Fluidized Dense phase conveying (FDC) (1000 ≲ solids mass flux (Gs) ≲ 3000 kg/m2s), for slightly cohesive Geldart A powders (Hausner ratio < 1.25), by resolving their flow regimes and transitions of vertical upflow and horizontal flow. The vertical upflow phase map of Wirth (1988) and the horizontal flow phase map of Zenz (1949) were adapted to the powders, based on published experimental data, and uncertainties were validated by resolved Eulerian modelling with the MFiX-TFM code. The model covered the full spectrum of solids volume fraction (εS), as dense moving bed coexists with dilute phase during horizontal flow; the Simonin viscous stress model, which incorporates the turbulence model of Simonin for dilute flow conditions as well as the Granular Kinetic Theory for dense conditions, was complemented by the Princeton frictional stress model for near close packed conditions. Within the computing means, 2D long pipe models for vertical upflow, and a novel pseudo-3D disk model, with a single layer of 3D cells with axially periodic Boundary Conditions (BC), for horizontal flow were used. Key model limitations: (a) The horizontal flow model failed to predict the lateral displacement of solids, due to the lack of a slip shear lift force model and the apparent steady state caused by the Cartesian cut-cell coordinates with free-slip wall BC for solids phase; (b) The modelled powder is monodisperse with dominant gravity over van der Waals forces, atypical for FDC. Key findings for vertical upflow include: (a) FDC for finer Geldart A powders largely occurs under Dense Suspension Upflow (DSU) and for coarser powders under DSU and / or Fast Fluidization (FF); (b) Transition from FF to DSU, defined as the disappearance of the S-shaped axial εS profile, occurs at the GS at which the entire pipeline attains gross upflow with little backmixing; (c) DSU can be characterised as a transport regime with gross upflow of solids, with the granular temperature (Θ) in the bulk lower than that at the wall; (d) all the isofluxes (lines of constant GS) merge at the transition to turbulent fluidization, to follow the unique locus within captive beds; (d) Increasing the GS from a low value, the slip velocity increases to a maximum within FF and falls thereafter to low multiples of the terminal settling velocity within DSU; (e) Upper transport velocity for Geldart A powders is significantly greater than hitherto predicted; a new provisional correlation is proposed based on published direct measurements in circulating fluidized beds for typical Geldart A powders. Key findings for horizontal flow include: (a) A postulate that, for coarser powders, isofluxes may show a higher pressure gradient towards the feed zone (FZ), and a more pronounced pressure minimum earlier along the pipeline, than for finer powders. This is because coarser powders incur higher frictional losses towards the FZ due to higher εS ; along the pipeline, with increasing Vg , as frictional losses taper off with εS falling below the threshold of ~ 0.5, the viscous losses rise faster from being insignificant at the FZ to takeover; (b) Increase in pressure gradient towards the conveying limit for horizontal pipeline segments are nominal, suggesting that the minimum Vg limit for FDC powders is probably determined by the composite system characteristics including bends; (c) The > 2 orders of magnitude lower Θ in the dense moving bed, as predicted by numerical simulations, suggests that the transition from moving bed flow to dilute phase, defined as the point where the moving bed gets fully suspended, can be perceived from granular temperature (Θ).