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This paper is on an Eulerian-Eulerian (EE) approach that utilizes Godunov’s scheme to deal with a running shock that interacts with a cloud of particles. The EE approach treats both carrier phase (fluid phase) and dispersed phase (particle phase) in the Eulerian frame. In this work, the fluid equations are the Euler equations for the compressible gas while the particle equations are based on a recently developed model to solve for the number density, velocity, temperature, particle sub-grid scale stresses, and particle sub-grid scale heat fluxes. The carrier and dispersed phases exchange momentum and heat, which are modeled through incorporating source terms in their equations. Carrier and dispersed phase equation form a hyperbolic set of differential equations, which are numerically solved with Godunov’s scheme. The numerical solutions are obtained in this work for a two-dimensional normal running shock interacting with a rectangular cloud of particles. The results generated by the EE approach were compared against the results that were generated by a well-stablished Eulerian-Lagragian (EL) approach that treats the carrier phase in an Eulerian frame, while does the dispersed phase in a Lagrangian framework where individuals particles are traced and solved. For the considered configuration, the EE approach reproduced the EL results with a very good accuracy.
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Modeling pseudo-turbulent heat flux in gas-solid heat transfer
Flow past disperse solid particles or bubbles induces fluctuations in carrier fluid velocity, which correlate with temperature fluctuations in non-isothermal flows resulting in the pseudo-turbulent heat flux (PTHF). In the Eulerian-Eulerian (EE) two-fluid (TF) model, the transport of PTHF is shown to be an important contributor to the overall energy budget, and is modeled using a pseudo-turbulent thermal diffusivity (PTTD). The PTHF and PTTD were originally quantified using particle-resolved direct numerical simulation (PR-DNS) data, and correlations were developed over a range of solid volume fraction (0.1 ≤ 𝜀𝑠 ≤ 0.5) and mean slip Reynolds number (1 ≤ 𝑅𝑒𝑚 ≤ 100) for a Prandtl number of 0.7. However, the original PTTD correlation diverges to infinity as the solid volume fraction goes to zero, which is physically unrealistic. This singular behavior is problematic for EE TF simulations at particle material fronts where solid volume fraction values can fall below the lower limit of existing data (𝜀𝑠 =0.1) to zero in the pure carrier phase. In this work, additional PR-DNS data are reported for 𝜀𝑠 < 0.1, and improved correlations are developed for the PTHF and PTTD. The new PTTD correlation is non- singular, and both the PTHF and PTTD decay exponentially to zero as the solid volume fraction approaches zero, which is physically reasonable. This improves prediction of PTHF transport in dilute flow using EE TF heat transfer simulations.
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- Award ID(s):
- 1953298
- PAR ID:
- 10586776
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Chemical Engineering Science
- Volume:
- 283
- Issue:
- C
- ISSN:
- 0009-2509
- Page Range / eLocation ID:
- 119371
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.ces.2023.119371
