Computational Modeling and Experiments of Natural Convection for a Titan Montgolfiere

Abstract

Computational models are developed to predict the natural convection heat transfer and buoyancy for a Montgolfiere under conditions relevant to the Titan atmosphere. Idealized single-and double-walled balloon geometries are simulated using algorithms suitable for both laminar and (averaged) turbulent convection. Steadystate performance results are compared with existing heat transfer coefficient correlations. The laminar results, in particular, are used to test the validity of the correlations in the absence of uncertainties associated with turbulence modeling. Some discrepancies are observed, which appear to be primarily associated with temperature nonuniformity on the balloon surface. The predicted buoyancy for both the single-and double-walled balloons in the turbulent convection regime, predicted with standard two-equation turbulence models, showed trends similar to those with the empirical correlations. There was also good agreement with recently conducted experiments in a cryogenic facility designed to simulate the Titan atmosphere.

Reply by the Authors to G. E. Dorrington

“…1 for the net buoyancy as a function of gap width ( D i =D o ) for double-walled balloons. The corrected correlation gives a better match with simulation results for balloons with a larger gap size, but a poorer match for smaller gaps and thus does not affect the reported conclusions [2].…”

“…In his Technical Comment, Dorrington [1] raises several issues regarding the empirical natural convection correlations that are compared with computational fluid dynamics (CFD) models in our paper [2].…”

“…2, provides a better match with the laminar simulation results. For external convection, replacing Churchill's [6] correlation as quoted in our paper [2], with the suggested [1] modified version 10 13 10 14 Fig. 3 Net buoyancy versus nondimensional heat input for singlewalled balloons in the turbulent regime.…”

Semi-implicit direct forcing immersed boundary method for incompressible viscous thermal flow problems: A Schur complement approach

“…Another approach was proposed by Taira and Colonius [19], who utilized the distributed Lagrange multiplier to simultaneously satisfy the divergence-free and no-slip kinematic constraints by the solution of the modified Poisson equation in the framework of the projection method. The developed approach was then applied in various engineering fields, including active and passive flow control [19,20], optimization of performance of a hot air balloon [21] and the dynamic interactions between rigid-body systems and incompressible viscous flows [22].…”

An extension of the immersed boundary method based on the distributed Lagrange multiplier approach

“…The power of the coupled Lagrange multiplier scheme is that it can be straightforwardly adapted to various applications in fluid mechanics. In fact, the approach has been successfully utilized by a number of researchers, namely, by Taira and Colonius [16] for investigation of steady blowing into separated flows behind low-aspect-ratio rectangular wings; by Samanta et al [17] for prediction of the natural convection heat transfer and buoyancy for a hot air balloon; by Yiantsios [18] for the simulation of rigid-particle-laden flows; by Choi et al [19] for investigation of the forces and unsteady flow structures associated with harmonic oscillations of an airfoil; and recently by Wang and Eldridge [20] for simulating the dynamic interactions between incompressible viscous flows and rigid-body systems.…”