General model for shear stress and surface pressure distributions for flow over spheres
Abstract
A general physics-based model for the distribution of shear stress and surface pressure is developed for laminar flow over spheres. Although integral coefficients have been studied extensively for spheres, they do not capture the local surface distributions that govern phenomena such as heat transfer, phase change, and mass loss in multiphase and particle-laden flows. The model depends on the flow regime of the sphere (Re∞, M∞, Kn∞), local gas properties (γ, ω, Pr), and surface conditions (Tw/T0, σt, σn). The formulation incorporates boundary-layer scaling, flow separation, shock-wave physics, velocity-slip effects, and high-speed rarefaction, while recovering the known asymptotic behavior in the creeping-flow, hypersonic, and free-molecular limits. The proposed model is validated in the continuum and rarefied regimes using CFD and DSMC simulations from literature. In the continuum regime, it is compared with CFD simulations of flow over a sphere in air under subsonic, supersonic, and hypersonic conditions with varying surface temperatures. The model captures the CFD distributions very well over a wide range of Re∞, M∞, and Tw/T0. In the rarefied regime, it is compared with DSMC simulations of flow over a sphere in a monatomic gas under subsonic and supersonic conditions with fully diffuse and partial surface accommodation. It shows good agreement with the simulated shear stress and surface pressure distributions over a wide range of M∞ and Kn∞, while accurately capturing the effects of surface accommodation around spherical bodies.
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BibTeX
@misc{daniels2026general,
title = {{General model for shear stress and surface pressure distributions for flow over spheres}},
author = {Bryce Daniels and Thomas Schwartzentruber},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28658},
eprint = {2609.28658},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28658},
}
RIS
TY - UNPB
TI - General model for shear stress and surface pressure distributions for flow over spheres
AU - Bryce Daniels
AU - Thomas Schwartzentruber
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28658
UR - https://arxiv.org/abs/2609.28658
AB - A general physics-based model for the distribution of shear stress and surface pressure is developed for laminar flow over spheres. Although integral coefficients have been studied extensively for spheres, they do not capture the local surface distributions that govern phenomena such as heat transfer, phase change, and mass loss in multiphase and particle-laden flows. The model depends on the flow regime of the sphere (Re_∞, M_∞, Kn_∞), local gas properties (γ, ω, Pr), and surface conditions (T_w/T_0, σ_t, σ_n). The formulation incorporates boundary-layer scaling, flow separation, shock-wave physics, velocity-slip effects, and high-speed rarefaction, while recovering the known asymptotic behavior in the creeping-flow, hypersonic, and free-molecular limits. The proposed model is validated in the continuum and rarefied regimes using CFD and DSMC simulations from literature. In the continuum regime, it is compared with CFD simulations of flow over a sphere in air under subsonic, supersonic, and hypersonic conditions with varying surface temperatures. The model captures the CFD distributions very well over a wide range of Re_∞, M_∞, and T_w/T_0. In the rarefied regime, it is compared with DSMC simulations of flow over a sphere in a monatomic gas under subsonic and supersonic conditions with fully diffuse and partial surface accommodation. It shows good agreement with the simulated shear stress and surface pressure distributions over a wide range of M_∞ and Kn_∞, while accurately capturing the effects of surface accommodation around spherical bodies.
ER -