Huanxin Lai, Yuying Yan and Keqi Wu
This paper aims to develop a numerical method for analysing the time‐dependent conjugate heat and fluid flows inside and around single bubbles rising in a hot liquid.
Abstract
Purpose
This paper aims to develop a numerical method for analysing the time‐dependent conjugate heat and fluid flows inside and around single bubbles rising in a hot liquid.
Design/methodology/approach
The procedure combines the moving mesh method for flows in time‐dependent geometries and the zoned calculation algorithm for conjugate viscous flows. A moving axisymmetric boundary‐fitted mesh is used to track the deformable gas‐liquid interface, while conjugate flows in both gas and liquid sides are calculated by a two‐block zoned method. The interfacial stresses are employed to calculate the velocity value and to decide the time‐dependent bubble shape simultaneously. Governing equations for the rising velocity and acceleration of the bubble are derived according to the forces acting on the bubble.
Findings
A calculating procedure for time‐dependent conjugate heat and fluid flows inside and around a rising single bubble has been developed. The algorithm has been verified, and can be employed for further analysing heat, mass and momentum transfer phenomena and their relevant mechanisms.
Originality/value
The paper developed a method to obtain high fidelity results for the heat and fluid flow details in the vicinity of a time‐dependent moderately deformable rising bubble; the physically zero‐thickness of a gas‐liquid interface is guaranteed. The governing equations for the time‐dependent rising velocity and acceleration are derived.
Details
Keywords
Huanxin Lai, Gailan Xing, Shantong Tu and Ling Zhao
The purpose of this paper is to present a pressure‐correction procedure for incompressible flows using unstructured meshes. A method of implementing high‐order spatial schemes on…
Abstract
Purpose
The purpose of this paper is to present a pressure‐correction procedure for incompressible flows using unstructured meshes. A method of implementing high‐order spatial schemes on unstructured grids was introduced.
Design/methodology/approach
The procedure used a collocated cell‐centered unstructured grid arrangement. In order to improve the accuracy of calculation, the widely used high‐order schemes for convection, developed for structured grids and in the form of either the normalized variable and space formulation (NVSF) or the total variation diminishing (TVD) flux limiters (FL), were introduced and implemented onto the unstructured grids. This implementation was carried out by constructing a local coordinate and introducing a virtual upstream node.
Findings
The procedure was validated by calculating the lid‐driven cavity flows which had benchmark numerical solutions. For comparison, these flows were also computed by a commercial package, the FLUENT. The results obtained by the present procedure agreed well with the benchmark solution although very coarse grids were used. For the FLUENT, however, worse agreements with the benchmark solutions were obtained although the grids used for computation were the same. These demonstrated the robustness of the presented numerical procedure.
Originality/value
With the present method, high‐order schemes in either NVSF or TVD FL forms for structured grids can be easily implemented onto unstructured grids. This provides more choices of high‐order schemes for calculating complex flows.