Abstract
A closed-form analytical model is developed for estimating the 3D boundary-layer-displacement thickness of an internal flow system at the Sanal flow choking condition for adiabatic flows obeying the physics of compressible viscous fluids. At this unique condition the boundary-layer blockage induced fluid-throat choking and the adiabatic wall-friction persuaded flow choking occur at a single sonic-fluid-throat location. The beauty and novelty of this model is that without missing the flow physics we could predict the exact boundary-layer blockage of both 2D and 3D cases at the sonic-fluid-throat from the known values of the inlet Mach number, the adiabatic index of the gas and the inlet port diameter of the internal flow system. We found that the 3D blockage factor is 47.33 % lower than the 2D blockage factor with air as the working fluid. We concluded that the exact prediction of the boundary-layer-displacement thickness at the sonic-fluid-throat provides a means to correctly pinpoint the causes of errors of the viscous flow solvers. The methodology presented herein with state-of-the-art will play pivotal roles in future physical and biological sciences for a credible verification, calibration and validation of various viscous flow solvers for high-fidelity 2D/3D numerical simulations of real-world flows. Furthermore, our closed-form analytical model will be useful for the solid and hybrid rocket designers for the grain-port-geometry optimization of new generation single-stage-to-orbit dual-thrust-motors with the highest promising propellant loading density within the given envelope without manifestation of the Sanal flow choking leading to possible shock waves causing catastrophic failures.
Highlights
An accurate estimation of the boundary layer displacement thickness is inevitable for the design and development of high-speed internal flow systems obeying the adiabatic compressible viscous flow theory,[1] for various industrial applications
This can be explained; as succinctly reported in the previous connected paper of Sanal Kumar et al.[2,3,4,5] that, owing to the viscous friction, a boundary layer will be formed on the walls and their thickness will increase in the downstream direction to the divergence location
The closed-form analytical model presented is found unique for predicting the 3D boundary layer displacement thickness of any internal flow system at the fluid-throat induced Sanal flow choking condition
Summary
An accurate estimation of the boundary layer displacement thickness is inevitable for the design and development of high-speed internal flow systems obeying the adiabatic compressible viscous flow theory,[1] for various industrial applications. It is an admitted scientific fact globally that a closed-form analytical model capable of predicting the boundary layer displacement thickness without diluting the flow physics is considered as credible for the verification, calibration and validation of various viscous flow solvers Such models will be useful for the design and development of new generation single-stage-to-orbit HVT dual-thrust motors with the highest. Sanal Kumar, et al.[2,3,4,5] It aims for predicting unambiguously the non-dimensional boundary layer blockage at the sonicfluid-throat of any internal flow system from the known values of the inlet Mach number and heat capacity ratio of the fluid for CFD code verification, calibration and validation In this regard, the mathematical modeling efforts for predicting the boundary layer displacement thickness of 2D and 3D internal flow systems obeying the compressible adiabatic viscous flow theory at the steady state condition are discussed in the subsequent sections
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