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.

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The theoretical discoveries of the Sanal flow choking [V. R. Sanal Kumar et al., “Sanal flow choking: A paradigm shift in computational fluid dynamics code verification and diagnosing detonation and hemorrhage in real-world fluid-flow systems,” Global Challenges 4, 2000012 (2020)] and streamtube flow choking [V. R. Sanal Kumar et al., “Deflagration to detonation transition in chemical rockets with sudden expansion/divergence regions,” AIAA Paper No. 2020-3520, 2020] achieved significant contemplation in all branches of science and engineering for resolving various unanswered scientific questions brought onward from the beginning of this era [V. R. Sanal Kumar et al., “A closed-form analytical model for predicting 3D boundary layer displacement thickness for the validation of viscous flow solvers,” AIP Adv. 8, 025315 (2018)]. The applications of these flow choking phenomena are more significant in aerospace industries [V. R. Sanal Kumar et al., “Nanoscale flow choking and spaceflight effects on cardiovascular risk of astronauts—A new perspective,” AIAA Paper No. 2021-0357, 2021] and medical sciences [V. R. Sanal Kumar et al., “Lopsided blood-thinning drug increases the risk of internal flow choking leading to shock wave generation causing asymptomatic cardiovascular disease,” Global Challenges 2021, 2000076]. Herein, as an offshoot of the Sanal flow choking phenomena, the proof of the concept of boundary-layer-blockage (BLB) persuaded external-flow-choking (EFC) at aircraft-in-ground (AIG)-effect is presented. When the aircraft's ground clearance is relatively low, the evolving BLB factor from both planes (the bottom surface of the aircraft and the ground) creates a transient fluid-throat, leading to the Sanal flow choking and supersonic flow development in the duct flow region. In this physical situation, the pressure ratio (Ptotal/Pstatic) at the external flow choking region is exclusively a function of the specific heat ratio of the fluid. The EFC is more prone for the low wing aircraft flying in the near vicinity to the ground and/or sea with relatively high subsonic Mach number and low angle of attack. At this flying condition, the underside of the aircraft (fuselage and/or wing) and the ground creates the convergent-divergent duct flow effect leading to the EFC at the critical total-to-static pressure ratio. The accurate estimation of the BLB factor at the location of the EFC at AIG effect is presented in this manuscript as a universal yardstick for two-dimensional (2D) in silico simulation. For establishing the proof of the concept of external flow choking and supersonic flow development and shock wave generation, the 2D in silico results are presented for both stationary and moving airfoils in ground effect. In silico results show that the airfoil at stationary position exhibits relatively higher BLB factor and an immediate occurrence of the EFC than the same airfoil moving with the identical inflow Mach number and Reynolds number. We could establish herein that the moving vehicle simulation is inevitable for capturing actual flow physics and further precise examination of the BLB factor and the possibilities of the occurrence of the EFC for credible trajectory optimization of high-speed ground-effect vehicles.