A closed-form analytical model for predicting 3D boundary layer displacement thickness for the validation of viscous flow solvers

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.

RETRACTED: Sanal Flow Choking: A Paradigm Shift in Computational Fluid Dynamics Code Verification and Diagnosing Detonation and Hemorrhage in Real‐World Fluid‐Flow Systems

“…Therefore, a priori knowledge of the HCR of the evolved gas is essential for predicting the occurrence of Fanno flow choking, Rayleigh flow choking, and Sanal flow choking conditions in any wall-bounded fluid flow system. Authors [1,[5][6][7][8][9][10] reported that at the LCHI, the blood vessel with bifurcation and without any plaque and stent could experience the Sanal flow choking due to the blockage factor ( Figure 2f) leading to asymptomatic hemorrhage/stroke as a consequence of the transient pressure overshoot as a result of the shock wave generation. [6] The research findings of the authors corroborated that, [1,6] at the Sanal flow choking condition, when the BPR reaches the LCHI anywhere in the circulatory circuit with sudden expansion or bifurcation region the chances of the physical occurrence of cavitation and shock waves are very high because of the off-designed CD nozzle-shaped-channel flow in blood vessels.…”

“…Authors [1,[5][6][7][8][9][10] reported that at the LCHI, the blood vessel with bifurcation and without any plaque and stent could experience the Sanal flow choking due to the blockage factor ( Figure 2f) leading to asymptomatic hemorrhage/stroke as a consequence of the transient pressure overshoot as a result of the shock wave generation. [6] The research findings of the authors corroborated that, [1,6] at the Sanal flow choking condition, when the BPR reaches the LCHI anywhere in the circulatory circuit with sudden expansion or bifurcation region the chances of the physical occurrence of cavitation and shock waves are very high because of the off-designed CD nozzle-shaped-channel flow in blood vessels. Certainly, the Sanal flow choking is more severe near the heart valves, which create a CD nozzle flow effect leading to cavitation due to the geometrical shape or orientation of leaflets or cusps.…”

“…During the development phase, [37][38][39][40] dual-thrust rockets with high propellant loading density (l/d > 27) experienced catastrophic failures at the subsonic igniter jet flow conditions during the ignition transient period of operation presumably due to an unexpected detonation due to the Sanal flow choking phenomenon. [1,5] Kumar et al [37][38][39][40] reported conclusively that at the subsonic inflow conditions, or at the creeping inflow conditions, after attaining the CPR in the flow system, there are the likelihood of the existence of the fluid-throat which induced the Sanal flow choking followed by shock waves leading to an undesirable sharp pressure overshoot in dual-thrust SRMs with high propellant loading density (Figure 3a,b) within the given envelope (L/d > 44, l/d ≥ 27). And the authors further highlighted that there is a limiting value of the l/d ratio in any dual-thrust chemical rocket, which determines the safe transition location for prohibiting the undesirable Sanal flow choking phenomenon.…”

“…[7][8][9] Note that during the traditional blood test across the globe the BHCR is not estimating for the diagnosis, prognosis, prevention and treatment of various diseases including the Covid-19, as its significance is still unknown to medical science. Note that the BHCR is regulating the CPR for the Sanal flow choking [1,[5][6][7][8][9][10] condition in the base fluid as well as nanofluid, which is a remarkable finding reported herein first time for the risk assessment of catastrophic failure of any internal nanofluid flow system at the creeping inflow condition without any iota of symptoms of plaque deposit (atherosclerosis) or stenosis. In light of the Covid-19 pandemic, the BHCR alterations due to virus effects need to be examined due to the increased risk of cardiovascular diseases (CVDs), which was reported worldwide in Covid-19 patients.…”

“…The beauty and novelty of these models stem from the veracity that at the Sanal flow choking condition for diabatic flows (flows that involve transfer of heat), all conservation laws of nature are satisfied at a unique sonic-fluidthroat location. [1,5] The fact is that at the condition prescribed by the Sanal flow choking model for real-world fluid flows, the internal flow choking due to heating (thermal choking, [3] -Rayleigh flow effect) and that of the frictional effects (Fanno flow effect [3] ) converge at a unique location of the fluid-throat, where the Mach number reaches unity. Therefore, the exact value of the blockage factor predicted at the Sanal flow choking condition, corresponding to any fluid with the known HCR, could be taken as an infallible data worldwide for the certification, confirmation and standardization of various computational fluid dynamics (CFD) flow solvers authentically for meeting the future needs of various high fidelity multiphase and multispecies in silico simulations.…”