The theoretical finding of the Sanal-flow-choking [PMCID: PMC7267099] is a methodological advancement in predicting the deflagration-to-detonation-transition (DDT) in the real-world-fluid flows (continuum/non-continuum) with credibility.[1,2] Herein, we provide a proof of the concept of the Sanal-flow-choking and streamtube-flow-choking causing DDT in wall-bounded and free-external flows. Once the streamlines compacted, the considerable pressure difference attains inside the streamtube and the flow gets accelerated to the constricted region for satisfying the continuity condition set by the conservation law of nature. If the shape of the streamtube in the internal/external flow is similar to the convergent-divergent (CD) duct the phenomenon of the Sanal-flow-choking and supersonic flow development occurs at a critical-total-to-static pressure ratio (CPR) in yocto to yotta scale systems and beyond, which leads to shock wave generation or detonation as the case may me. At the lower critical detonation or hemorrhage index, the CPR of the reacting flow and the critical blood-pressure-ratio (BPR) of the subjects (human being/animal) are unique functions of the heat-capacity-ratio (HCR) of the evolved gas in the CD duct. In silico results are presented herein to establish the proof of the concept of the Sanal-flow-choking and streamtube-flow-choking causing shock-wave/detonation in diabatic flow systems and asymptomatic-hemorrhagic-stroke in biological systems. The physics of detonation chemistry presented herein sheds light for exploring supernova explosions.[107]
Article
The Physics of Detonation Chemistry: A Radical Theory in Predicting the Deflagration to Detonation Transition
https://doi.org/10.21203/rs.3.rs-86415/v1
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Deflagration-to-detonation-transition (DDT)
detonation
nanofluid flow system design
hemorrhagic-stroke
Sanal flow choking
streamtube-flow-choking
Chemical rocket.
Although the underlying knowledge in advanced science of real-world flows (continuum / non-continuum) with the multi-disciplinary focus has been evolved over the centuries there are still many unresolved problems due to the lack of fundamental understanding of physics and chemistry of diabatic fluid flows (flow involves transfer of heat).[1] Such problems of urgency to the scientific communities are the prediction and attenuation of detonation in reacting fluid flow systems and that of asymptomatic stroke (AS) in the human circulatory system (HCS). Note that the deflagration to detonation transition (DDT) in reacting fluid flow systems and the creeping flow to asymptomatic hemorrhagic stroke (AHS) in biological systems could happen due to the consequence of the Sanal flow choking.[1-9] Over the decades several in vitro and in silico studies were reported on DDT in various energy systems from yocto to yotta scales but there were no authentic answers on the fundamental cause of DDT in real-world fluid flow systems.[10-20] Modeling and simulation of nanoscale fluid flow is truly intricate, because in the contrary to milli-scale or macroscale fluid flow, the governing-equations capturing exact flow physics and chemistry are not well delineated.[21-26] Hence, even if the in silico method is well suited for the solution of considered problem, in vitro methods in nanoscale are having inherent inaccuracy for generating benchmark data for in silico code verification. Therefore, one should rely up on the exact solution for generating benchmark data for solving unresolved problems carried forward over the centuries with credibility. Such models should scrupulously satisfy the conservation laws as imposed by our nature. Therefore, the Sanal flow choking models[1] should be invoked for in silico model validation, verification and calibration before featuring fluid flow characteristics of yocto to yotta scale diabatic fluid flow systems and beyond with reliability.
Of late, small scale systems have got significant attention in the industry because mostly micro/nano-electromechanical systems (MEMS/NEMS) are based on the fluid motion.[21] This is particularly true in the nano medicine for drug discovery and nano/micro thrusters for aerospace systems design. Obviously, the nano scale fluid flow system development in microgravity aerospace application is a challenging research topic. Furthermore, such systems in atmospheric conditions applicable to physical, chemical, and biological sciences are also challenging areas for research due to the pragmatic difficulties to perform in vitro and in silico studies and in addition the lack of closed-form analytical models for benchmarking. Various researchers reported through in vitro and molecular dynamics simulations that the surface friction compared to the fluid flow is very low for carbon nanotubes (CNT).[26-29] The fact is that the reported results were not supported with benchmark data generated from any exact solution for meeting all the conservation laws of nature.
Qi-Long Yan et al.[30] reported (2016) that encapsulation of energetic molecules into CNTs is extremely challenging and still demanding additional analytical and in vitro studies to understand its sensitivity and performances[31-34] having with highly sensitive energetic material (EMs). Gunpowder, a firearm propellant, invented in ancient China is believed as the earliest energetic material,[30] which generally does not detonate but rather deflagrates. The deflagration and detonation properties of black powder however differ significantly from new generation high energetic solid propellants[35, 36] and there are no authentic predictive models available as on the date to forecast these properties at nanoscale. Therefore, in silico simulation of DDT in the real-world nanofluid flow system is the need of the 21st century; and it must be verified with an exact solution for a credible decision making.[36-38] Admittedly, there are no literature available on in silico simulation of DDT in milli-scale or nanoscale systems having port with the sudden expansion/divergence region.[39-45]
The Sanal flow choking, a compressible fluid flow effect, is a radical theory in advanced science of real-world fluid flow systems,[1] which is capable to provide solutions to many unanswered research questions in the continuum and non-continuum fluid flows moved ahead over the centuries.[46-62] Note that the non-continuum or nanoscale fluid flows obey all conservation laws of nature. Indeed, all fluids available in our nature are compressible.[1] In the case of nanoscale fluid flows, when pressure increases the Knudsen number reduces causing the compressible viscous flow effect due to the decrease in the average mean free path heading to zero-slip wall boundary condition. All these deliberations corroborate that the Sanal flow choking model puts a focal role in interdisciplinary science for performing in-silico experiments with credibility in the continuum and non-continuum fluid flows in yocto to yotta scale systems. Certainly, at the Sanal flow choking condition for diabatic flows (flow involves transfer of heat) all conservation laws of nature are contented. Any fluid flow solver calibrated with the Sanal flow choking condition of diabatic flow could be capable to predict a priori the risk of DDT in chemical energy systems and AHS in biological systems.[1] It could be achieved by predicting the lower critical detonation index (LCDI) and the lower critical hemorrhage index (LCHI) as the case may be. It is pertinent to note that both the LCDI and the LCHI are representing the critical pressure ratio of the respective systems. These indexes are regulated by the heat-capacity-ratio (HCR) of the evolved gas with the lowest HCR.
In this article we are primarily focusing on analytical modeling and in silico simulation of a diabatic fluid flow system aiming to demonstrate the Sanal flow choking, streamtube flow choking, shock wave generation and pressure overshoot for proving the concept of the occurrence of DDT in a classical straight-tube ending with a divergent port geometry at the subsonic inflow condition. This physical situation is analogous to the creeping flow to the choked flow condition in an artery with the divergent/bifurcation/vasospasam region causing AHS (see Figure 1(a-h) as the central illustration). Herein, we made an effort to correlate the radical theory of the Sanal flow choking in the human circulatory system (HCS) because blood is a compressible fluid.[1] Furthermore, in vitro study shows (see Fig.2) that carbon dioxide (CO2) gas is predominant in fresh-blood samples of the healthy human-being than Guinea-pig at a temperature range of 37-400 C (98.6-1040 F), which increases the risk of flow-choking leading to AHS. It is an admitted fact that the Sanal flow choking steers to the shock-wave generation in viscoelastic tubes with vasospasm (see the attached in vitro results as movie S1 and S2) like blood vessels, which create memory effect leading to AHS in the later stage.
Over the decades many blood flow simulation studies have been carried out with the incompressible fluid flow assumption [63-78], which are useful only for simulating the creeping flow conditions in HCS. Herein, we established the proof of the concept of DDT and AHS at the creeping inflow condition in an internal diabatic flow system (see Figure 3) through in silico modeling at a critical total-to-static pressure ratio (CPR) where the compressibility effect is significant. The importance of this interdisciplinary study design is succinctly reviewed in the subsequent background section for highlighting the research question pertaining to an authentic prediction of LCDI and LCHI.
Of late many in silico studies have been reported in base fluids and nanofluids for various industrial applications without an authentic validation of the results with benchmark data. As the pressure of the nanofluid rises, average-mean-free-path diminishes and thus, the Knudsen number lowers heading to a zero-slip wall-boundary condition with compressible viscous (CV) flow regime.[2] V.R.S.Kumar et al.[1-3] presented an exact analytical solution, which is capable to predict precisely the three-dimensional boundary-layer blockage factor (named herein as blockage factor) of diabatic fluid flow systems at the zero-slip-length. The innovation of the Sanal flow choking model was established through the entropy relation, as it meets all the conservation laws of nature.[1] The physical insight of the Sanal flow choking and streamtube flow choking demonstrated herein sheds light on getting answers of several unanswered research questions in advanced science.
V.R.S.Kumar et al.[1-9] established that there are likelihoods of Sanal flow choking in HCS (see Figure 1(a-h) as the central illustration), after attaining the critical blood pressure ratio.[1,7] The experiences gained from the theoretical and in vitro findings (see Figure 2) prompted us for the internal flow simulation of the straight duct ending with a divergent port for examining Sanal flow choking and streamtube flow choking (see Figure 3 and Figure 4(a-b)) through the reliable in silico simulation. It is a well-recognized fact that, the entire governing equations for viscous flows are extremely challenging to solve analytically using the existing mathematical tools. Using the developing system of non-linear equations, the in silico simulation with multi-phase and multi-species composite fluid flow with oscillating boundary wall is also a challenging task. It is because of the fact that an accurate, strong and competent solution with the super fine grid system is critical for the high reliability in silico modelling.[1-3]
Physics of Sanal flow-choking received significant attention in the global scientific community for solving various research problems of topical interest.[1,2,7,8] Certainly, using the Sanal flow choking model to predict the 3D blockage factor, the chemical rocket motor designer could optimize the grain port geometry with the maximum possible propellant loading density with the allied igniter, without inviting DDT and without any costly empirical design technique or in silico simulation.[2] Of late (2020) V.R.S.Kumar et al.[2] highlighted the physical significance of the detonation kernel associated with the 3D blockage factor and the critical pressure ratio (CPR) causing the phenomenon of Sanal flow choking in a constant area duct ending with a divergent port. Through this study,[2] the fundamental cause of DDT in the chemical rocket has come to the foreground. Over the centuries the scientific communities under the strong impression that at the creeping inflow condition DDT won’t occur in a straight duct ending with a divergent region. We could authentically disprove this wrong notion on DDT through a closed-form analytical model, in silico results[3] and the full motor static test results.[1] Thereby, a popular research question revolving through the globe over the centuries has been settled with a cogent answer. In brevity, it says that due to the Sanal flow choking the creeping or low subsonic flow (continuum or non-continuum) will get augmented to the supersonic flow condition in a straight duct ending with a divergent port and create possible shock waves and shock diamonds due to streamtube flow choking (see Figure 4 (a-b)). Note that the Sanal flow choking and the streamtube flow choking are new theoretical concepts applicable to both the continuum and non-continuum fluid flows. Once the streamlines compacted, the considerable pressure difference attains within the streamtube and the flow within the streamtube gets enhanced to the constricted section for satisfying the continuity condition set up the conservation law of nature, which leads to the Sanal flow choking and supersonic flow development at a CPR due to the convergent-divergent (CD) shape of the streamtube (see Figure 4(a-b)). For authenticating the proof of the concept the analytical and in silico methodologies are presented in the subsequent section.
Analytical and in silico methodologies are invoked herein for establishing the proof of the concept of the occurrence of DDT and AHS at the creeping inflow condition in a constant area duct ending with a divergence/bifurcation region (see Figure 3). Figure 3 is highlighting the Sanal flow choking condition in such a classical model of a real-world fluid flow system and Figure 4(a) is depicting the Sanal flow choking and streamtube flow choking corresponding to Figure 3. Figure 4(b) shows the enlarged view of streamline pattern and the streamtube flow choking in yocto to yotta scale internal and external flow systems. It is highlighting the CD duct flow effect in a streamtube leading to detonation in the chemical energy and environmental systems at a CPR. Physical situations of flow choking depicted in Figure 3 and Figure 4(a-b) are meeting the conditions set by the conservation laws of nature. This is a remarkable finding for solving various unresolved problems in aerospace, biomedical, chemical, environmental, material, mechanical and nanotechnology, oil and natural gas industries.[1]
At the unchoked flow condition pressure in the constricted region of the streamtube will be lower than the wider region and this physical situation leads to choked flow condition at the CPR. Note that CPR is governed by HCR. When the streamtube is compressed, the reduction in internal energy is transformed into an accelerated fluid flow motion to satisfy the law of conservation of mass, which leads to the Sanal flow choking in CD shaped streamtube heading to the generation of supersonic flow causing shock waves, pressure-overshoot and detonation in the downstream region of the streamtube. These analytical findings are corroborated with the in silico results presented in the subsequent section.
The fluid-throat induced internal flow choking in real-world fluid flow systems at the creeping inflow condition is a new concept, which is defined as Sanal flow choking,[1] a phenomenon occurs due to the boundary layer blockage.[1-9] The exact solution of the 3D boundary layer blockage (BLB), corresponding to LCDI (i.e., considering the lowest value of HCR (γlowest) of the evolved gases), at the Sanal flow choking for diabatic flows (continuum / non-continuum) with respect to Figure 3 is given in Equation 1. Mi is the subsonic upstream inflow Mach number. Figure 5 is the solution curve of Equation 1. Note that irrespective of the magnitude of the BLB factor, the Sanal flow choking occurs anywhere in the circulatory circuit once the flow attains the critical pressure ratio (see Figure 5). The critical pressure ratio is dictated by the heat capacity ratio (HCR or γ ) of the evolved gas with the lowest HCR (see Equation 2 and 3). Note that BLB will never be zero in any real-world fluid flow system.[1, 82] Equation 2 represents the LCDI, which is estimated based on the γlowest for attaining the Sanal flow choking condition. Equation 2 reveals that in any flow system, the total-to-static pressure ratio (Ptotal/Pstatic), should at all times be lesser than the LCDI for negating the undesirable detonation. In the case of biological flows Equation 2 is re-cast with respect to the blood pressure ratio (BPR) and the blood/biofluid heat capacity ratio (BHCR) for
Equation 4 shows the inlet Mach number estimation for getting diabatic flow choking in a straight duct.[1] Equation 5 is a remarkable closed-form analytical model capable to predict the average friction coefficient, of any wall-bounded flow system, without any empiricism, for an authentic in silico simulation.[3] If we know and the length-to-diameter (l/di) ratio we could fix the inflow Mach number for prohibiting DDT. Equation 5 will enable us for getting a choked flow condition at station 2 (see Figure 3) for the calibration of various in silico flow solvers by matching the numerically predicted blockage factor and the exact analytical solution.
The Sanal flow choking and streamtube flow choking are regulated by the physical situations set by Equations 1-6. It is a well known fact that for negating the flow choking Mach number should always be less than one in the system (see Equation 6). Equations 6(a-d) are the corollary of Equation 6. The self-explanatory Equations 6(a-d) derived from the compressible flow theory[1,4, 83] are representing Mach number, which are complimenting with Equation 2 and Equation 3. All these equations set the conditions for prohibiting Sanal flow choking and streamtube flow choking in any real-world fluid flow system. The individual or coupled effects of vessel geometry (stenosis) and the thermo-physical properties on flow choking can be easily discerned from Equations 6(a-d). These equations (Equations 6(a-d)) are well correlated with the clinical findings.[5-8] It is evident from Equation 6(a,c,d) that an increase in blockage factor (i.e., a decrease in the port-cross-sectional-area), in any vessel due to plaque and/or boundary layer induced blockage, could increase the risk of Sanal flow choking in the creeping inflow condition. As directly evidenced from Equations 2, 3 and 6(b-d), the risk of Sanal flow choking could be negated by increasing the HCR of the evolved gas in the vessel. Note that the left hand side of Equations 6(a-d) are representing the magnitude of Mach number, which could be estimated from the biofluid properties and the vessel port area for estimating the risk of internal flow choking (see Figure 5). It is important to note that the flow Mach number must always be less than one in the circulatory circuit including the vasa vasorum for retaining the unchoked flow condition. In a nutshell, Equations 6(a-d) are the useful tools, highlighting the geometric and thermo-fluid dynamics parameters, for maintaining an unchoked flow condition in the circulatory circuit for negating the risk of AHS. It is important to note that an overdose of blood-thinning drug for reducing the blood-viscosity augments Reynolds number leading to high-turbulence and enhanced boundary-layer-blockage (BLB), which increases the chances of cavitation and the Sanal-flow-choking leading to the shock wave and pressure-overshoot causing memory effect (stroke history) in viscoelastic vessels. Therefore, designing the precise blood-thinning regimen is vital for attaining the desired therapeutic efficacy and negating undesirable flow-choking leading to AHS. Briefly, the analytical models reveal that the relatively high and low blood viscosity are risk factors of AHS.
It is a well ascertained physical condition in the compressible flow theory that supersonic flow will be developed in the divergent region of a choked CD duct flow passage similar to an artery with divergent or bifurcation or vasospasm regions (see Figure 1 as the central illustration). At this physical situation[1,84] there is a possibility of shock wave generation and pressure-overshoot, causation of asymptomatic aneurysm and/or AHS as the case may be.[1,37]
Largely, in the HCS the flow is laminar and it becomes turbulent due to blood thinners and/or due to local or seasonal effects. Note that the over dose of anticoagulant drugs decrease the dynamic viscosity of blood dramatically and as a result Reynolds number increases leading to enhanced BLB causing the Sanal flow choking. The flow turbulence increases the loss of energy in the form of friction, which augments the blockage factor in the vessels and generates heat and enhance the internal energy resulting a reduction in the blood/biofluid heat capacity ratio (BHCR). The flow turbulence augments the perfusion pressure vital to push the flow of blood, leading to internal flow choking and shock wave generation. It leads to establish that at a CPR in any straight duct ending with the sudden expansion / divergent / bifurcation region could lead to detonation at a low subsonic inflow condition.
It is crystal clear from the SANAL chart given in Figure 5 (the solution curve of Equation 1) that, irrespective of the percentage of blockage factor, the risk of detonation could be negated by retaining the total-to-static pressure rato in a fluid flow system always lower than LCDI. Similarly, irrespective of the percentage blockage of any artery, the risk of AHS could be reduced by maintaining the SBP/DBP ratio lower than LCHI, which is a unique function of HCR. For instance, if an internal flow system is having 50 % port area blockage, there will NOT be any possibilities of the Sanal flow choking leading to detonation or hemorrhage provided the system maintains a flow Mach number lower than 0.3 or BPR < LCHI. The upper critical hemorrhage index (UCHI) could be estimated from the HCR of blood. At a CPR, the Sanal flow choking would occur in a vessel with gas embolism (i.e., when BPR > LCHI) or without gas embolism (i.e., whwn BPR > UCHI) irrespective of the blockage factor (plaque and/or boundary layer blockage). In a nutshell, Figure 5 is explicitly showing the condition of DDT and ASH in an internal fluid flow system of any scale at the Sanal flow choking condition.
For demonstrating the proof of the concept of the Sanal flow choking and streamtube flow choking in a classical fluid flow system in silico studies have been conducted using a validated flow solver.[3,4,85] The results generated from the in silico modeling (see Figure 6(a-c) and Figure 7(a-f)) are conveying the message to the scientific community on the occurrence of the Sanal flow choking and streamtube flow choking in a diabatic fluid flow system leading to detonation and asymptomatic stroke. Please see movie S3 containing the in silico results.
It is appropriate to mention here that, the simulation of chemical reaction mechanisms containing shock waves and detonation reported in the open literature are not unique.[2] Therefore, we deliberately set aside the reacting flow simulation in this fundamental pilot study for establishing one of the basic causes of DDT in the internal flow system. Figure 6(a-c) and Figure 7(a-f) show the in silico result highlighting the axial Mach number variations, sharp pressure spike and diminishing shock waves at the downstream region of the duct with bifurcation due to the Sanal flow choking and streamtube flow choking. Note that in the HCS, the large BPR oscillations could lead to the choking and unchoking phenomena creating high risk to the subjects (human being / animal) leading to an arrhythmia. Due to the periodic Sanal flow choking any valve, including heart valve, with CD duct shaped flow passage will get more defects than convergent type valves as time advances in any flow circuit. This is corroborated with the clinical findings.[1,7,8] The fact is that during the Sanal flow choking the divergent region of the valve will experience the shock wave and pressure overshoot causing damage. Most heart valve problems involve the aortic and mitral valves, possibly because of its geometric shape similar to CD duct flow passage. The valve defects can happen in water pipe line due to cavitation and shock waves.[1] Further discussion on the defects of various types of valves is beyond the scope of this article.
Figures 7(a-f) are showing the enlarged view of the streamtube, demonstrating the shape of the streamtube and the Mach number contours at different time intervals before and after the Sanal flow choking. It is crystal clear from Figure 6 and Figure 7 that the streamlines are compressed and the pressure differences are significant within the streamtube and as a result the flow gets enhanced to the narrow region of the streamtube for satisfying the conservation law, which leads to Sanal flow choking and detonation due to the convergent-divergent (CD) shape of the streamtube. Normal shock and oblique shock waves are evidenced in the in silico results. The Sanal flow choking location, the strength of shock, and shock diamonds can be observed in Figure 6(a-c). Packed streamlines could be discerned in the constricted area of the streamtube (see Figure 6(a-b) and Figure 7(a-f)) where low pressure is evident. In the case of biological flows, the sonic-fluid throat location discerned in Figure 6(a-c) could alter due to the BPR oscillation, wall flexibility of the viscoelastic blood vessel, chemistry of multi-species and multiphase fluid flow, and pathophysiological conditions.
The objective of this study was to establish the phenomenon of the Sanal flow choking and streamtube flow choking through the analytical and in silico modeling of diabatic fluid flows, which we could achieve herein. In the case of HCS, the blood and/or biofluid could get evaporated at the higher temperature creating an undesirable formation of gases within the duct creating a detrimental flow choking due to low HCR of the evolved gas leading to gas embolism.[1-9] Figure 6(a-c) and Figure 7(a-f) are analogous to biofluid choking effect in the circulatory circuit due to gas embolism. Briefly analytical and in silico results established that predicting the conditions of LCDI and LCHI, based on the lowest HCR of evolved gas, are inevitable for negating the undesirable DDT and ASH in any fluid flow system with credibility.
Despite 40 years of study (Hoyle & Fowler 1960), the mechanism whereby a degenerate carbon-oxygen white dwarf explodes, producing a Type Ia supernova (SN Ia), remains poorly understood. Early calculations assumed that central carbon ignition would lead to a detonation (Arnett 1969) that would incinerate the star entirely to iron. This proved inconsistent both with observations of features in the supernova spectrum from intermediate-mass elements and with detailed calculations of isotopic nucleosynthesis. Nowadays it is understood that prompt detonation does not occur because the core at ignition time is insufficiently isothermal.
Although it is controversial whether the deflagration will later make a transition to a detonation (Niemeyer & Woosley 1997; Khokhlov et al. 1997; Niemeyer 1999), it is universally assumed that the runaway begins as a deflagration (Nomoto et al. 1976).
Indeed, there may be great difficulty getting a viable supernova explosion if all the ignition occurs on one side (Niemeyer et al. 1996). Unless a transition to detonation occurs, or pulsational oscillations, it will be difficult to ever burn the other side. The explosion will then be subenergetic and produce too little 56Ni.
(Ref> The Astrophysical Journal, 607:921–930, 2004 June 1)
Nature-2020.
We do not know whether the burning wave propagates through the white dwarf as a supersonic detonation or as a subsonic deflagration. We do not understand the details of initial ignition and runaway. We do not know the nature of the binary companion that feeds the white dwarf—whether it is a main sequence star, a subgiant star, a giant star, or another white dwarf. All these types of companions might occur with some frequency.
The result of all this ignorance is that theorists cannot predict—from first principles and with sufficient precision—the 56Ni yields, explosion energies, light curves, and spectra of type Ia supernovae to justify them as cosmological theodolites
The theoretical discovery of Sanal flow choking received considerable attention in the central science for resolving centuries long unresolved problems. Understanding flow physics and the transport of fluid from creeping inflow to the supersonic flow at the yocto to yotta scale systems are of significant interest for testing classical theories of the continuum and non-continuum fluid flows for solving varieties of industrial problems with credibility. Gotthard Seifert[102] reported ab initio in silico simulations, which provide a sign of the development of the molecular and electronic structure of an explosive undergoing detonation. Moseler and Landman[103] used molecular dynamics (MD) simulations of nanoscale jets to encounter a rupture profile not illustrated by macroscopic theory. Of late (2020), Chengxi Zhao[104] reported that the soundness of the traditional theories at the microscale and nanoscale has been taken into question. Authors reported that the thermal fluctuations are spontaneously occurring within molecular dynamics (MD) simulations. D.M.Holland et al.[105] further reported that the time dependent mass flow rate predicted using their enhanced in silico simulation matches well with full molecular dynamics (MD) simulation and highlighted that the traditional in silico results of such cases are incompetent. It leads to say that in real world scientific experiments of complex nano-microscale systems the robustness of in silico model needs to be tested to featuring the actual fluid characteristics in a non-trivial geometry at the nanoscale. Singh and Myong [106] reported that for improved modeling efforts, the joint effect of material properties, the scale and shape of the flowing medium on fluid flow must be taken into account, which we conclusively addressed herein through the closed-form analytical models capable to solve real-world fluid flow (continuum / non-continuum) problems experiencing deflagration to detonation transition of any scale.
The physics of detonation chemistry presented herein through the Sanal flow choking/ streamtube flow choking phenomenon is a pointer for prediting detonation in yocto to yotta scale systems and beyond, which includes supernova explosion.[107] Note that the mechanism whereby a degenerate carbon-oxygen white dwarf explodes, producing a Type Ia supernova (SN Ia), still remains poorly understood.[108] Earlier researchers do not know whether the burning wave propagates through the white dwarf as a supersonic detonation or as a subsonic deflagration.[107-121]. Herein, we provide the proof of the concept of the Sanal flow choking and streamtube flow choking causing the sharp pressure spike due to shock wave formation. The streamtube flow choking is a radical theory in predicting the deflagration to detonation transition in both internal and external flows. At the low subsonic inlet conditions, the real-world fluid flow (continuum / non-continuum) system with the divergent/bifurcation duct could incline to deflagration-to-detonation-transition (DDT) due to the phenomenon of the boundary-layer-blockage (BLB) factor induced the Sanal flow choking in a wall-bounded or streamline bounded flows at a critical pressure ratio. The Sanal flow choking is vulnerable to catastrophic failures of reacting and non-reacting fluid flow systems with sudden expansion/divergent port due to the cavitation, shock wave and detonation as the case may be. At the lower critical detonation or hemorrhage index, the critical pressure ratio of the chemical energy system and the blood pressure ratio (BPR) of the subjects (human being / animal) are unique functions of the heat capacity ratio (HCR) of the gas in the duct. Numerical simulations are carried out with creeping inflow conditions using a calibrated viscous flow solver[3] for demonstrating the novel concept of the fluid-throat induced Sanal flow choking followed by the shock wave generation and pressure overshoot in a straight-tube ending with a divergent port, similar to an artery with the divergent / bifurcation region. We concluded that the detonation kernel is more sensitive in the reacting flows generating the leading species with low HCR. We also concluded from the analytical solution that the biofluid / blood with low HCR is more susceptible to asymptomatic hemorrhagic stroke (AHS) in the circulatory circuit of all subjects due to an early flow choking. The risk of Sanal flow choking and streamtube flow choking could be negated by breaking the blockage and/or increasing the HCR of the evolved gases in the tube for keeping the total-to-static pressure ratio always lower than the lower critical detonation / hemorrhage index in any fluid flow system. In silico results reported herein shed light for the biological, chemical, energy, environmental, material and aerospace systems design and drug discovery. The result of this study is a strong exposition to the industry for the elimination of the detonation in any energy system with confidence, which was an unknown fact to the scientific communities for several decades.[1-4, 86-91]
Using the exact solution reported herein a detonation free energy system could be devised authoritatively by regulating the inflow condition, selecting the fluid viscosity, HCR and the average wall-friction coefficient based on the upstream length-to-diameter ratio of the flow system for achieving the condition LCDI > (Ptotal/Pstatic)fluid-throat. In other words, we can reduce the risk of DDT by increasing the HCR. In the case of biological systems by keeping BPR < LCHI, we could reduce the risk of AHS.[1-9] It can be achieved by increasing the BHCR, which could simultaneously reduce blood viscosity and turbulence. A fluid-structural simulation could be useful to offer cogent answers to clinical questions pertaining to AHS and aneurysm, which are beyond the scope of this manuscript. In a nutshell, this basic research article sheds light for discovering the likelihoods of biofluid flow choking, Sanal flow choking and Streamtube flow choking in real-world fluid flow system. Briefly, analytical, and in silico results highlighted in this article will complement preclinical in vivo assessments in mega and nanotubes and can fine-tune decision making steps in biomaterial design and drug discovery through the nanotechnology.[89-101] This article is a part of the scientific odyssey that resulted from a collaboration among members from various research groups, viz., rocket propulsion, physical and material science, chemical science, environmental science, biomaterials, biomedical, cardiology, nanotechnology and nanomedicine.
Movie S1: In vitro result demonstrating the shock wave generation in a viscoelastic tube with vasospasm at a critical pressure ratio: https://youtu.be/59E6pI3L5Rc
Movie S2: In vitro result demonstrating the internal flow choking and the shock wave generation in a viscoelastic tube with vasospasm at different locations at a different pressure ratio: https://youtu.be/UQqtpQaUVHg
Movie S3: In silico result demonstrating the boundary layer blockage induced the Sanal flow choking at a critical pressure ratio: https://youtu.be/eFndUAU_m5I
Acknowledgments
The first author thanks SERB/DST, Government of India for the necessary support for originating this historical work.
Data availability
The raw data required to reproduce the in silico results are available with the corresponding author and could be shared on request.
[1] V.R.Sanal Kumar, Vigneshwaran Sankar, Nichith Chandrasekaran, Ajith Sukumaran, Sulthan Ariff Rahman Mohamed Rafic, Roshan Vignesh Baskaran, R.S.Bharath, Charlie Oommen, Pradeep Kumar Radhakrishnan, Shiv Kumar Choudhary, “Sanal Flow Choking: A Paradigm Shift in Computational Fluid Dynamics Code Verification and Diagnosing Detonation and Hemorrhage in Real‐World Fluid‐Flow Systems,” Global Challeges, Wiley Publication, May 2020, PMCID: PMC7267099, PMID: 32837737, https://doi.org/10.1002/gch2.202000012
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