Flow Patterns Research Articles

Design Considerations and Flow Characteristics for Couette-Type Blood-Shear Devices

Cardiovascular prosthetic devices, stents, prosthetic valves, heart-assist pumps, etc., operate in a wide regime of flows characterized by fluid dynamic flow structures, laminar and turbulent flows, unsteady flow patterns, vortices, and other flow disturbances. These flow disturbances cause shear stress, hemolysis, platelet activation, thrombosis, and other types of blood trauma, leading to neointimal hyperplasia, neoatherosclerosis, pannus overgrowth, etc. Couette-type blood-shearing devices are used to simulate and then clinically measure blood trauma, after which the results can be used to assist in the design of the cardiovascular prosthetic devices. However, previous designs for such blood-shearing devices do not cover the whole range of flow shear, Reynolds numbers, and Taylor numbers characteristic of all types of implanted cardiovascular prosthetic devices, limiting the general applicability of clinical data obtained by tests using different blood-shearing devices. This paper presents the key fluid dynamic parameters that must be met. Based on this, Couette device geometric parameters such as diameter, gap, flow rate, shear stress, and temperature are carefully selected to ensure that the device’s Reynolds numbers, Taylor number, operating temperature, and shear stress in the gap fully represent the flow characteristics across the operating range of all types of cardiovascular prosthetic devices. The outcome is that the numerical data obtained from the presented device can be related to all such prosthetic devices and all flow conditions, making the results obtained with such shearing devices widely applicable across the field. Numerical simulations illustrate that the types of flow patterns generated in the blood-shearing device meet the above criteria.

Experimental study of cryogenic oxygen–nitrogen mass transfer characteristics on microtextured plates

The detailed effects of microtexture on the distillation performance of the cryogenic fluids are seldom reported. In this work, sinusoidal microtextured plate was applied to carry out falling film visualization and mass transfer experiments of cryogenic oxygen–nitrogen system. The flow pattern and wetting of LN2 on the microtextured plate and the flat plate were analyzed through the recorded images. Gas-liquid countercurrent mass transfer experiments of oxygen–nitrogen system on the microtextured plate were conducted. Results show that the F-factor in cryogenic distillation operation should be lower than that of common chemical processes to avoid the deterioration of mass transfer performance. Furthermore, experiments on the effect of microtexture size on oxygen–nitrogen mass transfer performance were conducted. Results show that increasing the amplitude and decreasing the periodic length can optimize the interfacial mass transfer performance of cryogenic distillation. Finally, new mass transfer correlations for cryogenic distillation are proposed.

Comparison of Maximum Heat Transfer Rate of Thin Vapor Chambers with Different Wicks under Multiple Heat Sources and Sinks

In this paper, we present a new analytical model to investigate the maximum heat transfer rate of a thin vapor chamber (TVC) with multiple heat sources and sinks. The model can specifically consider different heat flux conditions for each heat source. Both capillary limitations and allowable maximum temperature constraints were employed to determine the maximum heat transfer rate. The liquid and vapor pressure distributions within the TVC were analytically derived using the Brinkman-extended Darcy equation and the Hagen–Poiseuille equation, respectively. Additionally, the theoretical wall temperature distribution was calculated based on the 3D energy equation, considering different heat flux conditions for multiple heat sources with a weighting factor. Our results demonstrate that the heat flux conditions applied to the heat sources significantly impact the internal flow pattern of the TVC. These changes in flow patterns influence the pressure distributions of the liquid and vapor, thereby affecting the maximum heat transfer rate. Furthermore, the effects of wick parameters on the maximum heat transfer rate under various heat flux conditions were examined.

Impact of inclined magnetic field on natural convection in ferrofluid within a semi-circular enclosure with a heated wavy surface

Ferrofluids are liquids that exhibit distinctive magnetic properties when subjected to a magnetic field. Due to their magnetic susceptibility, ferrofluids have recently gained considerable scientific attention. They find tools in different fields, such as electronics, mechanical engineering, and materials science. The inclusion of the semi-circular enclosure inscribed around a heated wavy cylinder provides innovative perspectives essential for engineering applications involving induction furnaces and cancer therapy devices. This paper aims to conduct a computational investigation into the influence of an inclined magnetic field on the free convection within a semi-circular cage stuffed with a ferrofluid featuring an internally undulating surface. It is considered that the interior wavy cylinder was warmed ( T h ) , and the outer semi-circular enclosure is cold ( T c ) . The analyzed system’s governing equations are computed using the Galerkin finite element method (GFEM). The ferrofluid’s flow pattern and thermal transport rate are investigated about relevant non-dimensional values, such as the wave numbers, the number of Hartmann ( 0 ≤ Ha ≤ 20 ) , the number of Rayleigh ( 10 3 ≤ Ra ≤ 10 6 ) , and the volume fraction ( 0.00 ≤ ϕ ≤ 0.09 ) . Evaluating the results involves examining isotherms, analyzing the distribution of flow velocities, and calculating the Nu avg , all while considering variations in fundamental physical parameters. As the Hartmann number ( Ha ) decreases and both the number of Rayleigh ( Ra ) and volume fraction ( ϕ ) rises, the Nu avg of the ferrofluid exhibits an increased. As a result of incorporating ferroparticles, the simulation identifies a maximum value of 35.86 for the Nu avg . It is worth noting that an enhance in Hartmann numbers is associated with an 80% decrease in the velocity stream function. On the other hand, an escalation in ferroparticle values leads to a 9.7% reduction, while elevated Rayleigh numbers result in a 60.8% surge in the stream function. Moreover, the irreversibility stemming from fluid friction, transfer of heat, and the magnetic field can be minimized for ferrofluid fluids ( n = 1 ), by employing the optimal parametric combination.

Effect of flip-chip ball grid array structure on capillary underfill flow

During the capillary underfill (CUF) process in flip-chip packaging, issues like incomplete filling, voids, wire sweeping, and overflow can impact product reliability and the relatively long filling time required. Therefore, finding ways to improve filling efficiency is a critical challenge. Conducting experiments to address these issues can be costly. As a result, the industry often relies on simulation software to simulate the actual manufacturing process, predict potential problems, compare results with experimental data, and analyze ways to improve the process. This approach helps enhance the package yield and further improves production efficiency.This study investigates the capillary underfill (CUF) process through simulation. Firstly, the viscosity and reaction kinetics of the underfill material are measured to establish the necessary data for the simulation. Then, Moldex3D, a mold flow simulation software, is used to create the model, generate the mesh, and perform the process simulation analysis. The effects of material properties and process parameters on the capillary underfill process are considered. The simulation results are compared with experimental data to validate the feasibility of the simulation. Subsequently, different flip-chip package structures and CUF process parameters are analyzed through simulation to explore the impact of these parameters on the flow pattern and filling efficiency of the adhesive material during the filling process.According to the simulation results, the filling speed is faster when the bump pitch and gap height are larger. However, the required filling time still has a considerable relationship with the volume of the filling region. Dispensing from the side with lower bump density can shorten the filling time when the bump distribution is uneven.

Heat and mass transfer analysis of hybrid nanofluid flow over a rotating permeable cylinder: A modified Buongiorno model approach

Many external factors influence the properties of nanoparticles in the working fluid, which subsequently determines the efficacy attributes of the ensuing nanofluid. Incorporating these factors is essential for studying heat and mass transfer in hybrid nanofluids, as it provides a detailed representation of the mechanism. Such factors are porous medium, heat source, Thermophoresis, and Brownian motion. The rotation of a cylinder can alter the flow field and boundary layer around it, which could be used for flow management scenarios such as drag reduction or separation of boundary layers control, and the complex flow patterns generated through a rotating cylinder could be utilized for improved mixing and heat transfer in processes in industry. Thus, the current novel aspect of the study examines the impacts of thermophoresis and Brownian motion over a rotating cylinder in the presence of a porous media comprised of water-based TiO2 and Fe2O4. The physical circumstances are primarily represented as PDEs based on the considered flow conditions, which then get transformed into a system of ODEs using the relevant similarity variables. The numerical solution is obtained by using RKF-45th and the shooting procedure. The flow symmetry and the effects of the specific variables associated with the problem are examined and delivered graphically. The findings confirm that the drag coefficient improves with porous material, altering fluid dynamics. Heat transmission steadily drops as the thermophoretic parameter gets larger, but mass transfer displays a contrary trend for evolving Brownian motion parameters. Also, the current results are validated with existing past studies.

Deracemization of sodium chlorate by hydrodynamic attrition of Taylor vortex flow

We investigated the deracemization of sodium chlorate in the unique hydrodynamic environment of Taylor vortex flow (TVF) in Couette-Taylor (CT) crystallizer. Our findings revealed a remarkable enhancement in the deracemization due to the effective hydrodynamic attrition of crystals, as compared to conventional mixing tank (MT) crystallizers utilizing the turbulent eddy flow (TEF). So, the deracemization of initial ee = 0 % in the CT crystallizer was significantly enhanced as increasing the rotation speed whereas the deracemization in the MT crystallizer occurred seldom with increase of agitation speed. Using the sparsely soluble solvent, it was demonstrated the TVF was much more effective for the hydrodynamic attrition of the crystals than the TEF. The deracemization depended not only on the flow intensity (viscous energy dissipation) but also the flow pattern. So, the TVF always produced the higher deracemization than the TEF at the same viscous energy dissipation. Also, the flow intensity and flow pattern significantly dictated the crystal agglomeration of homo-chiral (L-form and D-form) and hetero-chiral (L/D-form) forms during the deracemization. Our findings demonstrated the potential of the periodic TVF in the deracemization. The hydrodynamic attrition effect in the CT crystallizer provides a means to enhance enantiomeric purity and offers insights into the design of novel deracemization systems.

Job Flow Patterns and Productivity Dynamics in Turkish Manufacturing

In this paper, we analyze the job creation and destruction process, and the productivity dynamics in Turkish manufacturing by size, export status, import status and ownership by using a comprehensive firm-level dataset for the period of 2010–2015. Our focus is on the effect of turnover, which is due to the entry and exit of firms, on both job flows and industrial productivity growth. Our results show that while small firms contribute most to job creation, it is the large firms that contribute most to productivity growth. Regarding ownership, domestic private firms perform better than foreign firms in both job creation and productivity growth. With respect to export status, even though non-exporters outperform exporters in job creation, exporters dominate the productivity growth. As for import status, in job creation, like in the case of export status, non-importers do better but in productivity growth, unlike in the export status, no group of firms dominate, more specifically importers’ and non-importers’ contributions are close to each other. Another interesting finding is that, turnover effect on industry productivity is positive but very low. The role of incumbent firms in generating productivity growth is much higher than that of entering and exiting firms.

Analysis of unsteady internal flow characteristics in axial pump with varying number of blades using computational modelling and vibration techniques

Axial pumps were extensively applied in many varying applications because of their large flow and low head. In this research investigation, the comparative analysis of the findings unveiled that the predominant source of hydraulic-induced vibration in the pump stemmed from pressure pulsations at the impeller inlet. Notably, similar patterns in amplitude were observed as flow rates increased. Furthermore, time-domain analysis confirmed that pressure pulsations and vibrations are highly correlated under high flow rates. Pressure pulsation's Frequency-domain analysis also revealed that it was a multiple of shaft frequency and changed from one multiple to three multiples of vibration. While analyzing the flow rate characteristics pertaining to pressure pulsation and vibration, it was determined that pressure pulsations at the impeller inlet had the potential to generate frequency components across a broad spectrum, encompassing both low and high flow rates, as well as their respective multiples. This phenomenon was particularly pronounced in regions characterized by unstable and high flow rates. Vibration ingredients likely influenced by pressure pulsation at the impeller inlet could be as low as design flow rates and as high as high flow rates. A vibration frequency with a multiple did not seem to be influenced by pulsating pressure at the impeller entrance. The present study focuses on investigation of flow behaviors in an axial pump with varying numbers of blades. It is an important geometric parameter that significantly affects the pump's performance. Therefore, the dynamic flow patterns in a pump, considering changed flow and impeller blade configurations, are investigated by employing the sliding mesh technique in combination with SST (k-ω) turbulence model. The numerical results exhibit a commendable alignment with the existing experimental data, enhancing the predictive accuracy of pump performance. Qualitative analyses encompass static pressure, shear stress, and various velocity components. Concurrently, quantitative investigations delve into pressure fluctuations and average pressure across a spectrum of operating conditions and impeller blade configurations. These comprehensive findings underscore the substantial influence of the impeller blade on pressure, velocity magnitudes radial, axial, tangential shear stress, average pressure within the system.

Rational Design of Liquid-Liquid Microdispersion Droplet Microreactors for the Controllable Synthesis of Highly Uniform and Monodispersed Dextran Microspheres.

Hydrogel microspheres are biocompatible materials widely used in biological and medical fields. Emulsification and stirring are the commonly used methods to prepare hydrogels. However, the size distribution is considerably wide, the monodispersity and the mechanical intensity are poor, and the stable operation conditions are comparatively narrow to meet some sophisticated applications. In this paper, a T-shaped stepwise microchannel combined with a simple side microchannel structure is developed to explore the liquid-liquid dispersion mechanism, interfacial evolution behavior, satellite droplet formation mechanism and separation, and the eventual successful synthesis of dextran hydrogel microspheres. The effect of the operation parameters on droplet and microsphere size is comprehensively studied. The flow pattern and the stable operation condition range are given, and mathematical prediction models are developed under three different flow regimes for droplet size prediction. Based on the stable operating conditions, a microdroplet-based method combined with UV light curing is developed to synthesize the dextran hydrogel microsphere. The highly uniform and monodispersed dextran microspheres with good mechanical intensity are synthesized in the developed microfluidic platform. The size of the microsphere could be tuned from 50 to 300 μm with a capillary number in the range of 0.006-0.742. This work not only provides a facile method for functional polymeric microsphere preparation but also offers important design guidelines for the development of a robust microreactor.

Practice of Low Flow Anaesthesia and Volatile Agents Choices among Anaesthesia Providers at Muhimbili National Hospital and Muhimbili Orthopaedic Institute

With the availability of modern workstations and heightened awareness of the Health services cost and environmental effects of waste anaesthesia gases, anaesthesia providers worldwide are practicing low flow anaesthesia. In most developing countries Low Flow Anaesthesia is still underutilized due to lack of monitoring equipments and sufficient knowledge. Tanzania appears to have a paucity of studies on the prevailing practice pattern of fresh gas flow. Objective; The study aimed at assessing the practice of low flow anaesthesia and volatile agents choices among anaesthesia providers at Muhimbili national hospital and Muhimbili orthopaedic institute. Methods: A descriptive cross-sectional study was carried out for a period of 8 months involving 158 anaesthesia providers. A Structured questionnaire was used to collect data which included demographic, practice setting of Low Flow Anaesthesia, Workstations, scavenging, monitoring equipments, Volatile agents routinely used and preferred Agent. Data were analysed using the IBM Statistical package for social science’s version 23.0. Result: Prevalence of Low flow anaesthesia was 27.2%, however, only 6% used the fresh gas flow of 1l/min – 500mls/min. All anaesthesia providers had workstations and only 2.3% displayed Minimum Alveolar concentration (MAC), 79.1% worked in theatre with functioning scavenging systems, 55.8% used capnography, 6.9% monitored inspiratory Oxygen and none of anaesthesia providers used Bispectral and Agent Analyzers. Isoflurane was the most routinely used inhalational agents (100%) followed by Sevoflurane (69%), then Halothane (32%). Desflurane still not available in these hospitals. Conclusion: Low flow anaesthesia is seldom practiced in our locality despite having strong evidence of attractive advantages in medical practice and ergonomics.

Practice of Low Flow Anaesthesia and Volatile Agents Choices among Anaesthesia Providers at Muhimbili National Hospital and Muhimbili Orthopaedic Institute

With the availability of modern workstations and heightened awareness of the Health services cost and environmental effects of waste anaesthesia gases, anaesthesia providers worldwide are practicing low flow anaesthesia. In most developing countries Low Flow Anaesthesia is still underutilized due to lack of monitoring equipments and sufficient knowledge. Tanzania appears to have a paucity of studies on the prevailing practice pattern of fresh gas flow. Objective; The study aimed at assessing the practice of low flow anaesthesia and volatile agents choices among anaesthesia providers at Muhimbili national hospital and Muhimbili orthopaedic institute. Methods: A descriptive cross-sectional study was carried out for a period of 8 months involving 158 anaesthesia providers. A Structured questionnaire was used to collect data which included demographic, practice setting of Low Flow Anaesthesia, Workstations, scavenging, monitoring equipments, Volatile agents routinely used and preferred Agent. Data were analysed using the IBM Statistical package for social science’s version 23.0. Result: Prevalence of Low flow anaesthesia was 27.2%, however, only 6% used the fresh gas flow of 1l/min – 500mls/min. All anaesthesia providers had workstations and only 2.3% displayed Minimum Alveolar concentration (MAC), 79.1% worked in theatre with functioning scavenging systems, 55.8% used capnography, 6.9% monitored inspiratory Oxygen and none of anaesthesia providers used Bispectral and Agent Analyzers. Isoflurane was the most routinely used inhalational agents (100%) followed by Sevoflurane (69%), then Halothane (32%). Desflurane still not available in these hospitals. Conclusion: Low flow anaesthesia is seldom practiced in our locality despite having strong evidence of attractive advantages in medical practice and ergonomics.

Detailed visualization experiments on the start-up process and stable operation of double-layered pulsating heat pipes under vertical and horizontal orientations

The thermal characteristics in a double-layered 3D-CLPHP are investigated by visualization experiments. The results are compared with those of a single-layered CLPHP under the vertical and horizontal orientations and a filling ratio (FR) of 35%, 50%, or 65%. The tube's inner diameter (ID) is 6 mm, slightly over the limiting value for water. The orientation is found highly determinative to the flow pattern of liquid slug trains in each tube layer. The flow behavior appears similar for the two layers under the vertical orientation but apparently different under the horizontal orientation. When horizontally placed, the liquid slug trains tend to drain down to the lower layer, thereby not only triggered but sustained continuous pulsation motion. Intense cross-layered flow motion, attributed to the interaction between the downward gravity and upward gaseous expansion or buoyancy effect, is recorded during the operation. Sufficient working fluid distribution inside each layer for the overall FR of 65% is recommended. Instead, the single-layered CLPHP fails to maintain a stable oscillation motion without the assistance of gravity. The double-layered CLPHP outperformed the single-layered CLPHP by 12.8−15.1% in thermal resistance even under the vertical orientation.

Numerical Investigation and Statistical Analysis of the Flow Patterns Behind Square Cylinders Arranged in a Staggered Configuration Utilizing the Lattice Boltzmann Method

Numerical Investigation and Statistical Analysis of the Flow Patterns Behind Square Cylinders Arranged in a Staggered Configuration Utilizing the Lattice Boltzmann Method

Implementation of external magnetic field to improve strength of St37 steel resistance spot weld

AbstractThe magnetic assist technique involves the interaction between an external magnetic field and electrical current which produces Lorentz force that influences the flow pattern of molten metal and ultimately impacts the appearance and microstructure of the weld. Many parameters may influence on this process such as welding current, time, and force as well as the working magnet distance (MD). In this study, the effects of the distance between the permanent magnet’s MD on the heat-affected zone (HAZ) and weld nugget zone (NZ) were examined through mechanical and macro- and microstructural analyses. The results demonstrated that MD has a strong influence on the magnetic flux density which determines the joint appearance, quality, and microstructure of St37 steel. Results showed that with increasing MD, HAZ increased from 8 to 22 mm2 while NZ decreased from 26 to 19 mm2, and also, the grain size increased with increasing MD and reaching 48 µm at MD was set to 9 cm. Moreover, hardness decreased at both areas through increasing MD from (120–110) HV at HAZ and from (170–150) HV at NZ. Under the action of (electromagnetic filed) EMF, weld tensile shear strength and the cross tensile strength give the highest values equal to 172 MPa and 155 MPa, respectively, when MD is set to 4.5 cm. Besides, soundness joint was obtained at MD = 4.5 cm which confirms that this is the best distance between magnets.

Low genetic differentiation despite high habitat fragmentation in an endemic and endangered species of Iridaceae from South America: implications for conservation

Abstract To conserve threatened species effectively, it is crucial to map the genetic variation of the remaining populations. Thus, using 15 microsatellites markers, from which 10 were specially developed for this study, we investigated genetic structure and gene flow patterns of Herbertia zebrina Deble, a critically endangered species endemic from grasslands of southern Brazil. We also investigated the degree of habitat fragmentation and the impacts on levels of genetic diversity, mating system and pollinators of the species. STRUCTURE and discriminant analysis of principal components identified the existence of three genetic clusters. Populations were not isolated by distance, and genetic differentiation among populations was low (7.0%). Migration rates were also low, but no evidence of genetic bottlenecks was found. However, effective population-scaled mutation rates (Θ) were < 1, suggesting that populations could be experiencing genetic drift, but the reason remains unknown. The results indicate that measurements of habitat fragmentation were not significantly correlated with genetic diversity estimates, which tend to increase with fragment size. H. zebrina was identified as an outcrossing species and specialized pollinators, such as Chalepogenus goeldianus and Lanthanomelissa betinae were rarely observed. Our findings suggest that genetic differentiation across multiple populations within the entire geographic distribution of H. zebrina is very low and populations may struggle to adapt to the current environmental and pollination changes. However, habitat fragmentation is still too recent to detect significant impacts on the levels of genetic variation. Thus, conservation plans are necessary to avoid further declines of this species.

Conversion augmentation of an industrial NH3 oxidation reactor by geometry modification to improve the flow and temperature pattern uniformity using CFD modeling

BackgroundThe optimization of flow and temperature patterns in industrial reactors is crucial for achieving efficient and uniform chemical reactions. This study's major goals are to pinpoint possible areas for improvement in the NH3 oxidation reactor's performance and to deal with the problem of uneven flow distribution inside the reactor. MethodsIn this study, the reactor building design has been changed by extending the feed pipeline vertically and increasing the number of incoming feed streams in order to achieve uniformity in the property distribution on the catalyst surface of an industrial NH3 Oxidation reactor. Thus, using the CFD approach and the finite volume method, a three-dimensional model has been suggested. The results are contrasted with the actual geometrical configuration. The property alteration along the catalyst surface and the reactor length have been assessed. Significant findingsBy expanding the feed pipeline, the flow pattern at the reactor entry is fully developed and becomes uniform. As a result, NO2 production could go up by as much as 11 %. The rates of NH3 conversion, NO yield, and HNO3 generation consequently increased by 12.5 %, 3.1 %, and 8.0 %, respectively. Additionally, this alteration results in a uniform distribution of temperature and pressure across the catalytic surface, prolonging the lifetime of the catalyst. The pressure and temperature difference over the surface of the catalyst with the original reactor configuration was also found to be approximately 250 Pa and 423.15 K, according to the data. Pressure and temperature difference were reduced to 15 Pa and 273.15 K, respectively, as the feed line's length was increased at the same time.

Experimental study on flow characteristics of gas–solid two-phase flow in inclined pipes

In a fluid catalytic cracking unit, inclined pipes are mainly used for particle transportation and to maintain the pressure balance between the reactor and regenerator. In this experimental inclined pipe device, the characteristics of gas–solid two-phase flow were studied by measuring and analyzing the dynamic pressure and particle concentration parameters in different flow states. Corresponding relationships between pressure fluctuation and particle concentration on the one hand and flow patterns on the other were discovered. These were used for the quantitative identification of flow patterns. Measurement data from an analysis of bubble and particle velocities in an inclined pipe revealed a critical mass flow rate, Gs, in the mutual transformation of different particle flow patterns. The critical mass flow rate Gsc1 of lean-phase and dense-phase flows was 149kg/(m2·s). The critical mass flow rate Gsc2 of packed-bed and dense-phase flows was 240kg/(m2·s). This study enriches the basic theoretical knowledge on flow patterns in inclined pipes and provides a theoretical basis for the adjustment of inclined pipe operation in industrial fluid catalytic cracking units.

Fractional derivative modeling of heat transfer and fluid flow around a contracting permeable infinite cylinder: Computational study

Understanding the complex interplay between the contracting behavior of the cylinder and the fluid flow dynamics has implications for the design of porous structures for heat exchange and filtration systems. In this study, we investigate the dynamics and thermal behavior of fluid flow past a contracting permeable infinite cylinder. First, we developed a mathematical model based on the Navier–Stokes equations to describe the fluid dynamics around the contracting permeable infinite cylinder. A new simple well-behaved definition of fractional derivative called conformal fractional derivative introduced by authors Khalil et al., (2014) is employed to generalize the PDE’s of momentum and energy. The similarity transformation technique is utilized to transform the proposed mathematical problem into a non-linear ODE’s. Then, we utilized IPS technique to numerically solve the governing equations and obtain detailed insights into the flow patterns and thermal characteristics. We observed significant changes in the flow velocity and temperature distribution as the cylinder contracted, highlighting the intricate thermal behavior of the system. Additionally, the changes in the fraction order was found to have a notable impact on the overall flow patterns and heat transfer processes.

Fully appreciating the impossibility of shock wave regular reflection from the axis of symmetry in axisymmetric internal flows

This study investigates the reflection of shock waves in internal axisymmetric flows and conclusively shows that regular reflection cannot occur over the axis of symmetry. The analysis employs the curved shock theory to examine flow gradients behind the axisymmetric shock. The curved shock equations are presented in explicit form using influence coefficients, which establish a direct relation between flow gradients in polar coordinates and shock curvatures. The gradient information reveals that the flow behind the incident shock around the reflection point is governed by the Taylor–Maccoll equation, indicating that the flow pattern is locally conical. By analyzing the singularity of internal conical flows, the only possible structure of conical shock reflection with a smooth singularity is constructed. After a thorough theoretical analysis of this conical shock reflection structure, the study concludes with definitive proof that this specific flow pattern cannot occur in practical applications because it requires the incident shock angle to be less than the freestream Mach angle. This suggests that regular reflection is impossible to occur over the axis of symmetry in internal axisymmetric flows.