Convergent-divergent Research Articles

Innovative Metal Powder Production Using CFD with Convergent-Divergent Nozzles in Wire Arc Atomization

This study aims to enhance the production of metal powders using a novel approach that integrates computational fluid dynamics (CFD) with convergent-divergent (C-D) nozzles in wire arc spraying atomization (WASA). The primary objective is to investigate the influence of nozzle design on particle size distribution and production efficiency. Utilizing the ANSYS CFD Fluent program, simulations were conducted to analyze the effects of various parameters, including throat diameter and divergent angles, on gas dynamics and metal droplet behavior. The findings reveal that C-D nozzles facilitate the acceleration of gas flow to supersonic speeds, significantly improving the shear force acting on the molten metal, thereby promoting the fragmentation of droplets into smaller particles. Notably, the optimized nozzle configuration achieved a median particle size (D50) of 44.42 µm, suitable for additive manufacturing applications. The novelty of this work lies in its comprehensive simulation framework that allows for rapid virtual testing, potentially leading to significant improvements in the efficiency and quality of metal powder production processes. This research addresses critical gaps in the existing literature and provides a robust foundation for future studies in the field of metal powder manufacturing. Doi: 10.28991/HIJ-2024-05-03-02 Full Text: PDF

Exploring Near-Wake Structures: Bio-Inspired Convergent-Divergent Riblets on Circular Bluff Bodies

Abstract Convergent-divergent (C-D) riblets represent a pioneering rough surface inspired by the skin of fast-swimming sharks and flight feathers of the birds. In this study, we applied convergent-divergent riblets to the outer surface of a circular cylinder to examine their influence on the near-wake flow structure behind the cylinder. Various experimental techniques, such as particle image velocimetry (PIV), hot-wire anemometer, and a load cell for force measurement, were employed for this study. The experimental measurements have been conducted at different Reynolds numbers ranging from (6–12) ×103. The findings from force measurement indicate a decrease in the mean drag coefficient of around 14%, 15%, 11%, and 12% obtained by riblets at Re = 6000, 7500, 10,000, and 12,000, respectively. The time-averaged flow field including streamlines, velocity field, Reynolds shear stress, vorticity, and turbulent kinetic energy were measured. The measurements suggest that the wake's size has decreased by using convergent-divergent riblets. Furthermore, data obtained from the hot-wire anemometer reveal that these riblets alter the vortex shedding frequency to a higher value and impact the amplitude peak of the power spectrum at various Re numbers.

Experimental study on effect of submergence depth on steam jet shape characteristics in direct contact condensation

The phenomenon of direct contact condensation is frequently utilized in the industrial sector due to low driving potential requirements and proficient heat and mass transfer characteristics. This experimental study investigates the influence of nozzle submergence depth by condensing steam through a straight pipe (SP) and converging-diverging (CD) nozzle. The effect of operating conditions i.e. steam pressure and water temperature in addition to nozzle geometry were also studied on steam cavity shape characteristics. Six different shapes were manifested including unstable, conical, ellipsoidal, cylindrical, divergent, and double expansion-contraction. The dimensionless penetration length of plumes was observed in a range of 1.46–3.91 and 2.14–4.41 for the CD and SP nozzle, respectively while the maximum expansion ratio was determined to be 1–1.25 for the CD nozzle and 1.16–1.58 for the SP nozzle. It has been observed that jet length increases with an increase in submergence depth, steam pressure, and water temperature. The maximum expansion ratio was observed to decrease with the increase in submergence depth and increase with an increase in steam pressure and water temperature. The empirical correlations for dimensionless penetration length were developed and predicted results were found to be lying between ±10 % and ±7 % for CD and SP nozzle respectively.

Multi-objective optimization and performance improvement of CD nozzle design parameters for cold spray coating process using RSM, ANN and GA

This study presents the multi-objective optimization of the convergent-divergent (CD) nozzle for the cold spray (CS) process and investigates the impact of five key nozzle design parameters. A 2D axisymmetric baseline nozzle was optimized through face central composite design (FCCD), computational fluid dynamics (CFD) simulations, response surface methodology (RSM), artificial neural networks (ANN), and genetic algorithms (GA). The nozzle performance in the CS process advances the manufacturing technologies by significantly optimizing the four response variables. Comparative analysis shows that RSM models (R² = 0.9893) were more accurate on average than ANN models (R² = 0.9848), although ANN provided a deeper understanding of complex interactions with an overall correlation coefficient of 0.99191. Sensitivity analysis suggested that increasing convergent length (Lc) increases particle velocity (PV) before it stabilizes while particle temperature (PT) decreases due to cooling effects. Divergent length (Ld) increases PV to an optimal range, but reduces PT, indicating energy loss. Smaller injector inner diameter (Did) enhances PV but reduces PT. Injector length (Li) increases PV to a certain limit, beyond which benefits stabilizes, and also increases surface pressure (SP). Expanding the exit diameter (De) increases PV, drops PT and heat flux (HF), and reduces SP, indicating decreased flow resistance. Optimization with RSM coupled with numerical simulation (RSM-DF) improved PV, PT, HF, and SP by 9.1 %, 4.4 %, 17.9 %, and 27.6 % respectively. Further optimization with a 5–6–4 ANN and GA (NSGA-II) improved PV by 5 %, PT by 5.4 %, HF by 15.7 %, and reduced SP by 20.9 %. Integrating CFD, RSM, ANN, and GA provides an effective approach for optimizing CD nozzle parameters.

An optical investigation on macro spray characteristics of convergent-divergent ducted fuel injection under high ambient pressures

The fuel-air mixing process can be improved via straight (ST) ducted fuel injection along with the risk of greater heat transfer loss due to prolonged spray tip penetration (STP) and spray impingement. We proposed the convergent-divergent (CD) duct spray in this study to produce acceptable STP and wider spray cone angle (SCA) for improving engine efficiency. STP and SCA are closely related to ambient pressure. This paper aims to explore the influence of ambient pressure on the macro spray characteristics of CD duct spray for better fuel-air mixing with the analysis of spray air entrainment (SAE). The Schlieren system was used to record the spray morphology of different duct sprays under ambient pressures of 20, 30, 40, and 50 bar. The results showed that compared with free spray, with the increase of ambient pressure, the application of CD duct can more effectively improve the SCA increase rate of free spray. With the ambient pressure changes from 20 to 50 bar, the SCA increase rate is up to 20.17% for free spray, and the SCA increase rate increased more than three times to 76.96% with ST3 duct and more than eight times to 173.06% with CD 4.5 duct compared with free spray respectively. The SAE of CD3 and ST3 duct sprays is higher than that of other sprays. CD4.5 and CD6 duct sprays reduce the probability of spray-wall impingement but along with a certain reduced amount of SAE.

Influence of Cavity on Base Pressure Manipulation in Suddenly Expanded Flow from Converging Diverging Nozzle for Area Ratio 5.29

This study delves into the intricate interplay of cavity placement, Nozzle Pressure Ratio (NPR), and Mach numbers, examining their collective influence on manipulating base pressure within a duct. Employing numerical simulations, the research explores the cavity's effectiveness in altering base pressure dynamics in the duct's base area. The investigation comprehensively studies various factors, including length-to-diameter ratio, nozzle pressure ratio, Mach number, and cavity location. The simulations are conducted for a singular cavity at multiple positions concerning the duct's diameter, maintaining a fixed cavity width-to-height ratio of 1. The NPR ranges from 2 to 8, and the Mach numbers under scrutiny span from 1.2 to 1.8. The study meticulously analyses variations in base pressure and alterations in the pressure field resulting from these variables. Notably, the findings demonstrate the cavity's adeptness in controlling base pressure, particularly at NPR values of 4 and 6 for Mach numbers 1.2 and 1.4. In contrast, ineffectiveness is observed at NPR 2 and 8 due to specific flow reattachment points. However, the cavity effectively influences base pressure at NPR values of 4, 6, and 8 for Mach numbers 1.6 and 1.8. These discernments offer invaluable insights for the optimization of duct designs in diverse engineering applications.

Fracture Morphology Influencing Supersonic CO2 Transport: Application in Geologic CO2 Sequestration

AbstractGeologic carbon sequestration requires CO2 injection into the storage formation at high‐injecting pressure. Such high pressure could induce choked flow accompanying huge variations in thermodynamic properties of CO2 at a converging‐diverging (CD) fractures in the storage formation. In this study, high‐velocity CO2 transport through CD fractures was investigated to quantify the effect of fracture morphology on occurrence of both choked flow and shockwave that constrain the mass flow rate of fluid. In addition, variations in thermodynamic CO2 properties including Mach Number (Ma), defined by the ratio of fluid velocity to sound speed, and shock properties were investigated. The morphological characteristics of CD fractures were determined by nine properties, such as throat diameter, throat length, inlet diameter, outlet diameter, throat diameters of two‐connected CD fractures, fracture wall curvature, roughness amplitude, and frequency. As a result, the throat diameter crucially affected choked flow occurrence and maximum Ma. When the inlet and outlet diameters varied, the profiles for Ma variation were consistent in the converging and diverging segments, respectively. In addition, regardless of change in the throat length, the position of maximum Ma was nearly constant with showing the position length ratio of 0.13–0.14. However, roughness of fracture wall significantly influenced the Ma variation and occurrence of shock. In particular, backflows segregated from the main CO2 flow were observed near the wall roughness.

Numerical study on thermal hydraulics characteristics during steam submerged jet condensation from rectangular CD nozzle

The phenomenon of steam-water direct contact condensation (DCC) has significant importance in nuclear industry due to its rapid and efficient heat and mass transfer rates. In this numerical study, three dimensional simulations of steam submerged jet condensation from rectangular converging-diverging (CD) nozzle into subcooled water has been investigated. The steam condensation phenomenon has been captured from thermal phase change model as user defined function (UDF) in ANSYS Fluent software. The computational results were validated using experimental results as well as previously published numerical study. The effects of steam pressure and water temperature on distributions of various thermal hydraulics parameters including velocity, pressure, temperature, heat and mass transfer characteristics have been studied. The steam pressure and water temperature have been kept in the range of 200–500 kPa and 20–60 °C, respectively. The maximum value of jet velocity and heat transfer coefficient have been found as 803 m/s and 2.73 MW/m2K respectively. The peak velocity value increases with steam pressure. After maximum expansion point, the velocity profile curve is shifted downstream with steam pressure. The axial pressure distribution first decreases and then increases from expansion-compression waves. The axial temperature profile followed the similar trend as observed for axial steam pressure distribution. At constant steam pressure, the maximum rate of heat transfer coefficient decreases with the increase in water temperature. The maximum mass transfer rate under prescribed flow conditions has been found as 2789.8 kg/m3s. The peak mass transfer rate decreases with steam pressure and water temperature. The peak rates for heat and mass transfer have been observed in the nearby vicinity of nozzle exit location.

Effect of Convergent Angle on different Flow Parameters of a Convergent-Divergent Nozzle

Nozzle is defined as a device which is being used to convert the pressure energy into the kinetic energy. It basically controls the mass flow rate, pressure and velocity of the fluid stream. Consisting of three sections convergent, throat and divergent section, this device basically converts subsonic flow into supersonic flow. An extensive study have been conducted by the authors in the past about the divergent angle effect on flow parameters of a C-D (Convergent-Divergent) nozzle. In this paper, detailed study have been done to find the most optimum value of convergent angle of a C-D nozzle for the best flow parameters. Convergent angles under consideration are 15°, 20°, 25°, 30° and 35°.

Thermal Analysis of MHD‐Modified Hybrid Nanofluid Flow Inside Convergent/Divergent Channel With Heat Generation/Absorption and Viscous‐Ohmic Dissipation

Enhancing heat transfer efficiency and understanding fluid behavior in complex engineering systems is quite challenging. Here, we examine the rate of heat transfer of magnetohydrodynamic (MHD) flow of a modified hybrid nanofluid between two convergent/divergent (CD) channels, considering viscous dissipation, ohmic heating, along with heat production and absorption. The spherical form of nanoparticle provides a basis for dynamic viscosity and thermal conductivity. The transformed ordinary differential equations (ODEs) are solved numerically. The behavior of various physical parameters particularly channel angel (α), magnetic parameter (M), heat source (Hs), and Eckert number (Ec) are stimulated. It is revealed that the velocity behavior is opposite for magnetic strength while temperature increases as the Ec increases for both CD channels. The tetra hybrid nanofluid improves the rate of heat transfer up to 16.783% as compared to the traditional fluid.

Design and CFD Simulation of Supersonic Nozzle by Komega turbulence model for Supersonic Wind Tunnel

This paper presents an impressive design of a convergent divergent (C-D) nozzle using the method of characteristics for a Mach number 2 test section. The nozzle’s geometry was meticulously crafted in SolidWorks, and its performance was evaluated through a CFD simulation in Ansys Fluent R22 software. Results showed excellent agreement between the simulation and analytical data, with the Mach number ranging from 1.78 to 2. The study also compared turbulence modeling techniques, concluding that the k-omega model produced superior results. The supersonic wind tunnel achieved remarkable efficiency, completing a run at 1.8 Mach number in just 6 seconds. Overall, the study showcased exceptional accuracy and meticulousness.

Investigation of cross-diffusion effect on radiative Jeffery-Hamel flow in convergent/divergent stretchable channel with Lorentz force and Joule heating

This article documents the hydro-magnetic, incompressible Jeffery-Hamel flow in convergent/divergent (CD) channels with stretchable walls. Although there seem to be several works on the subject in the available literature, only a few attempts have been made to work into mass and heat transfer analysis. Consequently, novelty of present study is to investigate the significance of Soret/Dufour. Joule heating, and chemical reaction effects on Jeffery-Hamel flow. The governing coupled system of PDEs showing the mathematical framework of the current physical problems is converted into ODEs through proper transformations. The numerical solution of the obtained couple of ODEs is simulated with the assistance of Mathematica-11 solver NDSolve. The computed outcomes depict that Lorentz force developed due to the magnetic field decays the fluid motion for both convergent and divergent channels. Furthermore, incorporating the heat source and Dufour effects yields a sustainable increase in temperature distribution, whereas the Soret number has reverse features on concentration. Furthermore, the numerical outcomes reflect the significant variation in Nusselt number against magnetic, radiation parameter and Soret number.

Orthogonal analysis method for multi – Objective optimization of CO2 nozzle thermodynamic performance

In this study, the structural parameters of the converging diverging (CD) nozzle in a subcritical or supercritical CO2 cycle system were optimized by L16 (44) orthogonal design. The established model was used to analyse the effect of divergence length Ld, divergence angle θ, convergence angle α and throat diameter Dth on the nozzle thermodynamic performance, and further optimization of CD nozzle structural parameters was carried out using comprehensive evaluation coefficients and comprehensive scores. The results indicate that Ld is the primary factor, and while the effects of θ and Dth were inconsistent in different application scenarios, attention should be paid to the size parameters of the nozzle divergence part during design. For CD nozzles with supercritical inlet pressure, there is a linear relationship between Ld and exergy destruction, while for subcritical CD nozzles, the effect of Ld is reduced. For a CD nozzle used in subcritical or transcritical cycles, the outlet exergy and exergy efficiency of the modified nozzle could be increased by 16.4% and 16.2%. For supercritical nozzles used in the Brayton cycle, the optimized exergy destruction was relatively reduced by 37%. The mass flow rate of the nozzle before and after optimization was reduced, with a maximum decrease of 22.7%, which is beneficial for improving the entrainment ratio of the ejector. In addition, it was found that considering this in the modelling process would lead to conservative optimization results. These research results could provide a reference for the design of the CO2 nozzle or motive nozzle of ejector.

Cartesian grid-based hybrid NS-DSMC methodology for continuum-rarefied gas flows around complex geometries

This work presents a coupled numerical methodology, based on a hybrid Navier-Stokes (NS) and Direct Simulation Monte Carlo (DSMC) method, for high-speed compressible gas flows—involving a combination of continuum and rarefied flow regions. Implementation details of coupling cycle are presented along with the validation and performance studies for three cases (Mach number M a 1 = 3.38 , 6.5 and 9) of normal shock waves in argon and three cases (Inlet pressure pin = 1.0 atm, 0.5 atm and 0.1 atm) of flow through a micro-scale convergent-divergent (CD) nozzle. In comparison with our DSMC method-based solutions in the complete domain, the hybrid NS-DSMC method solutions achieve almost similar accuracy in a substantially reduced computational time—44% to 50% for the normal shock problem and 67% to 85% for the micro-scale CD nozzle problem. For the first time in literature, the hybrid NS-DSMC method is presented as a Cartesian-grid method, which is becoming popular nowadays.

CFD Analysis of Over-Expanded Flow in Convergent Divergent Nozzles

The classical one-dimensional inviscid theory does not reveal the complex flow features in an over-expanded nozzle accurately. The code Fluent has been used to simulate the viscous fluid (air) flow passing through three different 2-D Convergent-Divergent (C-D) nozzles for nozzle pressure ratios (NPR) corresponding to over-expanded flow. The steady state RANS equation with five different turbulence models has been simulated for turbulence model study. Two different types of boundary layer grids: grid1 (y<sup>+</sup>=1) and grid 2 (y<sup>+</sup=50) have been simulated. Shear Stress Transport k-w (SSTKW) turbulence model with grid 1 has been chosen for turbulence modeling. Both inviscid and viscous flows have been simulated. The converged solutions captured asymmetric lambda shock in all the three nozzles at higher NPRs for viscous flows. It also predicted aftershock and flow separation depending upon NPR. The shock wave angle of the incident and reflected shock generally reduces with increase in NPR for NPR£1.92. The thrust co-efficient of all the theoretical, predicted inviscid and predicted viscous solutions reduce with increase in NPR upto a certain value of NPR and then starts increasing. The predicted viscous results (shock structure, shock location, size of normal shock, aftershock and asymmetric lambda shocks) are close to the experiments in most of the cases. The aftershock phenomenon provides dual mode flow at the exit of the nozzle.

Effect of Relative Jet Temperature in Supersonic Dual-Impinging Jets

Short takeoff and vertical landing aircraft configurations involve multiple jets that impinge onto the deck surface in tandem and lead to several adverse effects. This study reports on the experimental characterization of supersonic dual-impinging jets by systematically varying their relative jet temperature. A sonic converging and Mach 1.5 converging–diverging (CD) nozzles are employed. The expansion ratio of the converging nozzle is maintained at 0.96, 1.19, and 1.59, and the CD nozzle is operated at a fixed nozzle pressure ratio of 3. The temperature ratio of the jet from the CD nozzle is varied from 1.0, 1.3, and 1.7. For a fixed momentum of the jet pair, an increase in jet temperature intensified the nearfield noise and unsteadiness on the impingement surface. At short impingement heights, resonance in the heated jet was the primary source of unsteadiness. At a fixed impingement height, an increase in jet temperature led to a systematic increase in tonal frequency, while jet instability mode shapes were retained. Furthermore, the mean flowfield of sonic jet and fountain regions remain unaffected, and an increase in supersonic jet velocity is observed. This is also accompanied by an increase in unsteadiness in the fountain upwash.

Large eddy simulation of fuel-air mixing process in a convergent-divergent duct spray under non-vaporizing conditions

The spray mixing process can be improved via straight (ST) duct fuel injection, but there is a risk of potential heat transfer loss due to prolonged spray tip penetration (STP) and spray impingement. We proposed a convergent-divergent (CD) duct spray to produce an acceptable STP along with improved spray air entrainment and spray cone angle (SCA), which is validated in optical spray experiments. How the CD duct enhances the fuel–air mixing and why the spray left–right swing phenomenon occurs near the outlet of the CD duct is still unknown. This study focuses on the spray mixing process inside CD and ST ducts using large eddy simulations. Results showed that the larger vortex cluster is formed in the divergent outlet with the large diameter of 4.5 mm and 6 mm, named CD4.5 and CD6 ducts, which leads to the unstable fluctuations of the separated shear flow and a large number of vortex shedding from the inner wall of the CD duct outlet to promote the radial fuel–air mixing with the left–right swing phenomenon, which further enlarges the SCA and appropriately shortens the STP with reduced spray energy. Compare to free spray, there are two turbulence kinetic energy (TKE) peaks in the spray axial centerline, indicating that duct spray brings extra disturbance to spray and is conducive to promoting the fuel–air mixing process. The strongest TKE region appears near the outlet of CD4.5 and CD6 duct sprays that are consistent with the left–right spray swing motion phenomenon.

Experimental investigation of nozzle submergence depth on steam cavity thermal characteristics in direct contact condensation

Direct contact condensation has found wide applications in an industrial sector because of its enormous mass and heat transfer capabilities. In the current experimental investigation, effect of submergence depth has been analyzed on the thermal characteristics of steam plume issuing into water tank from two geometrically different steam spray nozzles i.e. converging–diverging (CD) nozzle and straight pipe (SP) nozzle. The steam cavity images were taken using high-speed camera which were processed by MATLAB image-processing tool for the measurement of steam-water interfacial area. It was observed that axial temperature distribution rises with the increase in submergence depth while for radial temperature distributions reverse was found to be true. Additionally, the temperatures at nozzle exit were noted to be independent of submergence depth. The heat transfer coefficient decreases as the steam pressure, water temperature and submergence depth is increased for both the nozzles and found in range of 1.661–2.91 MW/m2·K and 1.472–1.989 MW/m2·K for the CD and SP nozzle, respectively. Moreover, the effect of submergence depth was found to be almost negligible at the higher submergence depth values.

Bio-inspired Surface Texture Fluid Drag Reduction using Large Eddy Simulation

Skin friction drag can be reduced through the application of bio-inspired riblet surfaces. Numerical simulations were performed using Large Eddy Simulation (LES) to investigate the effect of using riblets on reducing skin friction drag. In this study, three different riblet configurations were used; scalloped, sawtooth and a new design, hybrid, riblet. To validate the effect of using the proposed hybrid riblet design compared with other riblets used in the literature; before applying to complex geometries, they were initially applied to a flat plate in parallel arrangement. Results showed skin friction coefficient reduction of 14% using the proposed hybrid riblet. This reduction was 9.2 times and 1.2 times more compared to sawtooth and scalloped configurations, respectively. The hybrid riblet was then applied partially and fully to NACA 0012 airfoil. Skin friction coefficient reduction of 34.5% was obtained when the hybrid riblet fully applied on the airfoil surface. Furthermore, the Convergent-Divergent (C-D) arrangement was studied, where the riblets were placed fully on the NACA 0012 and aligned with a yaw angle with respect to the flow direction. The convergent lines are inspired by the sensory part of the shark skin, whereas the divergent lines or herringbone are found on the bird feather. The two different riblet configurations, sawtooth and hybrid were modeled with the C-D arrangement and the hybrid riblet with C-D arrangement contributed to higher skin friction coefficient reduction, 34.5%, than the sawtooth riblet shape, 26.75%. Moreover, the C-D arrangement was compared to the parallel arrangement and shown that the C-D arrangement increased the lift coefficient (cl) of the airfoil, the flow separation was delayed and the overall performance of the airfoil was enhanced.

Performance analysis of a gas cyclone with a converging-diverging vortex finder

In this study, the influence of a novel converging-diverging (CD) vortex finder on the performance of a gas cyclone was studied using the computational fluid dynamics (CFD) method. In addition, the influence of the CD outlet pipe on the erosion rate of the cyclone was investigated. The cutoff diameter, pressure drop, and erosion rates of the new vortex finder design were compared with those of the conventional straight outlet pipe cyclone. The throat of the CD pipe was at the same level as the cyclone's roof. The simulation showed that the CD outlet pipe significantly reduced the cyclone pressure drop. The height and diameter of the converging part of the vortex finder affected the cyclone pressure drop and separation efficiency. Increasing the converging part's inlet diameter reduced the outer vortex tangential velocity and the cyclone separation efficiency. Increasing the converging part inlet diameter reduced turbulent intensity at different cyclone levels. The CD vortex finder with the shortest height and inlet diameter of the converging part (model C1) reduced the cutoff diameter from 6.2 µm to 5.9 µm. The CD outlet pipe with the largest height and inlet diameter of the converging part (model C6) reduced the pressure drop by 42.2% compared to the conventional cylindrical vortex finder. The erosion rate also decreased significantly with an increase in the converging part inlet diameter. However, the converging part height only slightly affected cyclone performance.