Conical Flow Research Articles

Numerical simulation and experimental study on electrochemical recovery of copper using cylindrical and conical flow reactors

This study investigates the electrochemical recovery of copper from wastewater using cylindrical and conical flow reactors. Electrochemical approaches offer advantages such as environmental compatibility, operational versatility, and energy efficiency for heavy metal remediation. However, effective recovery from dilute effluents remains challenging due to mass transfer limitations. In this work, numerical simulations were conducted to analyze the flow field and current distribution in the reactors, with a focus on the copper reduction process. Experimental results were compared with transient simulations to assess the influence of geometry and operating parameters on the performance of the reactors. The study identified that conical reactors, particularly those with a narrowing electrode gap, enhanced mass transfer rates, leading to improved copper removal efficiency. Key findings include the relationship between electrolyte flow rates, Coulombic efficiency, and copper recovery efficiency. This work contributes to the investigation of electrochemical processes for sustainable heavy metal remediation.

A deep learning framework for solving the prediction and reconstruction problem of Bingham fluid flow field

As a typical non-Newtonian fluid, Bingham fluid is employed in a multitude of fields, including petroleum, construction, and the chemical industry. However, due to the intricate intrinsic properties of Bingham fluids and the necessity for precision and efficacy in specific engineering applications, the rapid and precise prediction and reconstruction of its flow field information has become a challenge and a focal point of contemporary research. In this paper, we introduce a novel deep-learning approach to address the two-dimensional laminar motion of Bingham fluids. The proposed Papanastasiou Regularization Physics-Informed Neural Network (PR-PINN) framework effectively predicts and reconstructs the flow field of Bingham fluids. Initially, the framework applies Papanastasiou regularization to the governing equations of Bingham fluids, enhancing the network's adaptability to solving the flow field problem by incorporating boundary conditions and an adaptive weight assignment strategy. We consider two scenarios: equal-diameter circular pipe flow and conical pipe flow. The PR-PINN network is utilized for flow field prediction and reconstruction. Our results show that PR-PINN achieves high accuracy in flow field prediction and can reconstruct velocity and pressure fields using limited measurement data. Based on these findings, we explore the impact of boundary constraints, the effect of large intrinsic parameters on prediction accuracy, and the influence of measurement points and boundary constraints on flow field reconstruction. In summary, the PR-PINN network exhibits satisfactory performance and significant potential for predicting and reconstructing Bingham fluid flow fields.

Isolator shape transition impact on hypersonic internal waverider intake flow distortion

This paper examines the impact of scramjet isolator shape transition on hypersonic internal waverider (IWR) intake. The IWR intake is designed using the osculating axisymmetric flows and streamline-tracing methods. The new Internal Conical Flow “M” basic flowfield is utilized to provide the flow information for the design method. The intake is equipped with three isolators: one with a constant cross section and two with variable cross sections with circular and rectangular exits. The entrance shape and area of the three isolators are fixed to the intake throat shape and area. The exit area of the three isolators is maintained as the entrance one. Numerical computations of three-dimensional configurations reveal that the isolators with variable cross section shapes demonstrate a higher uniformity index than those with constant cross section shape. Thus, the isolator shape transition has decreased the flow distortion of the hypersonic IWR intake system. The three isolators exhibit varied wall pressure distribution depending on the isolator cross section shape, and the total pressure recovery ratios at the three isolators' exit planes are similar. The wall pressure distributions and key performance parameters at the intake throat section, including total pressure recovery, compression ratio, and Mach number, remained consistent across the first part of the intakes. Therefore, changing the cross section shape of the isolator while keeping the area constant could enhance the flow uniformity of compressed air without negatively impacting the intake system's performance. This allows a separate shape selection of the IWR intake throat and the scramjet combustor entrance to fulfill their special requirements.

A study of conical and curved shock waves via the streamline transformation method

The axisymmetric conical and curved shock waves are studied theoretically via the streamline transformation method (STM), which integrates the differential geometries of streamlines into the conservation laws and solves the flow field geometrically. Under the condition of a straight shock wave, the governing equation is significantly simplified, from which the assumptions of the conical flow and geometric self-similarity are mathematically proved. The simplified equation is also demonstrated as equivalent to the classical Taylor–MacColl equation. The flow mechanism after a conical shock wave is discussed from a geometric perspective, where the key factor is the dimensionless lateral distance between symmetric planes. The corresponding geometric and flow parameters, e.g., the distance between streamlines, the streamline curvature, and the Mach number, are computed for the demonstration of this mechanism. In the flow field over a circular cone, the isentropic compression is modeled geometrically. Due to the isentropic compression, the conical shock wave remains approximately a Mach wave at small semi-angles and the detachment is suspended at large semi-angles. For the axisymmetric curved shock wave, the flow field is computed directly by the streamline transformation method, where both the concave and convex shock waves are considered. Along the wall streamline, an explicit proportional relation between the shock curvature and the orthogonal derivatives of flow parameters is also provided and verified numerically. These results are applicable in the theoretical analysis and inverse design of axisymmetric shock waves.

JWST study of the DG Tau B disk-wind candidate

Context. The origin of outflows and their impact on protoplanetary disk evolution and planet-formation processes are still crucial open questions. DG Tau B is a Class I protostar associated with a structured disk and a rotating conical CO outflow and was recently identified by ALMA as one of the best CO disk wind candidate. It is therefore a perfect target for studying these questions. Aims. We aim to map and study any outflow component intermediate between the axial jet and the CO outflow in order to constrain the origin (irradiated or shocked disk wind or swept-up material) of the redshifted molecular outflows in DG Tau B. Methods. We analyzed observations obtained with James Webb Space Telescope NIRSpec-IFU and NIRCam, supplemented with IFU data from the SINFONI/VLT instrument. We investigated the morphology, kinematics, and excitation conditions of the ro-vibrational H2 emission lines and their relation with the atomic jet and CO outflow. We focus our analysis on the redshifted outflow lobe. Results. We observe a global layered structure of the redshifted outflows in DG Tau B, with the atomic jet inside the H2 cavity, which in turn is nested inside the CO conical outflow. We also find temperature, velocity, and collimation to be increasing towards the axis of the flow. The redshifted H2 emission traces a narrow conical cavity (semi-opening angle of 9.4°) that is wider than the axial jet but nested just inside the CO outflow. Both the jet and the H2 cavity originate from the innermost regions of the disk (r0 < 6 au). The redshifted H2 cavity flows with a constant vertical velocity of Vz = 22.5 ± 0.8 km s−1, twice faster than the conical CO flow. The excitation conditions imply a hot H2 gas (Tex ≃ 2200 K) with an average mass flux of Ṁ(H2) = 3 × 10−11 M⊙ yr−1, which is significantly lower than the jet and CO values. Conclusions. The global layered H2-CO structure in temperature, velocity, and collimation in the DG Tau B redshifted lobe is consistent with a magneto-hydrodynamic disk wind scenario. The hot H2 could trace the inner, dense photodissociation layer in the wind. An H2 launching region at disk radii of 0.2−0.4 au combined with a large ejection efficiency (ξ ≃ 1) would account for the mass flux and kinematics. Alternatively, the near-IR ro-vibrational H2 could be emitted in the interaction layer driven by successive jet bow shocks into an outer disk wind or envelope. Further constraints on both scenarios will be obtained from the analysis of MIRI observations.

Improved Design Method for Hypersonic Intakes Using Pressure-Corrected Osculating Axisymmetric Flows Method

The efficient design of air intake is crucial for high-speed airbreathing propulsion systems. This paper presents a novel design method that integrates the recently introduced internal conical flow M (ICFM) basic flowfield (Musa et al., “New Parent Flowfield for Streamline-Traced Intakes,” AIAA Journal, Vol. 61, No. 7, 2023, pp. 2906–2921) with the pressure-corrected osculating axisymmetric flows and streamline tracing techniques. The new design method takes into account the effects of lateral pressure gradients by incorporating pressure corrections into the original design method using crossflow velocity information from the ICFM flowfield. Additionally, new entrance and throat profiles are introduced for designing two hypersonic internal waverider intakes with shape transition. One intake is designed using the new method, and the other using the original method. Viscous simulations have been performed at design (i.e., Mach 6.0) and off-design (i.e., Mach 4.0 and 3.5) conditions. The results indicate that the pressure-corrected intake exhibits superior performance in terms of total pressure recovery and reduced flow distortion. This reveals that the new design method can achieve a smooth shape and efficient aerodynamic transitions between the intake entrance and throat. The new entrance and throat profiles realized better performance than the typical ones. The startability analysis reveals that the Van Wie curve controls the considered intakes. Thus, combining the pressure-corrected osculating axisymmetric flows with the ICFM flowfield enhances the performance of hypersonic intakes, making this approach a promising avenue for future hypersonic vehicles.

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.

Assessment of Multi-Physical Fields Reconstruction Approaches in Three-Dimensional Supersonic Flow with Shocks

The paper evaluates the application of several multi-physical fields reconstruction approaches based on the Tomographic Particle Image Velocimetry (PIV) in three-dimensional supersonic flows with shock waves, including the pressure, temperature, and density. The MacCormack method and the Flux Vector Splitting method with outstanding performance in two-dimensional supersonic flow are extended into three-dimensional forms. The conventional Poisson method is also considered because of its widespread application and high accuracy in subsonic and transonic flow. All of these approaches are established by the conservative Navier-Stokes equations and solved by the time-marching iteration process, combined with the perfect gas law and adiabatic flow assumption. The performances are evaluated by numerical velocimetry data. To simulate the typical three-dimensional features, the cases of uniform freestream at Mach 0.78 and 3 past a cone with a 20° half-angle are selected to obtain a sufficient spanwise velocity component. The results confirm the feasibility of the PIV-based reconstruction methods in the conical flow field. The conventional Poisson method performs well only in the subsonic case while the Flux Vector Splitting method has a better performance in supersonic flow, including higher accuracy, stability, and efficiency, with a low-level root-mean-square error of 0.449% and local maximum relative error of 1%.

Preparation of inorganic salt particles by reactive crystallization in an annular swirling flow reactor

This study investigates the performance of an annular conical swirling flow reactor in liquid–liquid reactions for the preparation of inorganic salt particles. Utilizing Particle Image Velocimetry (PIV) measurements and Computational Fluid Dynamics (CFD) simulations, it was observed that the conical design effectively inhibited the attenuation of swirling flow intensity along the axial direction, with the primary mass transfer region close to the central conical wall. In comparison to a stirred reactor, calcium carbonate particles synthesized in the swirling flow reactor exhibited more uniform morphology, smoother and defect-free surface. Notably, the average particle size remained consistently within 5–6 μm (excluding the 0.3 M feedstock), whereas stirring led to particles with an average size ranging from 8-11 μm. Analysis of the residence time distribution curve revealed minimal back mixing in the swirling flow reactor, ensuring nearly equal growth time for salt particles, thus yielding particles with a uniform size distribution. As a result, the swirling flow reactor presents compelling prospects for applications in reactive crystallization.

Improving heat transfer in indirect liquid-based battery thermal management systems through turbulator-equipped conical flow paths

To guarantee the safe operation of Li-Ion Cells (LICs) in various applications, such as electric vehicles, an efficient Battery Thermal Management System (BTMS) is necessary. The design of BTMSs, as documented in the literature, typically involves the use of cooling channels with uniform and smooth configurations. However, these configurations encounter the challenge of temperature non-uniformity in the battery module, which stems from elevated coolant temperatures along the flow direction. In this study, a 3D numerical analysis is conducted to develop a novel indirect liquid-based cooling system for the BTMS of a module with cylindrical LICs. The study explores the effects of conical cooling channels, both with and without twisted turbulators, across various coolant mass flows during a 2C discharge process of LICs. Within the studied ranges, diverging cooling channels improve the overall thermal and hydraulic performance of the BTMS by an average of 40%, increasing the heat transfer coefficient by a maximum of 32.6%, and decreasing pressure drop by up to 35.1%. The application of turbulators proves effective in reducing the maximum temperature difference within the LICs, demonstrating a decrease of approximately 34.2% at the minimum mass flow rate and 74.4% at the maximum mass flow rate. This emphasizes the more substantial impact of turbulator utilization at higher coolant mass flow rates. An increased coolant flow rate leads to a significant enhancement of the heat transfer coefficient, ranging from 70.5% to 79.0% for the BTMS incorporating turbulators. Moreover, the study highlights a more pronounced impact of increasing mass flow rates in the BTMS designed with converging cooling channels compared to those designed with diverging channels. Finally, the results of this analysis demonstrate that the proposed system is capable of efficiently regulating the temperature of the entire battery module, ensuring that it consistently maintains a normal and safe operational range suitable for vehicular applications (below 40 °C).

Startability analysis of hypersonic overboard spillage internal waverider intake based on new basic flowfield

The current work is undertaken to examine the capability of a recently developed ICFM (internal conical flow M) basic flowfield [Musa et al., AIAA J. 61, 1–16 (2023)] to design hypersonic internal waverider intakes. The osculating axisymmetric flows concept is employed alongside the streamline-tracing method to design three internal waverider intakes with different contraction ratios, i.e., 6.0, 9.0, and 25. The three intakes have similar capture and throat shapes and entrance areas. Then, the starting characteristics of designed intakes were investigated at different design and off-design conditions. The selected design condition is the flight at Mach 6.0 and 28 km altitude. Viscous computations have been performed at Mach 6.0, 5.0, 4.0, 3.9, 3.8, 3.5, and 3.0 for the intake with a contraction ratio of 6.0, and at Mach 6.0, 5.0, 4.7, and 4.0 for the intake with contraction ratio of 9.0. The intake with a contraction ratio of 25 is simulated at Mach 6.0 and 5.0. Successful intake starting has been achieved up to Mach 3.8 for the first intake and up to Mach 4.7 for the second intake. The intake with a contraction ratio of 25 attained an unstart state in the design condition due to a very high contraction ratio. Thus, the starting limit of internal waverider intakes designed using ICFM basic flowfield is found to be controlled by Van Wie empirical limit. It is concluded that the ICFM basic flowfield can effectively design high-performance fixed-geometry intakes with overboard spillage, demonstrating excellent performance and startability across a wide range of Mach numbers.

Novel design method for inward-turning inlets with non-uniform inflow

For the integrated design of the forebody and hypersonic inlet, the non-uniform inflows generated by the forebody have significant impacts on the inlet performance. Traditional inlet designed by the Internal Conical Flow C (ICFC) flowfield or Method of Characteristics (MOC) flowfield, is difficult to match non-uniform inflows, which can easily lead to reduced captured flow and total pressure recovery. Hence, this paper proposes a novel design method for inward-turning inlets to overcome these problems. The key of this method is the parent flowfiled called the Internal Conical Flow N (ICFN). A multi-objective design optimization is integrated into the design of the two-dimensional ICFN flowfield, which enables the “design-optimization” to implement simultaneously. The new ICFN flowfield makes full use of the high compression effect and avoids the existence of Mach reflection at the focal point. Complete details of the design method of ICFN flowfield and inward-turning inlet are presented. The flowfield structure of ICFN flowfield and inlet are analyzed. Numerical simulation results indicate that the new inward-turning inlet can effectively increase captured flow and total pressure recovery. This reveals that the design method gained here can be usefully applied to the design of high-performance inward-turning inlets.

Structural design and multi-objective optimization of a novel asymmetric magnetorheological damper

The MRD with continuously adjustable damping, small compression, and large extension for asymmetric output may improve all-terrain vehicle impact resistance and vibration reduction performance in a variety of conditions. A novel conical flow channel asymmetric MRD (CFC-MRD) is proposed to solve the structure complexity stroke sacrifice, and lack of failure protection concerns in currently studied asymmetric MRD structures. In the design, the non-parallel plate magnetic circuit characteristics of CFC-MRD are investigated, including theoretical analysis and finite element modeling, and the correctness of the model is proved by testing. Considerations in multi-objective optimization include special performance imposing extra restrictions, and making the work more complicated and prone to local optima. To address this, the Nelder–Mead approach is utilized, which decreases the complexity of the optimization model while simultaneously managing performance conflicts. And a collaborative optimization strategy employing Comsol and Matlab tools is applied to improve optimization efficiency. The greatest difference between theoretical optimized values and real values is less than 6.77% in the experiments, showing the efficiency of the CFC-MRD structure design and optimization process.

Numerical Investigation on the Conical Flow of Viscoelastic Fluids

The conical problem represents one of the important problems in the various fields of industrial as the automotive industry and the aerospace industry, due to their great role in controlling the flow of liquids and gases. This article covers a computational investigation of incompressible the Phan–Thien/Tanner shear-thinning viscoelastic fluid flow through a conical converging channel. Here, we select hybrid finite element/finite volume algorithm as a first time to treat such problem. This method consists of the combination of a Taylor-Galerkin/pressure correction finite element method (TGPC-FEM) and a cell-vertex finite volume approach (CV-FEA) to solve the system of partial differential equations that govern the fluid flow. The TGPC-FEM is employed to the momentum and mass conservation models, while the stress constitutive models are treated by finite volume implementation. The findings of current study are concerned with stress response, deformation rate, and pressure drop under variations in Weissenberg number and EPTT parameters. The effect of shear-thinning behaviour with the EPTT representation is also considered.

Flame stabilization characteristics in the supersonic combustor based on a circular cross-section strut

Flame stabilization characteristics in the supersonic combustor with a circular cross-section strut were experimentally investigated. The Mach number, stagnation pressure, and stagnation temperature of the inflow were 2.52, 1.60 MPa, and 1486 K, respectively. Compared to the wedge-shaped recirculation flow at the base of the rectangular cross-section strut, the conical recirculation flow at the base of the circular cross-section strut possessed a more favorable geometry characterized by a longer length, a larger volume, and a small surface. When fueled by hydrogen, the combustor equipped both with a circular cross-section strut and a rectangular cross-section strut could achieve self-sustaining combustion. In the tests with equivalence ratios of 0.08 and 0.12, the time-averaged flame chemiluminescence intensity in the combustor with a circular cross-section strut was higher than its counterpart in the combustor with a rectangular cross-section strut by 80% and 53%, respectively. Nevertheless, the standard deviations of the flame chemiluminescence intensities showed an opposite trend. Therefore, the reaction zone downstream of the circular cross-section strut was more vigorous and stable. When both kerosene and hydrogen were supplied to the combustor, these two struts failed to stabilize the flame. Although an unsteady hydrogen–kerosene flame was witnessed in the combustor, it extinguished within 2 ms because the recirculation flow at the base of the strut was too small. Shock wave generators were employed to enhance the flame stabilization ability of the strut with a circular cross section. The experimental results suggested that shock wave generators significantly enlarged the recirculation flow and created a region with high temperature and high pressure. The self-sustaining hydrogen–kerosene flame was achieved in the combustor equipped with shock wave generators.

Kinks on elliptical convergent shock waves in hypersonic flow

Kinks commonly appear on the convergent shock surface when an internal conical flow deviates from the axisymmetric state. In this paper, the formation mechanisms of kinks on internal conical shocks (ICSs) generated by elliptical ring wedges with typical entry aspect ratios ( $AR{\rm s}$ ) in a Mach 6 flow are revealed using a theoretical method, in which the spatial evolution of the three-dimensional elliptical ICS is converted into a temporal evolution of a two-dimensional elliptical moving shock (EMS) using the hypersonic equivalence principle. To simultaneously track the shock front of the EMS and the disturbances propagating along it, a front-disturbance tracking method (FDTM) based on geometrical shock dynamics is proposed. It is found that the shock–compression disturbances from the same family initially near the major axis catch up with the disturbance initially emitted from the major axis to form kinks on the EMS. The equivalent kink formation positions predicted by the FDTM always lag behind the real kink formation positions on the elliptical ICS because the applicability of the hypersonic equivalence principle decays as the shock strengthens along the incoming flow direction. The accuracy of the equivalent kink formation positions predicted by the FDTM gradually declines with the reduction in $AR$ , but it can be significantly improved for all $AR{\rm s}$ after a modification of the equivalent relationship using the shock angle in the major plane of the elliptical ICS, which provides a new way to solve the kinks on the elliptical ICS.

Theoretical switch model of novel asymmetric magnetorheological damper for shock and vibration application

This study proposed a novel asymmetric conical flow channel magnetorheological damper (CFC-MRD) for all-terrain vehicles (ATVs) to handle complex excitations with coexisting shocks and vibrations. CFC-MRD produces adjustable damping forces by utilizing magnetically controlled properties and achieves asymmetric force output (moderate compression force and strong extension force) with conical flow channels. This design could effectively absorb and dissipate energy. The paper first illustrates the structure and asymmetric principle of CFC-MRD. Then, the mechanism of asymmetric force generation in a non-parallel flat plate is derived, and utilizes the hydrodynamic theory to derive the pressure difference of Bingham fluid between the non-parallel plates. Considering the coexistence of vibration and shock, the study proposes a theoretical switch model that distinguishes between low and high velocity states based on the Reynolds number. Finally, the validity of the model is verified by experiments, and the results show that the CFC-MRD achieves the desired asymmetric force output. The asymmetric force ratio rises with higher excitation speed and drops with increased drive current. At a speed of 1 m s−1 without any applied current, the maximum asymmetric force reaches 1.21. The small peak error, averaging only 2.57%, between experimental and theoretical results affirms the accuracy of the proposed switch model.

Uniqueness of conical singularities for mean curvature flows

In this paper, we prove the uniqueness of asymptotically conical tangent flows in all codimensions. This is based on an early work of Chodosh-Schulze, who proved the uniqueness in the hypersurface case.

Yakınsak-Konik Nozulların Giriş ve Çıkış Çaplarının İtme Kuvveti ve Hacimsel Debi Üzerindeki Etkisinin Teorik, Nümerik ve Deneysel İncelemesi

It is possible to see convergent conical type nozzles everywhere, from daily life to rocket science. They are utilized as the main part of the propulsion system in many applications such as air blow guns for spraying, steam turbines for compression, rockets for thrust generation, satellites for altitude control and so on. Although the convergent conical nozzle is a well-known nozzle, there are few studies on the effects of geometric changes by comparing more than one approach together. Therefore, this study investigates thrust and volumetric flow rate for different inlet and exit diameters of the convergent conical nozzles theoretically, numerically and experimentally. In this study, the quasi-one-dimensional Euler equations are defined for the theoretical investigation of convergent conical nozzles. However, in this approach, many important features such as viscous losses are neglected. In fact, nozzle flows have highly complex features including shock waves, turbulence, and boundary layers due to compressible effects. Thus, Computational Fluid Dynamic (CFD) simulations are performed with ANSYS Fluent for numerical investigation of the nozzle in this study. CFD simulations provide a better understanding and illustration of convergent conical type nozzle flows. For a third approach, the experimental investigation is conducted for thrust and volumetric flow rate measurements. Theoretical and numerical results are compared with the experimental results and similarity ratios are defined to find the closest to the experimental results.

The Method of Determining Total Losses in the Nozzle Cascades of Turbomachines

To assess the level of aerodynamic efficiency of the nozzle cascades of steam and gas turbines, the method was suggested to determine the total loss coefficient instead of kinetic energy loss coefficient that takes into account both kinetic energy losses and kinematic losses. This method allows us to transform the original non-uniform spatial flow behind the cascade into an axisymmetric cylindrical flow. In the tested annular cascade with cylindrical meridional boundaries, the total loss coefficient is approximately 0.02 higher than the kinetic energy loss coefficient. By taking into account kinematic losses when performing thermal calculations for the turbines we eliminate the need for an unjustified correction of the kinetic energy loss coefficient of the nozzle cascade by 0.01–0.03, increasing thus the accuracy of calculations. To analyze the operation of individual sections of the nozzle cascade and to determine the relationship between kinetic energy losses and kinematic losses, it is advisable to use the averaging method proposed in 2021 that enables the transformation of the initial non-uniform spatial flow behind the cascade into an axisymmetric conical flow. The aerodynamic characteristics of this flow are the widely used kinetic energy loss factor and two averaged flow angles.