Turbulent Vortex Research Articles

Maximum drag enhancement asymptote in turbulent Taylor–Couette flow of dilute polymeric solutions

Direct numerical simulations in a wide-gap turbulent viscoelastic Taylor–Couette flow in the Reynolds number (Re) range of 1500 to 8000 reveals the existence of a maximum drag enhancement (MDE) asymptote. The statistical properties associated with the turbulent and polymer dynamics demonstrate that the turbulent drag enhances with the increase of the Weissenberg number (Wi) and eventually saturates above a critical Wi, namely, the flow reaches the MDE state. The mean velocity profile in MDE state closely follows a logarithmic-like law with an identical slope (κK=2.32) and a Re-dependent intercept. A detailed analysis of flow structures reveals that the MDE asymptote results from the creation and eventual saturation of small-scale elastic and inertio-elastic Görtler vortices in the inner- and outer-wall regions, respectively. These vortical structures arise due to competing effects of polymer-induced stresses that either suppress or promote turbulent vortices. A close examination of competing forces in the azimuthal direction shows that the ratio of polymeric to turbulent stresses reaches a large plateau, underscoring the elastic nature of the MDE state. Moreover, the energy production mechanism in the MDE state further supports: (1) the universal interplay between polymers and turbulent vortices in a broad range of curvilinear and planar turbulent flows, and (2) the fact that the elastically induced asymptotic saturation of drag modification is an inherent property of elasticity-driven and/or elasto-inertial turbulence flow states. Overall, this study provides concrete evidence for our earlier postulate that asymptotic flow states in unidirectional turbulent viscoelastic flows are of elastic nature.

Synthetic turbulence modelling for offshore wind farm engineering models using coherence aggregation

AbstractTurbulent wind fields are known to be a major driver for structural loads and power fluctuations on offshore wind turbines. At the single‐turbine scale, there exist well‐established design standards based on wind spectra and coherence functions calibrated from years of measurements, which are used to generate multiple 10‐min wind field realisations known as synthetic turbulence boxes, themselves used as input to turbine‐scale aero‐hydro‐servo elastic codes. These methods are however not directly applicable at farm scale. When analysing the dynamics of large offshore wind farms, measurements reveal the importance of large, low‐frequency turbulent vortices for power fluctuations and hence for wind farm control and grid integration. Also, farm‐scale wind fields are needed as input to farm‐scale aero‐servo‐elastic codes for the modelling of wake dynamics, affecting structural loads. These new concerns motivate an upgrade in the original turbine‐scale wind field representation: (1) spectral models need to be based on farm‐scale measurements, (2) the frozen‐turbulence assumption merging temporal and along‐wind coherence must be lifted, (3) simplifications are needed to reduce the number of degrees of freedom as the domain becomes excessively large. This paper suggests models and algorithms for aggregated farm‐wide corrrelated synthetic turbulence generation—lumping the wind field into space‐averaged quantities—adapted to the aero‐hydro‐servo elastic modelling of large offshore wind farms. Starting from the work of Sørensen et al. in the early 2000s for grid integration purposes, methods for structural load modelling (through wake meandering and high‐resolution wind field reconstruction) are introduced. Implementation and efficiency matters involving mathematical subtleties are then presented. Finally, numerical experiments are carried out to (1) verify the approach and implementation against a state‐of‐the‐art point‐based—as opposite to aggregated—synthetic turbulence generation code and (2) illustrate the benefit of turbulence aggregation for the modelling of large offshore wind farms.

Static and Dynamic Performances of Novel Aerostatic Bearings with Primary and Secondary Orifice Restrictors

Aerostatic bearings are crucial support components in ultra−precision manufacturing equipment. However, improvements in the load−carrying capability (LCC) of aerostatic bearings often lead to higher intensity nano−vibrations. This paper introduces a novel primary and secondary orifice restrictor (PSOR) designed to simultaneously enhance the LCC and mitigate nano−vibrations in aerostatic bearings. The static performance of complex turbulent flows occurring within the chamber of aerostatic bearings with PSORs was investigated. The dynamic performance of the turbulent flows was analyzed through 3D transient numerical simulation using the large eddy simulation method. The LCC and nano−vibration acceleration were measured experimentally, and the results indicated that the design of the secondary orifice diameter could enhance LCC and mitigate nano−vibrations, consistent with theoretical predictions. The accuracy of the proposed model was validated, confirming the effectiveness of PSOR. In the experiments, an aerostatic bearing with a secondary orifice diameter of 0.1 mm exhibited the lowest LCC and largest nano−vibration. Conversely, an aerostatic bearing with a secondary orifice diameter of 0.26 mm exhibited the highest LCC and weakest nano−vibration. This study provides insights into the formation mechanism of turbulent vortex and interaction mechanism among the primary orifice and secondary orifices in aerostatic bearings with a PSOR.

Detailed turbulent structures investigation around piers group induced flow

This paper aims to investigate the mean velocities and turbulence characteristics, which include Reynolds shear stresses (RSS) and turbulent intensities, in order to study temporal and spatial flow patterns around a complex three square-piers group. Measurements have been performed by acoustic Doppler velocimeter (ADV) to identify turbulence flow structures alteration and vortices formation in longitudinal, transverse, and vertical directions. In total, 164 locations around the bridge piers have been measured, while each location consists of no lesser than 15 vertical depth ADV data point measurements. To investigate the flow turbulence, critical locations have been observed from high vortex-influenced regions. The impacted mean velocity profiles have been compared to that at the unaffected region to study the flow alteration caused by piers group. The result reveals that the log-law layer near wall has been enhanced by the installation of pier. Furthermore, as identified from the most critical locations of turbulent structures across different measurement rows, the accelerated flow will result in lower observed turbulent structures. Although flow after each pier has been influenced by strong reversal velocities, vortices have managed to form at near wake. Analysis has been divided into inner and outer flow regions (IFR and OFR) based on flow depth to enhance the understanding of how bridge piers contribute to the development of flow turbulence.

Shallow relic gravitational wave spectrum with acoustic peak

We study the gravitational wave (GW) spectrum produced by acoustic waves in the early universe, such as would be produced by a first order phase transition, focusing on the low-frequency side of the peak. We confirm with numerical simulations the Sound Shell model prediction of a steep rise with wave number k of k 9 to a peak whose magnitude grows at a rate (H/k p)H, where H is the Hubble rate and k p the peak wave number, set by the peak wave number of the fluid velocity power spectrum. We also show that hitherto neglected terms give a shallower part with amplitude (H/k p)2 in the range H ≲ k ≲ k p, which in the limit of small H/k rises as k. This linear rise has been seen in other modelling and also in direct numerical simulations. The relative amplitude between the linearly rising part and the peak therefore depends on the peak wave number of the velocity spectrum and the lifetime of the source, which in an expanding background is bounded above by the Hubble time H -1. For slow phase transitions, which have the lowest peak wave number and the loudest signals, the acoustic GW peak appears as a localized enhancement of the spectrum, with a rise to the peak less steep than k 9. The shape of the peak, absent in vortical turbulence, may help to lift degeneracies in phase transition parameter estimation at future GW observatories.

Verification and validation for large eddy simulation of the turbulent flow around an underwater entity

The objective is to analyze the errors and uncertainty in the simulation results of the complex, unsteady turbulent flow and vortices. The implicitly filtered large eddy simulation (LES) with the boundary data immersion method is used to investigate the transient turbulent flow around a fully appended underwater entity model (SUBOFF) proposed by Groves et al. [Geometric Characteristics of DARPA Suboff Models: (DTRC Model Nos. 5470 and 5471) (David Taylor Research Center, 1989)] with emphasis on verification and validation. As for the verification, the five-equation method is used to assess the LES error, including the modeling error and numerical error in the transient flow. They offset each other, leading to a small total error. As for the validation, it has been achieved in the most area when the experimental result is located at the band of ysim ± UV (ysim is the simulation result, and UV is the validation uncertainty). There is a strong relationship between the validation uncertainty and the complex vortex interaction. The validation uncertainty becomes significant, which means less accuracy of the simulation result, within the tip flow region, adverse pressure gradient region, tip vortex interacting with the boundary layer region and shear layer region. Most all of these regions occur behind the appendage and at the shape changing position of the SUBOFF.

A design method of volute profile of multi-blade centrifugal fan based on DRBF model

The forward-curved multi-blade centrifugal fan is widely used in the ventilation and household appliance industries with limited space due to its small size factor, high pressure coefficient, and large outlet flow coefficient. Conventional centrifugal fan structural designs rely on empirical data, resulting in drawbacks during usage such as low airflow velocity, high noise levels, and high energy consumption. In order to optimize fan structure, enhance aerodynamic performance, and seek new, effective approaches for energy efficiency and emissions reduction, this paper focuses on a combined design method that integrates scroll line design with aerodynamic performance and noise control. The goal is to propose a noise prediction and analysis method for multi-blade centrifugal fans, addressing the design contradiction between optimal fan functionality and minimal noise within limited design dimensions. The dynamic radial basis function method is introduced to investigate the geometric parameters of the scroll line, utilizing coherence analysis to identify the reasons for insufficient aerodynamic performance and noise reduction measures. Through the research, it is found that unreasonable design leads to a large turbulent vortex region within the blade passage and internal flow field, particularly involving circulation and backflow, which significantly reduces the fan's aerodynamic performance and operational efficiency. The design incorporates a composite scroll with a logarithmic spiral and circular arc integrated into one, and algorithm-based optimization of the scroll tongue, facilitating the transition of turbulence at the scroll outlet and the gap between the scroll tongue and impeller. Numerical results show an increase in airflow of 3.04 m3/min and a noise reduction of 3.79%. This indicates that the composite scroll design with a logarithmic spiral plays a dominant role in accelerating the aerodynamic performance of the scroll and reducing noise radiation.

High efficiency separation of fine coke powders by the novel jet-swirl scrubber: Characteristics and mechanisms

The deep removal of fine coke powders is an urgent need and remains a great challenge for the stable operation of the delayed coke system. Herein, a novel jet-swirl scrubber was developed. A combined approach utilizing CFD and DPM was employed to investigate the mechanism of droplet fragmentation. The results indicated that droplets underwent two stages of fragmentation in the convergent and throat sections under the influence of turbulent vortex structures. This leaded to a rapid reduction in droplet size and an effective dispersion. Thorough mixing with the gas phase occurred in the divergent section, facilitating enhanced capture of coke powders. Cold model experiments were conducted to examine the relationship between droplet size, coke powders capture efficiency, and gas-liquid separation efficiency. Under the condition of optimized critical droplet size 0.106 mm by adjusting the flow rate, the removal efficient of coke powders was up to 99.57 %. This work provides valuable technical support for further development and process optimization of the decoking powder unit in delayed coking system.

Hierarchy of coherent vortices in turbulence behind a cylinder

To draw concrete pictures of the hierarchy of multiscale coherent vortices in turbulence behind a cylinder and to reveal their sustaining mechanism, we conduct direct numerical simulations of the turbulence at the Reynolds number, which is defined by the uniform inflow velocity and the cylinder diameter, $5000$ . The turbulence consists of three kinds of hierarchies of coherent vortices in three distinct regions: namely, the downstream region, the recirculation region just behind the cylinder and the separate shear layers. By tracking the temporal evolution of multiscale vortices in each of these regions, we demonstrate that, in all the three regions, smaller coherent vortices tend to align in the direction perpendicular to larger ones. This implies that smaller vortices are stretched and amplified in the strain-rate fields around larger ones. We also show the relevance of this observation to the energy cascade. Smaller-scale vortices receive the kinetic energy in the regions where they are stretched by larger-scale vortices; and, at the same time, they tend to compress larger ones, thus reducing larger-scale kinetic energy.

Formation of a scour funnel upstream of an orifice affected by a bottom-mounted cylinder

A scour funnel before a bottom orifice on a dam is able to help intaking water with low sediment concentration and thus protect the water turbine. Appropriate placement of pier-like structures in front of a bottom orifice may increase the size of a scour funnel. This work experimentally investigates the formation and development of a scour funnel upstream of a bottom orifice affected by a bottom-mounted cylinder. It is found that the cylinder blocks the flow so as to reduce the flow rate by as much as 8.27%. Nevertheless, the sizes of equilibrium scour funnel generally increase due to the use of a cylinder; for instance, the equilibrium scour depth may increase by as much as 36.1%. The enlargement of scour funnel is closely related to the motion of large-scale turbulent vortices caused by the cylinder. We found that the turbulent kinetic energy around the cylinder is significantly increased due to the presence of a cylinder with a maximum relative increase in 192.5%. The placement of a cylinder leads to a drastical increment of sediment erosion rate. For cases with a cylinder, it may take only 1.1% of the time (for the first time) to reach the same level of equilibrium scour depth in a same case without a cylinder. Therefore, by appropriately placing a cylinder before a bottom orifice, it is possible to achieve a larger-sized scour funnel in a very shorter time with smaller abandoned water. A formula is established to calculate the maximum equilibrium scour depth.

On Turbulent Helicity in the Surface Layer of the Atmosphere

Synchronous measurements of vorticity and velocity in the boundary layer of the atmosphere were carried out using the original 3-component acoustic circulator developed at the A.M. Obukhov Institute of Physical Physics in 2019–2020. The measurements were carried out in summer at the Tsimlyansk scientific station (in 2021, 2022) at altitudes of 1.75 and 30 m. For different realizations, turbulent helicity has negative values on average, which is possibly due to the presence of local (breeze) winds. The observed spectra of turbulent helicity exhibit a slope close to –5/3, which corresponds to the transfer of helicity along the spectrum towards small scales (direct cascade). Spectrum slopes of –4/3 are also observed, and in the low-frequency region – –1, associated with the convective component, wind shear, and submesoscale structures. The components of the turbulent vortex flow are calculated. The helicity values agree with the previously measured and theoretical estimates obtained for neutral conditions.

Topology of turbulence within collisionless plasma reconnection

In near-collisionless plasmas, which are ubiquitous in astrophysics, entropy production relies on fully-nonlinear processes such as turbulence and reconnection, which lead to particle acceleration. Mechanisms for turbulent reconnection include multiple magnetic flux ropes interacting to generate thin current sheets which undergo reconnection, leading to mixing and magnetic merging and growth of coherent structures, unstable reconnection current layers that fragment and turbulent reconnection outflows. All of these processes act across, and encompass, multiple reconnection sites. We use Magnetospheric Multi Scale four-point satellite observations to characterize the magnetic field line topology within a single reconnection current layer. We examine magnetopause reconnection where the spacecraft encounter the Electron Diffusion Region (EDR). We find fluctuating magnetic field with topology identical to that found for dynamically evolving vortices in hydrodynamic turbulence. The turbulence is supported by an electron-magnetohydrodynamic (EMHD) flow in which the magnetic field is effectively frozen into the electron fluid. Accelerated electrons are found in the EDR edge where we identify a departure from this turbulent topology, towards two-dimensional sheet-like structures. This is consistent with a scenario in which sub-ion scale turbulence can suppress electron acceleration within the EDR which would otherwise be possible in the electric field at the X-line.

A Critical Review of Turbulence Characteristics in Open Channel Flow

Abstract: This study subject encompasses a comprehensive evaluation of the available literature on turbulence in open channel flows. Open channel flows are characterized by intricate fluid dynamics, including the production of turbulent eddies and vortices that can profoundly alter transport processes and mixing of diverse fluids. The paper addresses the numerous forms of turbulence that can occur in open channels, such as coherent structures, secondary currents, and bed-generated turbulence. We investigate the elements that determine the intensity and features of these turbulent flows, including channel geometry, flow velocity, fluid properties, and roughness of the channel substrate. The paper also assesses the current theoretical models used to characterise open channel turbulence and the experimental techniques used to quantify and demonstrate turbulent flows in open channels. By critically scrutinising the strengths and limits of the current literature, this review outlines the essential research gaps that need to be addressed to expand our understanding of turbulent open channel flows. This study contributes to the development of enhanced models and techniques for managing and modulating open channel flows in diverse applications.

A comparative analysis of internal flow and spray characteristics in triangular orifices with diesel and biodiesel

This paper presents an inquiry into the internal flow and spray behavior of diesel and biodiesel in a triangular orifice, using experimental and numerical methods. The inner flow was analyzed through the implementation of Large Eddy Simulation model. Furthermore, two high-speed cameras were utilized to capture spray images of the major and minor axes of the triangle-shaped nozzle simultaneously. The investigation revealed that, in comparison to diesel, biodiesel exhibited a higher discharge coefficient. Additionally, the vorticity magnitudes and turbulence vortex structures for biodiesel were consistently lower than those for diesel. The use of biodiesel can hinder the occurrence of cavitation. Moreover, it was observed that the triangular spray cone angle displayed axis-switching phenomena for both fuels. The axis-switching phenomenon is suppressed by using biodiesel. The research also discovered that the triangular biodiesel spray has a longer spray tip penetration and a smaller angle in all view planes. This could be attributed to the higher viscosity and surface tension of biodiesel, as well as the inhibition of the spray axis-switching during the injection, leading to an increase in the spray tip penetration and a decrease in the spray cone angle for biodiesel.

Study on the flow mechanism and frequency characteristics of rales in lower respiratory tract.

The frequency characteristics of lung sounds have great significance for noninvasive diagnosis of respiratory diseases. The rales in the lower respiratory tract region that can provide rich information about symptoms of respiratory diseases are not clear. In this paper, a three-dimensional idealized bifurcated lower respiratory tract geometric model, which contains 3rd to 13th generation (G3-G13) bronchi is constructed, where , and then the large eddy simulation and volume of fluid are used to study the fluid flow characteristics. Ffowcs Williams and Hawkings model are subsequently used to study the frequency characteristics of rale of different generations of bronchi. The results showed that bronchial blockage and sputum movement will enhance the turbulence intensity and vortex shedding intensity of flow. The dominant frequency and highest value of sound pressure level (SPL) of rhonchi/moist crackles decrease with the increase of bronchial generation. The change rates of dominant frequency of rhonchi/moist crackles in adjacent generations were 5.0 ± 0.1~9.1 ± 0.2% and 3.1 ± 0.1~11.9 ± 0.3%, respectively, which is concentrated in 290~420Hz and 200~300Hz, respectively. The change rates of SPL of rhonchi/moist crackles were 8.8 ± 0.1~15.7 ± 0.1% and 7.1 ± 0.1~19.5 ± 0.2%, respectively, which is concentrated in 28~50dB and 16~32dB, respectively. In the same generation of bronchus (e.g., G8, G9) with the same degree of initial blockage, the dominant frequency and SPL of moist crackles can be 3.7 ± 0.2% and 4.5 ± 0.3% slightly higher than that of rhonchi, respectively. This research is conducive to the establishment of a rapid and accurate noninvasive diagnosis system for respiratory diseases.

Observation of reduced-turbulence regime with tungsten injection in HL-2A edge plasmas

A reduced-turbulence regime has been observed in HL-2A NBI-heated deuterium plasmas. The transition to this regime is achieved by injecting a certain amount of tungsten into the plasma based on the laser blow-off technique. It has been found that the amplitude of geodesic acoustic mode (GAM) zonal flow and turbulent vortex size together with eddy tilting angle are all significantly increased in the edge region after tungsten injection. However, the frequency of GAM zonal flow remains nearly unchanged. Measurement shows the nonlinear coupling degree of turbulence dramatically increases while the collisional damping of GAM zonal flow drops slightly. We conclude that the increased nonlinear coupling is the main cause of the excitation of GAM zonal flow, which consequently results in the reduction in turbulent transport as observed in this experiment. These results indicate that tungsten ions play an active role in turbulence-GAM dynamics through a symmetry-breaking mechanism, which could help us to better understand the inherent physical mechanisms governing turbulent transport in the presence of high-Z impurity ions in fusion plasmas.

Experimental investigation of the interconnections between turbulent structure and scouring topographic characteristics

Complex interactions between turbulence and sediment movement around bridge piers result in bridge damage. However, the scouring mechanism remains ambiguous owing to insufficient quantitative experimental analysis pertaining to scouring topographic characteristics and their relationships with turbulent flow. Hence, an experiment is performed in this study to clarify the relationships between turbulent vortex structures and scour topography. First, we measure the two-dimensional flow fields around a bridge pier using particle image velocimetry systems and then establish a three-dimensional scour topography using the structure-from-motion technique. Subsequently, according to the unified coordinate system, we perform an innovative quantitative analysis of the scouring topography and the distributions of the shear force and horseshoe vortex around the pier. The results show the maximum depth of the scour hole increases linearly with the flow intensity. For a single scouring hole, both the cross-sectional area and volume of the scour hole vary parabolically with the height from the pit bottom. The coupling of the flow and bed topography forms the maximum scour hole via shear stress, and the large streamwise vortices on both sides of the bridge pier result in the formation of long shallow grooves on both sides of the sand dune downstream.

Compact analogs of the models of vortex flows generated by aircraft flight

The subject of this work is the development of compact analogs of vortex flows models, which are used in the modeling of vortex structures observed during the flight of an aircraft and the motion of a body in a fluid. In particular, two significant misunderstandings prevailing in this area of science are highlighted. The first misunderstanding is that the stationary motion of fluid parcels in a circle is treated as an inviscid vortex. Therefore, any vortex flow model that does not explicitly contain viscosity is considered to describe inviscid vortex motion. It has been proven that this is not so: the stationary viscous motion of fluid parcels in circular orbits corresponds to the self-balance of one force - the force of viscosity. This conclusion, in an explicit form, was made for the first time. This is very important because it changes our ideas about force balance, where two or more forces of different natures must necessarily be present. Overcoming this misunderstanding opens the way for creating compact analogs of existing models of vortex motions. Along the way, one more - the second general misunderstanding in the field of vortex dynamics was eliminated. Wherever we read it, we can see that the compactness of the vortex flow is associated with the compactness of the vorticity field. This is facilitated by the fact that the equations for vorticity and not for velocity are considered. As a result, except for one or two models of vortices, which correspond to the rotation of the entire space, up to infinity, this violates the fundamental law of physics - the law of conservation and transformation of energy. It is about the fact that, as a second misunderstanding, an error is assumed when calculating the kinetic energy of the vortex flows: the Jacobian in cylindrical (polar) coordinates is not considered. As a result, all the mentioned models of vortex flows, which correspond to the hyperbolic law as their asymptotics in the periphery, have infinite kinetic energy. Certainly, this does not correspond to the formation and evolution of compact vortex structures. Therefore, in this work, based on overcoming the aforementioned misunderstandings, many previously obtained models of compact vortex flows, as well as those obtained for the first time, are presented. In particular, this applies to the turbulent vortex flow during the formation of a vortex sheet, which is a compact analog of the Burgers-Rott vortex - both the classical one corresponding to laminar motion and the one consisting of a laminar flow in the core and a turbulent flow on the periphery of the vortex. Research methods are entirely theoretical. Well-known theorems of theoretical mechanics, mathematical theory of field, and calculus of variations, etc. are used. The obtained solutions are compared with the existing corresponding analogs of non-compact flows. Conclusions. Using the methods of calculus of variation, it was possible to show the possibility of the formation of quasi-solid-like rotational motion in a boundary layer of an incompressible fluid. The very presence of viscosity, or rather its taking into account (boundary layer), indicates a possible transition of the flow from plane-parallel motion to the just-mentioned rotational one due to the Kelvin-Helmholtz instability. In addition, two new models of the Burgers-Rott vortex flow were obtained in this study. The first model uses the general solution obtained by Burgers, but this model corresponds to a combined vortex: although the velocity field is continuous, the vorticity field has a discontinuity - at the point of maximum velocity. It is proved that such an approach is quite possible: the equation of motion is satisfied everywhere, i.e., at every point in space, and the tangential stresses are continuous functions. Since the periphery of the Burgers-Rott vortex is an unstable flow, another model is proposed - with a laminar core and a turbulent periphery. Certainly, the motion of fluid parcels in the peripheral region is described by a velocity distribution other than that of Burgers. Finally, the possible use of known models of compact vortex flows to simulate the von Karman vortex street is considered, with an indication of the advantages of these models.

Numerical Simulation of the Formation and Motion of Turbulent Vortex Clouds (Puffs)

Numerical Simulation of the Formation and Motion of Turbulent Vortex Clouds (Puffs)

Study on the Turbulent Vortex Structure Characteristics of a Two‐Layer Impinging Stream Reactor

AbstractThe structure of the turbulent vortex in a two‐layer impinging stream reactor was studied by large eddy simulation. The distributions of vortex intensity, turbulent kinetic energy, and shear stress at different Reynolds numbers Re, nozzle spacings L, and nozzle layer spacings are discussed. The relationship between vortex structure and mixing effect in the flow field is revealed. The effects of longitudinal swirls and shear flow characteristics are analyzed. Finally, the field synergy theory is used for evaluation. With increasing Re, the vortex intensity and average shear stress increase. The nozzle spacing and layer spacing affect the mixing effect in the reactor by controlling the change of vortex structure in the flow field. When L/D = 3, where D is the nozzle diameter, the energy loss is the smallest and the mixing effect is the best. The research results provide a theoretical reference for the structural optimization of the impinging stream reactor.