Journal Of Applied Fluid Mechanics
Volume:14 Issue: 1, Jan-Feb 2021

This paper presents a comparative assessment of low Reynolds number k- models against standard k- model in an Eulerian framework. Three different low-Re number k- models: Launder-Sharma (LS), YangShih (YS) and AbeKondoh-Nagano (AKN) have been used for the description of bubble plume behaviour in stratified water. The contribution of the gas phase movement into the liquid phase turbulence has been achieved by using the Dispersed with Bubble Induced Turbulence approach (DIS+BIT).The results reveal that the oscillation frequency of gas-liquid flow are correctly reproduced by standard k- and LS models. In fact, we found for standard K- and LS a clear dominant peak at a frequency equal to 0.1 Hz. On the other hand, YS and AKN models have predicted chaotic oscillations. The oscillation amplitude of the bubble plume predicted from LS model seems to be in good agreement with the PIV measurements of Besbes et al. (2015). However, for the standard K- model the oscillation amplitude is low. The air-water interface shows that the bubble plume mixing with the stratified water is predicted to be stronger compared to standard k- model.

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This paper presents the numerical analysis of three types of magnesium-based, axial-flow automotive cooling fans. The numerical modeling is conducted for geometrically modified fan designs with and without bead structure. The effect of geometric modifications of the fan blades on the fan performances (P-Q curve), fan efficiency, and energy efficiency is investigated using unsteady Reynolds-Averaged Navier-Stokes (URANS) equations with the sliding mesh methodology. The baseline fan having no-beads is fabricated using 3D printing technology and tested to measure the flow velocity and volumetric flow rate which shows good agreement to the numerical results. Subsequently, fans with beads are further optimized to achieve a significant increase in fan performances. To investigate the fan vibrations, modal analysis is also carried out using magnesium-alloy AZ31 as the fan material. The modal analysis gives natural frequencies of all types of fans which are beyond the fan rotational frequency and seems satisfactory.

Aim of this study is to investigate the properties of mono-atomic gas flow through the porous medium by using Event-Driven Molecular Dynamics (EDMD) simulation in the transition regime. The molecules and the solid particles forming the porous structure were modelled as hard spheres hence molecule trajectories, collision partners, interaction times and post-collision velocities were calculated deterministically. The porous medium is formed of spherical particles suspended in the middle of the channel and these particles are distributed into the channel in a regular cubic array. Collisions of gas molecules with porous medium were provided by means of the specular reflection boundary condition. A negative pressure boundary condition was applied to the inlet and outlet of the porous media to ensure gas flow. Porosity, solid sphere diameter and Knudsen number (Kn) were initially input to the simulation for different Cases. Thus, the effects of these parameters on mass flow rate, dynamic viscosity, tortuosity and permeability were calculated by EDMD simulation. The results were compared with the literature and were found to be consistent.

The shroud is a key component of the frost-free refrigerator and its geometric parameters have great influence on the aerodynamic performance of the whole system. Previous researches mainly focused on the effect of other components, such as the fan, shelves, or plate-evaporator. In this paper, the influence of the shroud with multi-outlets on the flow distributions of a frost-free refrigerator is studied thoroughly with the help of Computational Fluid Dynamics (CFD) tools. A 1/2 3-D CFD model is developed, where the verification of turbulence models and mesh independence tests are performed by comparing the mass flow rate obtained by different model configurations. The standard k-epsilon is deemed as the most suitable turbulence model choice and a mesh with Fine level is considered as mesh independence. To obtain the boundaries of the developed CFD model, an airflow velocity test rig is built and constructed. To convert the measured data to CFD model, Structural Response Vector (SRV) method is implemented for velocity profile fitting, and the fitted surface is assigned by User Defined Functions (UDF) macros in simulations. A series of simulations are carried out with the developed model, and the results indicates that no streamline in the middle two cavities of the original freezer compartment and the airflow velocities at the three outlets of the investigated shroud show a certain difference. To optimize the flow distribution, the agent model based on the BP neural network is established, in which four critical parameters of the shroud are adopted as design variables. The results show that the velocity streamlines in the middle two cavities are significantly increased after optimization and the value of the mean square error model constructed in optimization has a reduction of 61.09% compared with the original design.

Numerical simulation of the supersonic turbulent reacting flow field in a dual throat- dual fuel rocket thrust chamber is presented. Future single stage to orbit and high lift space transportation missions aspire a reliable, efficient, and cost-effective propulsion systems. The dual throat-dual fuel concept is a simple altitude compensating propulsion alternative with reusable possibilities. Turbulent reacting supersonic flow field emanating from independent thrust chambers needs to be resolved for a better understanding of the flow structures and design modifications for the performance improvement. The operation of a dual throat nozzle brings about a unique shock train in reacting supersonic flow. Two-dimensional axis-symmetric compressible reacting flow field has been solved using HLLC (Harten, Lax, van Leer, with Contact wave) scheme based finite volume Riemann solver with multi-step finite rate chemistry model for hydrocarbon/hydrogen-oxygen combustion. The computational procedure has been validated with experimental data for species distribution of a coaxial supersonic combustor. Chemical species distribution in the supersonic free shear layer is analyzed in detail to explore the nature of active reaction zones in the flow field.

Improving the aerodynamic performance of the transonic fan in a turbofan engine can be beneficial for both the fuel consumption and maneuverability of an airplane. Deep insight into the supersonic aerodynamics is needed for the simultaneous improvement of all operating parameters of a transonic rotor, including the pressure ratio, efficiency, and surge margin. A design method was developed for an axial transonic rotor by using a combination of radial equilibrium theory, the free vortex method, and a distributed span-wise diffusion factor. The loading distribution obtained by this method was the highest in the hub section and gradually decreased in the tip section. To evaluate the method, a transonic rotor was designed using the geometric parameters and operating conditions of NASA rotor 67. A code was developed to determine a geometry for the new rotor and to modify it. The code was coupled with a RANS flow solver for 3D modification of the new designed rotor. Only standard multi- and double-circular arc airfoils were applied in different radial sections of the new rotor with no blade profile optimization. The results of the RANS equations solution for the new designed rotor showed 1.5% higher efficiency, 3% higher pressure ratio, and more than 1.5 times larger operating range in comparison to NASA rotor 67. The new designed method seems to be an efficient approach that not only improved the efficiency and pressure ratio but also increased the operating range of an axial transonic rotor.

Compared to a variety of mechanical vectoring nozzles, fluidic vectoring nozzles possess more research value nowadays. The dual throat nozzle is gradually developing into an outstanding technology to handle supersonic and hypersonic aircraft deflections. Three-dimensional, steady, compressible, and viscous flows in rectangular dual throat nozzles are numerically investigated by resolving Reynolds-averaged Navier-Stokes equations and shear stress transport k-omega turbulence model. Computational fluid dynamics results are verified against the existing experimental data, where a good consistency is gained. The impacts of nozzle pressure ratio, injection-to-mainstream momentum flux ratio, and setup angle of the slot injector on the systemic performance are examined. Useful conclusions are summarized for engineering designers. Firstly, pitching angles decline along with an increasing nozzle pressure ratio, while systemic thrust ratio and thrust efficiency increase. Secondly, thrust vector angles enlarge with an increase of the injection-to-mainstream momentum flux ratio, whereas both systemic thrust ratio and thrust efficiency decay. Finally, the setup angle of the slot injector impacts the systemic performance remarkably. Although the pitching angle for the setup angle of 120° is highest, comprehensive characteristics in terms of systemic thrust efficiency and systemic thrust ratio for the setup angle of 150° are more excellent.

The occurrence and development of the dominant unsteady flow structures in a vanless centrifugal pump impeller are revealed by the proper orthogonal decomposition (POD) method. The pressure and velocity data of four radial surfaces is selected as the variables of decomposition. The results show that this method is beneficial to the analysis of flow field when there is no strong interaction of flow structures. When the flow rate starts to decrease from the design flow rate, unstable flow phenomenon such as flow separation and wake begin to appear and develop in the impeller. The POD analysis reveals the influence of the main unsteady structures on the flow field when there is no mixed or have little interaction among flow structures. It outlines the development of flow separation near the suction side of impeller and the wake near the trailing edge as the flow rate changes. However, the flow field inside the impeller becomes more and more complex as the operation condition is far away from the design condition, which needs to be combined with other methods to better analyze the flow field.

Changes in the external geometry of the pipeline laid on the erodible beds may affect the local scour around pipe. If the scouring process below the pipe is accelerated, the pipe buries on the bed (known as self-burial of the pipe) and can be used as a cheap alternative to mechanical trench digging. In this study, the effect of changes in the external geometry of the pipe in order to accelerate the scouring and self-burial pipe processes by spoiler and piggy back under unidirectional flow on the erodible bed is investigated. The results showed that the time scale of self-burial process is less than that of the scouring process. At the angles of 180, 135 and 225°, the Spoiler and piggy back reduced the time scale of self-burial and scouring process and increased the scour and self-burial depths, as well as the lee erosion length as compared with the simple pipe. At angles of 90 and 270°, the scale time of scour and self-burial processes are increased, the scour and self-burial depths and the lee erosion length are decreased as compared with the simple pipe. It can be concluded that the performance of piggy back is similar to the spoiler, therefore, they are of similar application and could be a suitable alternative for the spoiler.

The stability and galloping characteristics of iced quad bundle conductor are studied in this paper. Firstly, the aerodynamic coefficients of iced quad bundle conductor and single conductor under four different working conditions are obtained by wind tunnel test. Secondly, the equivalent aerodynamic coefficients at the central axis of the quad bundle conductor are obtained, and the equivalent aerodynamic coefficients are compared with the aerodynamic coefficients of each sub-conductor of the quad bundle conductor. Then, based on the Den Hartog instability mechanism and Nigol instability mechanism, the stable and unstable range of the equivalent coefficients of the quad bundle conductor are analyzed. Finally, the galloping characteristics of the quad bundle conductor are studied by combining with the equivalent aerodynamic coefficients at the central axis of quad bundle conductor. The results of the wind tunnel test show that the aerodynamic coefficients increase with the decreasing of the wind speed. The stability analyses show that the higher the wind speed is, the smaller the Den Hartog coefficient is the easier the Den Hartog’ galloping would occur. Furthermore, the higher the wind speed is, the smaller the Nigol coefficient is, the easier the Nigol’ galloping would occur. The analysis of galloping characteristics shows that when the conductor is located at stable state, the displacement in the y-axis direction would be much greater than the displacement in the z-axis direction.

This experimental analysis encapsulates the influence of Reynolds number (Re), diameter of nozzle, height to diameter (H/D) ratio and position of nozzle such as in-line and staggered over the responses heat transfer coefficient, temperature and Nusselt number of a hot flat plate exposed to cooling by multi-jet air impingement. For this analysis, a 15 x 10 cm flat plate is being heated using a heating coil having a heat flux of 7666.67 W/m2 which is maintained as constant through entire experiment. An H/D ratio of 2D, 4D and 6D is considered along with pipe diameters of 4, 6 and 8 mm and Reynolds number are changed between 18000 to 22000. Experimental design was performed with response surface methodology based central composite design. For all output responses, a quadratic model is chosen for analysis and a second order mathematical model is evolved for predicting with a higher R2 value. Desirability analysis is performed for multi-objective optimization and the optimum input parameters obtained are Reynolds no. of 20347, pipe diameter of 8 mm, H/D ratio of 2 and in-line nozzle position with the maximum heat transfer coefficient of 189.411 W/m2 K, Nusselt number of 28.8712 and minimum temperature of 56.983°C. Optimum condition-based confirmation experiments result in enhanced Nusselt number and heat transfer coefficient.

In this paper, a simple passive device is proposed for drag reduction on the 35° Ahmed body. The device is a simple rectangular flap installed at the slant surface of the model to investigate the effect of slant volume, formed between the device and the slant surface, on the flow behaviour. The slant volume can be varied by changing the flap angle. This investigation is performed using the FLUENT software at a Reynolds number of 7.8 × 105 based on the height of the model. The SST k-omega model is used to solve the Navier-stokes equations. It is found that this passive device influences the separation bubbles created inside the slant volume and provides a maximum drag reduction of approximately 14% at the flap angle of 10°. Moreover, the device delays the main separation point, which changes the flow conditions at the back of the model. The drag reduction was found to mainly dependent on the suppression of the separation bubbles formed inside the slant volume, which leads to faster pressure recovery. The cause of this pressure recovery is found to be the reduction in recirculation length and width. Also, the addition of a flap reduces the turbulent kinetic energy, which lessened the wake entrainment in the recirculation region, leading to a drag reduction. Also, it hinders the formation of horseshoe vortex that provides a pressure recovery and influence the wake width. However, the investigation also reveals that this device does not reduce the induced drag due to longitudinal vortex from the side edges.

In order to meet the calculating requirements of high speed and miniaturized turbomolecular pump (TMP), a new modeling method is proposed for a rotor-stator row. In the same Cartesian coordinate system, the analytical equations of blade row are derived according to the real three-dimensional geometric model. A self-defining procedure is written to simulate the flow of gas molecules in TMP based on test particle Monte Carlo method. The procedure not only can calculate transmission probability of rotor row, stator row and a rotor-stator row but also evaluate the pumping performance of different blade parameters. The simulation results and known experimental data have a good agreement to confirm the feasibility of presented modeling method. The flow analysis shows that molecules at outlet of rotor row tend to accumulate in large radius and this phenomenon is obvious for high rotational speed. The differences were found between a single-stage row and a rotor-stator row. In rotor row, the molecular density at the rear blades is the highest. This is beneficial for pumping speed of TMP because 57% of molecules at the rear blades are likely to reach outlet. This will provide a direction for the structural optimization design of the blades in the future. In stator row, the molecular density reaching outlet does not significantly increase with the increase of blade velocity ratio, which indicates that the stator row is mainly used to increase the pressure ratio of TMP. The analysis of molecular density in each region reveals the pumping mechanism of TMP.

Kidney vortex has significant impact on film cooling effectiveness, and different kinds of film cooling hole geometry and configuration are developed to weaken or eliminate kidney vortex. This paper is focus on the mechanism of eliminating kidney vortex by optimizing the coolant delivery configuration, seven coolant delivery configurations are designed to conduct a comparative study with different blowing ratios. At high blowing ratio, the strong kidney-shaped vortex is formed outside the film cooling hole causing the low cooling effectiveness for β≤0˚. For β>0˚, the coolant ejection interacts with mainstream hot gas, and the coolant gas in low momentum region of upstream bypasses the large jet momentum coolant to attach film cooling surface at downstream. It increases the distance between the vortexes to weaken mutually reinforcing effect, resulting in high film cooling effectiveness. When the blowing ratio is 1.5, the average adiabatic film cooling effectiveness of β=+15˚ and β=+30˚ is increased by about 130% and 70% compared to case of β=- 60˚, respectively.

In this work, a numerical analysis based on CFD method is carried out to examine an unsteady laminar flow of Newtonian fluids in a two-dimensional simulation of a mixer, which is composed of two rods inside a moving cylindrical tank. Three stirring protocols are considered: Non-modulated “NM”, Continuously modulated “CM” and non-continuously modulated “ALT” by using the dynamic mesh technique and user defined functions “UDF’s” for the velocity profiles. The chaotic advection is obtained by temporal modulation of the rotational velocity of the cylinder and the rods to enhance the mixing of the fluid for very low Reynolds number. For this purpose, we applied the Poincaré map as a reliable mathematic tool to check mixing quality by tracking particles inside the fluid domain. Additionally, we investigated the evolution of local flow proprieties such as rotation rate, deformation rate and elongation rate at different time periods in order to see the effect of temporal modulation on the fluid kinematics. Among the considered protocols, the results of the mentioned simulation showed that it is possible to obtain a chaotic advection only for noncontinuously modulated protocol which enhance mixing fluid efficiency.

Several research projects developed processes for precise nanoparticle positioning with high production rates. Among the gas phase manipulation strategies, the study of the inertial properties received special attention for the fabrication of nanostructured systems. In particular, aerodynamic focusing technique has allowed particles concentration onto a single streamline, improving collimated particle beam formation and opening new perspectives for nanoparticles production in the gas phase. In this paper, the influence of the reactor design was investigated, particularly in respect to the gas phase characteristics, aiming to improve the nanoparticles focusing. It was observed that a concentrated beam can be obtained in the new tapered reactor design without significantly affect the production rate and temperature profile. In addition, the coupling of aerodynamic lenses to the tapered reactor was also investigated, showing that the flow can be better focused at the cost of an increase in the average temperature and pressure drop.

Importance of accurate fluid flow measurement in industry is crucial especially today with rising energy prices. There is no ideal measuring instrument due to numerous errors occurring during process of physical quantities measurement but also due to specific requirements certain instruments have like fluid type, installation requirements, measuring range etc. Each measuring instrument has its pros and cons represented in accuracy, repeatability, resolution, etc. Conventional single-hole orifice (SHO) flow meter is a very popular differential-pressure-based measuring instrument, but it has certain disadvantages that can be overcame by multi-holes orifice (MHO) flow meter. Having this in mind, the aim of this paper is to help gain more information about MHO flow meters. Both SHO and MHO gas (air) flow meters with same total orifice area and the pipe area ratio β were numerically studied and compared using computational fluid dynamics (CFD). Simulation results of 16 different orifices with four different β (0.5, 0.55, 0.6 and 0.7) were analysed through pressure drop and singular pressure loss coefficient. Standard k-ε turbulence model was used as a turbulence model. Beside singular pressure loss coefficient, pressure recovery as well as axial velocity for both the SHO and MHO were reported. Results showed lower (better) singular pressure loss coefficient and pressure drop as well as quicker pressure recovery in favour of the MHO flow meters. Also, centreline axial velocity results were lower for MHO compared to corresponding SHO. CFD simulation results were verified by experimental results where air was used as a working fluid. The influence of geometrical and flow parameters on singular pressure loss coefficient was also reported and results showed that MHO hole distribution did not have significant influence on singular pressure loss coefficient.

The hypersonic transient flow pass a blunt cone under three types of pulse disturbances is calculated using DNS. The response characteristic of hypersonic boundary layer among different types of pulse disturbance is compared. The distribution and evolution characteristics of disturbance modes are investigated by mode analysis. Results indicate that the receptivity characteristics induced by freestream pulse wave have both similarities and differences with that induced by freestream continuous wave. The interactions of different types of pulse waves with boundary layer and bow shock present different characteristics. The boundary layer thermodynamic characteristics under pulse fast acoustic wave are sensitive to mainstream disturbance wave, and that under pulse slow acoustic wave are sensitive to residual reflection wave. The type of pulse disturbance wave has a great influence on the production and mode distribution of boundary layer disturbance wave. In general, the disturbance amplitude in the pulse fast acoustic wave situation is the largest, the case of entropy wave is the second, and the case of slow acoustic wave is the smallest. For regional influence, the type of pulse disturbance has a huge impact on the disturbance modes in both the head and the non-head. For the three cases of pulse wave, the main mode group attenuation phenomenon which narrows the disturbance frequency band exists in the boundary layer. This group attenuation is the fastest for freestream slow acoustic wave, followed by entropy wave, and then fast acoustic wave. Under the action of pulse slow acoustic waves, the disturbance wave evolution of each order mode in the boundary layer along the streamwise is relatively stable, followed by entropy wave, and the case of fast acoustic wave is the most active.

Electrowinning is the process of depositing copper of the electrolyte solution inside the cell to the cathode. In the present study, the hydrodynamic simulation of the electrowinning cell of Miduk Copper Complex is studied using computational fluid dynamics. The Navier-Stokes and continuity equations are considered in the form of two phases of fluid and gas, turbulent, incompressible and steady state, and the equation for copper concentration in the electrolyte is solved with consideration of its specific boundary condition. The flow turbulence is modeled using 𝐾 − 𝜔 relationships. Due to large variations in the properties near cathode and anode, and also the large size of the electrowinning cell, to create a good grid, and increase the speed and accuracy of the results, global and local simulations are used together. The results of this simulation are the velocity vectors, the concentrations of acid and copper, turbulence Intensity, the amount of pressure, and the volume ratio of the oxygen phase in the entire electrowinning cell domain. For model validation, the model is compared with experiments conducted on actual cells in the industry. Results show high accuracy of this modeling technique. Then, the mass transfer coefficient values for the different electrode intervals are obtained by this modeling and the results are validated using the results of the experimental relations. In the next step, the electrolyte mixture containing different mass fractions of oxygen is sprayed into the electrowinning cell from the inlet of the simulated cell. Finally, effect of sparging different mass fraction of oxygen into electrowinning cell electrolyte, changing inlet temperature and flow rate of the electrolyte on the mass transfer coefficient is investigated by the obtained model.

This work numerically investigates the effects of combined rotational and transverse oscillations of a square cylinder on the flow field and force coefficients. The primary non-dimensional parameters that were varied are frequency ratio fR (0.5, 0.8), Re (50-200), phase difference (ϕ) between the motions and rotational amplitude (θ0) with the influence of the last three parameters being discussed in detail. The amplitude of transverse oscillations is fixed at 0.2D, where D is the cylinder width. The study has been validated using the mean drag coefficient for stationary and transversely oscillating square cylinders from literature. Output data was obtained in the form of force coefficient (Cd), vorticity and pressure contours. The governing equations for the 2- dimensional model were solved from an inertial frame of reference (overset meshing) using finite volume method. The interplay between the convective field and prescribed motion has been used to explain many of the results obtained. The relative dominance of cylinder motion over the flow stream was determined using Discrete Fast Fourier Transform. The influence of Re on Cd disappears when the motions are completely out of phase (ϕ = π). In general, the Cd for low Re flows exhibited low sensitivity to change in other parameters. Direct correlation has been observed between frontal area, vortex patterns and drag coefficient,

A fully obstructed Common Bile Duct (CBD) could lead to severe implications such as jaundice, cholangitis, and pancreatitis. A 2-D CFD model with the employment of Fluid-structure Interaction (FSI) formulations is established to investigate the interactions of bile with its surroundings. Ascertaining bile secretion against a total CBD obstruction is a major interest of this study. Therefore, a function is assigned to bile secretion pattern such that the resulting intraluminal pressure complies with clinical data. To cover the variation in the parameters representing the mechanical properties of the biliary system as well as bile secretion, specific piecewise ranges are given for each of them and consequently, numerous cases are simulated. Models which after simulation lead to pressure rises in the interval of 700 Pa to 1300 Pa are picked. This interval could roughly include the actual pressure rise of a vast majority of patients. It is determined that among numerous cases, higher distention does not necessarily correlate with higher pressure increase. Furthermore, the effect of alteration in each parameter in pressure rise is determined. This model is the first numerical step towards understanding the pathogenesis of complications resulting from a fully obstructed CBD and deformation of the CBD in general.

In order to study the effect of the anti-snow deflector on the wind-snow flow underneath a high-speed train, Detached Eddy Simulation (DES) approach and discrete phase model (DPM) are used to simulate the windsnow flow around the train. The distribution of snow particles underneath the train body is analyzed. Meanwhile, the influence of deflectors on the movement of snow particles around the train is investigated. The results show that lots of vortices shed from the bogie, and the entrainment vortices near the ground actuates the movement of the snow particles on the snow-covered track, which forms a wind-snow flow. The snow smoke around the train develops gradually from the bottom of the first bogie to the end of the tail car. The deflector installed in the front of the bogie will guide the vortices off the bogie region to the ground, which results in flying up more downstream snow particles and correspondingly the number of snow particles accumulated in the bottom of the rear car and around the rear skirt plate is increased. The installation position for the deflector has a certain effect on the snow accretion in the bogie region. When the deflector is installed in the front of the 2nd and 4th bogies, the snow particles captured in the bogie region are reduced by 42.3% and 15.6%, respectively.

Water entry is an interesting subject but many of its physical aspects have remained unknown so far. Using computational fluid dynamics (CFD), this study investigates the dynamic stability of cylindrical projectiles in the oblique water entry at shallow angles in the presence of three phases of air, water and water vapor. The three-dimensional and transient numerical model has been verified using the former experimental results in the literature. In this study, the effects of projectile length-to-diameter ratio (L/D) and water entry angle on the projectile stability within cavity were investigated. Accordingly, the water entry of six projectiles was simulated with aspect ratios of 2 to 6 at three water entry angles of 6, 9 and 12 degrees with respect to the free surface with an initial velocity of 280 m/s. At each of the aforementioned angles, the critical L/D, where the projectile avoids tumbling inside the cavity at a larger value, was determined. This study showed that in the oblique water entry of a cylindrical projectile at the angles of 6, 9 and 12 degrees, the projectile tumbled within the cavity with a L/D of less than 5, 4 and 3.5, respectively. The simulation results showed that increasing the L/D as well as the water entry angle relative to the free surface resulted in the improvement of the cylindrical projectile motion stability, which is in agreement with the experimental results. By analyzing the details of each simulation, it was found that the projectile stability within the cavity is correlated with the magnitude of the angular momentum which is generated in the projectile by the impact of the cavitator on the free surface and it was shown that the projectile with a specific L/D can withstand destabilizing angular momentum to a certain extent. Considering the fact that the atmospheric ballistics of gyroscopically stabilized projectiles lead to a limit for increasing L/D, this study showed that, for aluminum cylindrical projectiles in which air stability is achieved via the gyroscopic effect, the minimum water entry angle is 6° to attain the gyroscopic stability of the projectile in the air and stable motion inside the cavity. This fact is very important from a practical point of view.

Cavitation monitoring is particularly important for pump efficiency and stability. It is easy to misjudge cavitation by using a given threshold of a single eigenvalue. In this work, based on the vibration signal, a method for multi-resolution cavitation status recognition of centrifugal pump is proposed to improve the accuracy and universality of cavitation status recognition., wavelet packet decomposition (WPD) is used to extract the statistical eigenvalues of multi-scale time-varying moment of cavitation signal after reducing the clutter, such as root mean square value, energy entropy value and so on. The characteristic matrix is constructed. Principal component analysis method (PCA) is employed to reduce the dimension of the characteristic matrix and remove the redundancy, which constructs the radial basis function (RBF) neural network as the input. The results show that the overall recognition rate of non-cavitation, inception cavitation and serious cavitation by using the vibration signal of one measuring point is more than 97.7%. The recognition rate of inception cavitation is more than 80%. Based on the vibration signal information fusion method of two measuring points, the recognition rate of centrifugal pump inception cavitation status reaches more than 99%, and the recognition rate of vibration signal information fusion method of three measuring points reaches 100% for all three cavitation statuses. Due to the influence of factors such as change of external excitation and abrupt change of working conditions, sensor data acquisition is often subjected to unpredictable disturbance. To study the ability of single-point cavitation status recognition method to resist unknown disturbances, by constantly adjusting the value of the interference coefficient of the interference term. It is found that the recognition rate of cavitation status using single measuring point decreases almost linearly with the increase of the interference coefficient. When five measuring points are used for information fusion cavitation status recognition, the cavitation status recognition rate still reaches over 90% even if the interference factor of one measuring point reaches 50%.

Individual drops are suitable tools to study the liquid-fluid interfacial properties. In this work, forcedisplacement equation and non-linear oscillations of a pendent drop are numerically investigated. The presented novel force-displacement function allows following the dynamics of a pendent drop and realizing its elastic behavior. The growth and detachment of drop, which is pending due to gravity from a capillary tip, is considered (assuming high density and high viscosity ratios and immiscible two-phase flows). Twodimensional multi-relaxation time lattice Boltzmann method (MRT-LBM) was used to simulate growth, detachment, and oscillations of the drop using a conservative model for high-density ratio. The forcedisplacement function of a pendent drop (FDFPD), which is non-linear, was introduced. Using FDFPD, the non-linear elastic specifications of the pendent drop were determined. It was realized that the drop shows three different elastic behaviors simultaneously (hardening, linear, and softening). The drop superharmonic and subharmonic frequencies were calculated, using the natural frequency of the linear portion of FDFPD. Besides, the drop would grow as long as its displacement is between the extrema of FDFPD. In addition, a dynamic criterion for the onset of detachment was established. Also, increasing the Bond number from 0.11 to 1.96, while keeping Reynolds number equal to 0.023, accelerates the drop detachment and increases the linear portion of FDFPD. It was shown that increasing Capillary number from 1.8E-5 to 7.3E-4, while keeping Reynolds number equal to 0.023, accelerates the drop detachment and increases the non-linear portions of FDFPD.