NCCT for Micropolar Solid and Fluid Media Based on Internal Rotations and Rotation Rates with Rotational Inertial Physics: Model Problem Studies

This paper presents model problem studies for micropolar thermoviscoelastic solids without memory and micropolar thermoviscous fluid using micropolar non-classical continuum theories (NCCT) based on internal rotations and rotation rates in which rotational inertial physics is considered in the derivation of the conservation and balance laws (CBL). The dissipation mechanism is due to strain rates as well as rotation rates. Model problems are designed to demonstrate and illustrate various significant aspects of the micropolar NCCT with rotational inertial physics considered in this paper. In case of micropolar solids, the translational and rotational waves are shown to coexist. In the absence of microconstituents (classical continuum theory, CCT) the internal rotations are a free field, hence have no influence on CCT. Absence of gradients of displacements and strains in micropolar thermoviscous fluid medium prohibits existence of translational waves as well as rotational waves even though the appearance of the mathematical model is analogous to the solids, but in terms of strain rates. It is shown that in case of micropolar thermoviscous fluids the BAM behaves more like time dependent diffusion equation i.e., like heat conduction equation in Lagrangian description. The influence of rotational inertial physics is demonstrated using BLM as well as BAM in the model problem studies.

New Method of Givens Rotations for Triangularization of Square Matrices

This paper describes a new method of QR-decomposition of square nonsingular matrices (real or complex) by the Givens rotations through the unitary discrete heap transforms. This transforms can be defined by a different path, or the order of processing components of input data, which leads to different realizations of the QR-decomposition. The heap transforms are fast, because of a simple form of decomposition of their matrices. The direct calculation of the N-point discrete heap transform requires no more than 5(N-1) multiplications, 2(N-1) additions, plus 3(N-1) trigonometric operations. The QR-decomposition of the square matrix N × N uses about 4/3N3 multiplications and N(N-1)/2 square roots. This number varies depending on the path of the heap transform, and it is shown that “the optimal path” allows for significant reduction of number of operations in QR-decomposition. The heap transform and its matrix can be described analytically, and therefore, this transform can also be applied to the QR-decomposition of complex matrices.

Cereal-forage crop rotations and irrigation treatment effect on water use efficiency and crops sustainability in Mediterranean environment

Agricultural systems based on crop rotations favour sustainability of cultivation and productivity of the crops. Wheat-forage crops rotations (annual winter binary mixture and perennial alfalfa meadow) combined with irrigation are the agronomical techniques able to better exploit the weather resources in Mediterranean environments. The experiment aimed to study the effect of 18 years of combined effect of irrigation and continuous durum wheat and wheat-forage rotations on productivities of crops and organic matter of topsoil. The experiments were established through 1991-2008 under rainfed and irrigated treatments and emphasized on the effect of irrigation and continuous wheat and wheat-forage crop rotations on water use efficiency and sustainability of organic matter. The effect of irrigation increased 49.1% and 66.9% the dry matter of mixture and meadow, respectively. Continuous wheat rotation reduced seed yield, stability of production, crude protein characteristics of kernel and soil organic matter. The yearly gain in wheat after forage crops was 0.04 t (ha·yr)-1 under rainfed and 0.07 t (ha·yr)-1 under irrigation treatments. The crude protein and soil organic matter of wheat rotations, compared to those of continuous wheat under rainfed and irrigated was increase in term of point percentage by 0.8 and 0.5 in crude protein and 5.1 and 4.4 in organic matter, respectively. The rotations of mixture and meadow under both irrigated treatments increased the point of percentage of organic matter over continuous wheat (9.3.and 8.5 in mixture and 12.5 and 9.5 meadow under rainfed and irrigation, respectively). Irrigation reduce the impact of weather on crop growing reducing water use efficiency (mean over rotations) for dry mater production (15.5 in meadow and 17.5 in mixture [L water (kg·dry·matter)-1 ]) and wheat seed yield. The effect of agronomic advantages achieved by forage crops in topsoil expire its effect after three years of continuous wheat rotation.

Bilaterally Symmetrical Transformation between Independent Operators and Rotations

This report describes an approach for representation of quantum operators through rotations and rotation through quantum operators. The approach of the proposed method transforms rotation in a kind of a unitary matrix that corresponds to the rotation. Operations with qubits are very similar to the rotation, but with an added phase coefficient. This fact is used to create a process for rotation between unitary matrices. This approach could be used to modifying the controls to apply in a different basis.

Effect of various crop rotations on rice yield and nitrogen use efficiency in paddy–upland systems in southeastern China

To evaluate the effects of various rotation systems on rice grain yield and N use efficiency, a paddy–upland cropping experiment(2013–2016) was conducted in southeastern China. The experiment was designed using six different rice––winter crop rotations: rice–fallow(RF),rice–wheat(RW), rice–potato with rice straw mulch(RP), rice–green manure(Chinese milk vetch; RC–G), rice–oilseed rape(RO), and rice–green manure crop(oilseed rape with fresh straw incorporated into soil at flowering; RO–G) and three N rates, N0(0 kg N ha-1), N1(142.5 kg N ha-1), and N2(202.5 kg N ha-1). Average rice yields in the RF(5.93 t ha-1) rotation were significantly lower than those in the rotations with winter crops(7.20–7.48 t ha-1)under the N0 treatment, suggesting that incorporation of straw might be more effective for increasing soil N than winter fallow. The rice yield differences among the rotations varied by year with the N input. In general, the grain yields in the RP and RO–G rotations –were respectively 11.6–28.5% and 14.80–37.19% higher than those in the RF in plots with N applied. Increasing the N rate may have tended to minimize the average yield gap between the RF and the other rotations; the yield gaps were 18.55%, 4.14%, and 0.23% in N0, N1, and N2, respectively. However, the N recovery efficiency in the RF was significantly lower than that in other rotations, except for 2015 under both N1 and N2 rates, a finding that implies a large amount of chemical N loss. No significant differences in nitrogen agronomic efficiency(NAE) and physiological efficiency(NPE) were found between the rotations with legume(RC–G) and non–legume(RO and RW) winter crops, a result that may be due partly to straw incorporation. For this reason, we concluded that the return of straw could reduce differences in N use efficiency between rotations with and without legume crops. The degree of synchrony between the crop N demand and the N supply was evaluated by comparison of nitrogen balance degree(NBD) values. The NBD values in the RP and RW were significantly lower than those in the other rotations under both N1 and N2 rates. Thus,in view of the higher grain yield in the RP compared to the RW under the N1 rate, the RP rotation might be a promising practice with comparable grain yield and greater N use efficiency under reduced N input relative to the other rotations. The primary yield components of the RF and RP were identified as number of panicles m-2 and numbers of kernels panicle-1, respectively. The NAE and NPE were positively correlated with harvest index, possibly providing a useful indicator for evaluating N use efficiency.

ON CORRECT ACCOUNT OF FINITE ROTATIONS IN FINITE PLASTICITY THEORY

The non-uniqueness of the transition from nonobjective constitutive relations to objective oneswith the use of the principle of material frame-indifference(PMFI)is shown.To eliminate it,the concept offinite strain without rotations(FSWR)for a given material type and each strain component(elastic,plastic)is introduced.In FSWR the rotation is excluded with respect to the natural preferred configuration for agiven material.Considered are a simple solid,a liquid,a mouocrystal,a polycrystal and a composite.Theprocedure is proposed lbr consistent generalization of known infinitesimal relations for finite strains and rota-tions.The structure of constitutive relations is derived for anisotropic elasto-plastic mono-and polycrystallinematerials.

Numerical Investigation on Vortex-Induced Rotations of A Triangular Cylinder Using An Immersed Boundary Method

A numerical study of vortex-induced rotations(VIRs) of an equivalent triangular cylinder, which is free to rotate in the azimuthal direction in a uniform flow, is presented. Based on an immersed boundary method, the numerical model is established, and is verified through the benchmark problem of flow past a freely rotating rectangular body.The computation is performed for a fixed reduced mass of m~*=2.0 and the structural stiffness and damping ratio are set to zero. The effects of Reynolds number(Re=25-180) on the characteristics of VIR are studied. It is found that the dynamic response of the triangular cylinder exhibits four distinct modes with increasing Re: a rest position,periodic rotational oscillation, random rotation and autorotation. For the rotational oscillation mode, the cylinder undergoes a periodic vibration around an equilibrium position with one side facing the incoming flow. Since the rotation effect, the outset of vortex shedding from cylinder shifts to a much lower Reynolds number. Further increase in Re leads to 2 P and P+S vortex shedding modes besides the typical 2 S pattern. Our simulation results also elucidate that the free rotation significantly changes the drag and lift forces. Inspired by these facts, the effect of free rotation on flow-induced vibration of a triangular cylinder in the in-line and transverse directions is investigated. The results show that when the translational vibration is coupled with rotation, the triangular cylinder presents a galloping response instead of vortex-induced vibration(VIV).

Dynamic analysis on generalized linear elastic body subjected to large scale rigid rotations

The dynamic analysis of a generalized linear elastic body undergoing large rigid rotations is investigated.The generalized linear elastic body is described in kinematics through translational and rotational deformations, and a modified constitutive relation for the rotational deformation is proposed between the couple stress and the curvature tensor.Thus, the balance equations of momentum and moment are used for the motion equations of the body.The floating frame of reference formulation is applied to the elastic body that conducts rotations about a fixed axis.The motion-deformation coupled model is developed in which three types of inertia forces along with their increments are elucidated.The finite element governing equations for the dynamic analysis of the elastic body under large rotations are subsequently formulated with the aid of the constrained variational principle.A penalty parameter is introduced, and the rotational angles at element nodes are treated as independent variables to meet the requirement of C1 continuity.The elastic body is discretized through the isoparametric element with 8 nodes and 48 degrees-of-freedom.As an example with an application of the motiondeformation coupled model, the dynamic analysis on a rotating cantilever with two spatial layouts relative to the rotational axis is numerically implemented.Dynamic frequencies of the rotating cantilever are presented at prescribed constant spin velocities.The maximal rigid rotational velocity is extended for ensuring the applicability of the linear model.A complete set of dynamical response of the rotating cantilever in the case of spin-up maneuver is examined, it is shown that, under the ultimate rigid rotational velocities less than the maximal rigid rotational velocity, the stress strength may exceed the material strength tolerance even though the displacement and rotational angle responses are both convergent.The influence of the cantilever layouts on their responses and the multiple displacement trajectories observed in the floating frame is simultaneously investigated.The motion-deformation coupled model is surely expected to be applicable for a broad range of practical applications.

Soil Fertility Comparison between Rotations of Tobacco-Rice (TR) and Rape-Rice (RR)

Tobacco-planting plays an important role in ensuring the high-quality tobacco raw materials supply and the local social and economic development in Chenzhou City. In recent years whether tobacco-planting is better for the maintenance and improvement of soil fertility than other crop-planting has been highly concerned. In this study, 16 soil fertility indicators and soil integrated index (IFI) were compared by 21 pairs of fields in Chenzhou city under the rotations of tobacco-rice (TF) and rice-rice (RR), and results showed that, comparing the mean values of soil fertility indicators, the contents of OM, TN, AN, AK, S and IFI were extremely significantly higher in TR than those in RR (p < 0.01), the contents of Cu, Ca, Mg and Fe were significantly higher in TR than those in RR (p < 0.05), but Mn content was significantly lower in TR than those in RR (p < 0.05). Meanwhile the contents of TP, TK and AP were insignificantly higher in TR than those in RR, and the contents of B, Mo and Zn were insignificantly lower in TR than those in RR. The above significant differences in soil fertility indicators were mainly due to relatively higher fertilizer inputs and less nutrient removal during tobacco-growing season than during rape-growing season, the net increase of N, P2O5 and K2O are 8.61, 5.25 and 24.89 kg per 667 m2 respectively in tobacco-growing season, while the net decrease of N, P2O5 and K2O are 8.88, 4.70 and 4.62 kg per 667 m2 respectively in rape-growing season. C.V. of soil fertility indicators and IFI were meanly lower in TR (52.25% and 15.95%, respectively) than those in RR (63.07% and 22.12%, respectively). Comparatively, tobacco-planting can improve soil fertility better than rape-planting when rotated with late rice in Chenzhou city. For tobacco-planting, Mg fertilizer should be applied for 23.8% TR fields, while more N, K, Ca, Mg, S and B fertilizers should be applied for 42.86%, 23.81%, 14.29%, 47.62%, 80.95% and 47.62% RR fields, respectively.

TERTIARY BLOCK ROTATIONS AND PYRRHOTITE/ MAGNETITE GEOTHERMOMETRY IN THE TETHYAN HIMALAYA(SHIAR KHOLA,CENTRAL NEPAL)

In Mesozoic carbonates of the Tethyan Himalayas two characteristic remanent magnetisations(ChRM\-1 and ChRM\-2)were identified by their unblocking spectra.The ChRM\-1 is carried by pyrrhotite(unblocking spectra:270～340℃),acquired as a secondary thermoremanent magnetisation (TRM) during exhumation and cooling.The ChRM\-2 is carried by magnetite (unblocking spectra:430～580℃).A primary origin is indicated by calcite twin geothermometry and remanences consistent with the expected direction.Along an E—W profile of 10km length the ratio of remanence intensity of pyrrhotite to magnetite ( R PYR/MAG )changes systematically (from 0 38 to 1 00,Fig.1).It is known that pyrrhotite is formed in marly carbonates during low\|grade metamorphism (Rochette 1987).This occurs at the expense of magnetite.Thus the ratio R PYR/MAG is related to metamorphic temperatures and can be used as a geothermometer for temperatures≤300℃ in low\|grade metamorphic carbonates where other methods are rare.Stable remanence directions were used to estimate the amount of block rotation around vertical and horizontal axes(i.e.Klootwijk et al.1985,Appel et al.1991 & 1995).In the Shiar area the pyrrhotite remanence directions follow a small\|circle distribution with a best fit parallel to the N—S direction(Fig.2).

BLOCK ROTATIONS AT THE NORTHERN EDGE OF INDIA (SPITI,N-INDIA) AND THEIR CONTINUATION TO THE EAST (MALARI, N-INDIA)-REGIONAL SIGNIFICANCE FOR THE TECTONIC DEVELOPMENT OF THE TETHYAN HIMALAYAS

In carboniferous and triassic metacarbonates (anchizone to lower greenschist facies) of the Tethyan Himalayas the characteristic remanent magnetisations are carried by magnetite (ChRM\-1) and pyrrhotite (ChRM\-2;Klootwijk & Bingham,1980;Appel et al.,1991 & 1995;Schill et al.,1999).Magnetite may carry a primary remanent magnetisation whereas the pyrrhotite component is secondary and related to the last cooling event below 300℃. Pyrrhotite is formed in marly carbonates during low\|grade metamorphism.In Spiti the last cooling is represented by an 40 Ar/ 39 Ar age of 42～45Ma (Wiesmayr & Grasemann,1999).Five locations were sampled in the Spiti valley (Fig.1).Besides a present earth field direction,both remanent components (ChRM 1+2 ) are present in single specimens.The contribution to the total NRM is around 30% for the ChRM\-2 (coercivity of 20～100mT) and only around 8% for the ChRM\-2 (unblocking temperature of 250～330℃).Despite of the contribution stable remanence directions could be obtained for the ChRM\-2.For all sampling locations well grouping overall mean directions were obtained (Table 1,Fig.1).Results from Losar and the lower Pin valley are preliminary.They were estimated by great circle analyses or by taking the residual component after AF\|demagnetisation. Clockwise block rotations of around 10～40° in respect to stable India since 42 Ma are calculated by using the apparent polar wander path of Besse & Courtillot (1991).The α 95 \|angles show no overlapping (Fig.1 small figure).Therefore local rotations are not negligible.

Invalidity of Geometrical Interpretation of F-Spin Structure of Nuclear Rotations by Otsuka’s View

In Otsuka's view of nuclear rotations neutrons and protons are not rotating around a common axis,but rather around separate axis.In this letter,we pointed out that this invalidates the geometrical interpretation of F-spin structure of the neutron-proton interacting boson model,where the angle between the axis of symmetries of neutron ellipsoid and proton ellipsoid is used to determine whether a state is F-spin symmetric or mixed symmetric.

Dissipation function in turbulent plane Poiseuille and Couette flows subject to spanwise rotations

The dissipation function in turbulent plane Poiseuille flows(PPFs) and plane Couette flows(PCFs) subject to spanwise rotations is analyzed. It is found that, in the PCFs without system rotations, the mean part is constant while the fluctuation part follows a logarithmic law, resulting in a similar logarithmic skin friction law as PPFs.However, if the flow system rotates in the spanwise direction, no obvious dependence on the rotation number can be evaluated. In the PPFs with rotations, the dissipation function shows an increase with the rotation number, while in the PCFs with rotations,when the rotation number increases, the dissipation function first decreases and then increases.

Nematode infestation and N-effect of legumes on soil and crop yelds in legume-sorghum rotations

The effects of cowpea (Vignaunguiculata) and-groundnut (Arachis hypogea) on succeeding sorghum yields, soil mineral N and nematode infestationwere studied during five cropping seasons (2000 to 2004) in a weakly acid Ultisol of the agronomy research station of Farak?-Ba lo-cated in the Guinean zone of Burkina Faso, West Africa. A factorial 5x5 design of five crop rotations with five fertilizer treatments in a split-plot arrangement with four replications was used.Sorghum yields were affected by the two factors (rotation with legumes and fertilizer ap-plications) during the four years. But interactions were not observed between the two factors. Monocropping of sorghum produced the lowest yields and legume–sorghum rotations increased sorghum yields by50% to 300%. Ground-nut–sorghum and cowpea–sorghum rotations increased soil mineral N by36% and 52%, re-spectively. Crop rotation influenced nematode infestation but the effects on soil and sorghum root infestation differed according to the rotation. The cowpea–sorghum rotation increased soil and sorghum root infestationby nematodes while groundnut–sorghum decree-sed the nematode population. The soil of the cowpea-sorghum rotation contained 1.5 to 2 times more nematodes than the soil of the monocropping of sorghum. In contrast, the soil ofthe groundnut–sorghum rotation contained from 17 to 19 times fewernematodes than that of themonocropping of sorghum. However, nematode infestation did not affect any of the succeeding sorghum yields. It was concluded that the parasitic effect of nematodes was limited by the predominance of positive N-effects on the development of succeeding sorghum.

Collisions, or Reflections and Rotations, Leading to the Digits of π

We analyze a problem of elastic collisions between elements of a system composed of two balls and a wall. Thanks to a change of variables, the problem is reduced to a sequence of reflections and rotations. Moreover, the total number of collisions is easily found. For specific ratios of ball weights, the number of collisions is related to the first successive digits of π.

Reference Coordinate System of Nonlinear Beam Element Based on the Geometrically Exact Formulation under Large Spatial Rotations and Deformations

Analysis of slender beam structures in a three-dimensional space is widely applicable in mechanical and civil engineering. This paper presents a new procedure to determine the reference coordinate system of a beam element under large rotation and elastic deformation based on a newly introduced physical concept: the zero twist sectional condition, which means that a non-twisted section between two nodes always exists and this section can reasonably be regarded as a reference coordinate system to calculate the internal element forces. This method can avoid the disagreement of the reference coordinates which might occur under large spatial rotations and deformations. Numerical examples given in the paper prove that this procedure guarantees the numerical exactness of the inherent formulation and improves the numerical efficiency, especially under large spatial rotations.

Soil physical properties,nutrients,and crop yield with two-year tillage rotations under a winter wheat-summer maize double cropping system

Winter wheat and summer maize were planted from 2015-2017 to study the effects of different rotational tillage patterns on soil physicochemical properties,crop yield,water content,and fertilizer utilization.The tillage treatments were designed as wheat subsoiling-maize no tillage(WS-MN),wheat rotary tillage-maize subsoiling(WR-MS),wheat subsoiling-maize subsoiling(WS-MS),and conventional wheat rotary tillage-maize no tillage(WR-MN)as a control.Among the four treatments,WS-MN and WR-MS were single-season subsoiling treatments,and WS-MS was a two-season subsoiling treatment.The average soil bulk density decreased by 7.6%in the single-and double-season subsoiling groups compared to the WR-MN group,and the total porosity and noncapillary porosity increased by 10.7%and 12.2%,respectively.Single-or double-season subsoiling treatment was not conducive to water storage in the 0-20 cm soil layer but increased the water content of the 20-140 cm soil layer,and the average soil water content of the 0-140 cm layer was increased by 11.6%in the two-growing season treatment groups compared with the WR-MN group.In WS-MS and WS-MN groups compared with the WR-MN group,the soil ammonium nitrogen content was increased by an average of 18.6%in 0-20 cm soil and 16.8%in 20-100 cm soil;soil nitrate-nitrogen content was decreased by 13.5%in 0-100 cm soil;total organic carbon and microbial carbon contents in the 15-30 cm soil were increased by 18.1%and 12.7%,respectively;and soil urease,catalase,and alkaline phosphatase activities were increased by 46.1%,15.2%,and 23.1%,respectively.Annual crop yield and water use efficiency increased by 8.9%and 15.0%,respectively,in both the single-and double-season subsoiling treatment groups.This study demonstrated the advantages of subsoiling tillage and suggested that it is suitable for crop cultivation in the Haihe Plain,China.

Multi-blade rubbing characteristics of the shaft-disk-blade-casing system with large rotation

Blade rubbing faults cause detrimental impact on the operation of aeroengines. Most of the existing studies on blade rubbing in the shaft-disk-blade-casing(SDBC) system have overlooked the elastic deformation of the blade, while some only consider the whirl of the rotor, neglecting its spin. To address these limitations, this paper proposes a dynamic model with large rotation for the SDBC system. The model incorporates the spin and whirl of the rotor, enabling the realistic reproduction of multiblade rubbing faults. To verify the accuracy of the SDBC model with large rotation and demonstrate its capability to effectively consider the rotational effects such as the centrifugal stiffening and gyroscopic effects, the natural characteristics and dynamic responses of the proposed model are compared with those obtained from reported research and experimental results. Furthermore, the effects of the rotating speed, contact stiffness,and blade number on the dynamic characteristics of the SDBC system with multi-blade rubbing are investigated. The results indicate that the phase angle between the rotor deflection and the unbalance excitation force increases with the increasing rotating speed,which significantly influences the rubbing penetration of each blade. The natural frequency of the SDBC system with rubbing constrain can be observed in the acceleration response of the casing and the torsional response of the shaft, and the frequency is related to the contact stiffness. Moreover, the vibration amplitude increases significantly with the product of the blade number under rubbing, and the rotating frequency approaches the natural frequency of the SDBC system. The proposed model can provide valuable insight for the fault diagnosis of rubbing in bladed rotating machinery.

Modulation of High-Order Harmonic Generation from a Monolayer ZnO by Co-rotating Two-Color Circularly Polarized Laser Fields

By numerically solving the two-dimensional semiconductor Bloch equation,we study the high-order harmonic emission of a monolayer ZnO under the driving of co-rotating two-color circularly polarized laser pulses.By changing the relative phase between the fundamental frequency field and the second one,it is found that the harmonic intensity in the platform region can be significantly modulated.In the higher order,the harmonic intensity can be increased by about one order of magnitude.Through time-frequency analysis,it is demonstrated that the emission trajectory of monolayer ZnO can be controlled by the relative phase,and the harmonic enhancement is caused by the second quantum trajectory with the higher emission probability.In addition,near-circularly polarized harmonics can be generated in the co-rotating two-color circularly polarized fields.With the change of the relative phase,the harmonics in the platform region can be altered from left-handed near-circularly polarization to right-handed one.Our results can obtain high-intensity harmonic radiation with an adjustable ellipticity,which provides an opportunity for syntheses of circularly polarized attosecond pulses.

Research on Cavitation Characteristics and Influencing Factors of Herringbone Gear Pump

Cavitation is a common issue in pumps,causing a decrease in pump head,a fall in volumetric efficiency,and an intensification of outlet flow pulsation.It is one of the main hazards that affect the regular operation of the pump.Research on pump cavitation mainly focuses on mixed flow pumps,jet pumps,external spur gear pumps,etc.However,there are few cavitation studies on external herringbone gear pumps.In addition,pumps with different working principles significantly differ in the flow and complexity of the internal flow field.Therefore,it is urgent to study the cavitation characteristics of external herringbone gear pumps.Compared with experimentalmethods,visual research and cavitation area identification are achieved through computation fluid dynamic(CFD),and changing the boundary conditions and shape of the gear rotor is easier.The simulation yields a head error of only 0.003%under different grid numbers,and the deviation between experimental and simulation results is less than 5%.The study revealed that cavitation causes flow pulsation at the outlet,and the cavitation serious area is mainly distributed in the meshing gap and meshing area.Cavitation can be inhibited by reducing the speed,increasing the inlet pressure,and changing the helix angle can be achieved.For example,when the inlet pressure is 5 bar,the maximumgas volume fraction in themeshing area is less than 50%.These results provide a reference for optimizing the design and finding the optimal design parameters to reduce or eliminate cavitation.