An estimate for the mean square of the difference of velocities for homogeneous statistical solutions of the three-dimensional Navier-Stokes system

1989 ◽  
Vol 45 (5) ◽  
pp. 1367-1373
Author(s):  
M. I. Vishik ◽  
A. I. Komech
Author(s):  
J. M. Brookfield ◽  
I. A. Waitz ◽  
J. Sell

A study of the effects of freestream swirl on the decay characteristics of wakes shed from a rotating blade row is presented. The freestream swirl behind the rotor causes the wakes to skew tangentially, stretching the wakes as they are convected from the rotor to the stator. The effect of stretching on wake decay is illustrated using a simplified two-dimensional model. The model is described and the results are compared to 1) measurements from a two-dimensional cascade facility where no stretching or skewing of the wakes occurs, 2) solutions obtained using a three-dimensional, Reynolds-averaged Navier-Stokes solver, and 3) experimental wake measurements taken behind a low hub-to-tip ratio fan. For typical fan geometries with hub-to-tip ratios of approximately 0.5 and rotor-stator spacings of one to two rotor chord lengths, the wake can be stretched by over 50 percent. The stretching increases the mixing rate which leads to a reduction in the mean wake velocity deficit of approximately thirty percent and a widening of the wake of about fifteen percent. These effects account for much of the difference seen between cascade wake measurements and those taken behind rotating fan blade rows. It is therefore important to include such effects when using cascade data for prediction of fluid mechanic, acoustic, or structural phenomena associated with fan wakes. Finally, the study also suggests a potential for small (< 3 dB) reductions in wake-stator interaction noise through tailoring the fan loading distribution to produce particular span wise wake decay characteristics.


1982 ◽  
Vol 120 ◽  
pp. 155-183 ◽  
Author(s):  
Jon Lee

We have investigated a sequence of dynamical systems corresponding to spherical truncations of the incompressible three-dimensional Navier-Stokes equations in Fourier space. For lower-order truncated systems up to the spherical truncation of wavenumber radius 4, it is concluded that the inviscid Navier-Stokes system will develop mixing (and a fortiori ergodicity) on the constant energy-helicity surface, and also isotropy of the covariance spectral tensor. This conclusion is, however, drawn not directly from the mixing definition but from the observation that one cannot evolve the trajectory numerically much beyond several characteristic corre- lation times of the smallest eddy owing to the accumulation of round-off errors. The limited evolution time is a manifestation of trajectory instability (exponential orbit separation) which underlies not only mixing, but also the stronger dynamical charac- terization of positive Kolmogorov entropy (K-system).


1993 ◽  
Vol 15 (4) ◽  
pp. 1-6
Author(s):  
Di Paola Mario ◽  
Nguyen Dong Anh

Stochastic linearization method is one of the most useful tools for analysis of nonlinear systems under random excitation. The fundamental idea of the classical stochastic linearization consists in replacing the original nonlinear equation by a linear one in such a way that the difference between two equations is minimized in the mean square value. In this paper a new version of the stochastic linearization is proposed. It is shown that for two nonlinear systems considered the new version gives good results for both the weak and strong nonlinearities.


2018 ◽  
Vol 56 ◽  
pp. 130-135
Author(s):  
M. V. Tserenyuk ◽  
O. M. Tserenyuk

In addition to assessing the absolute performance of animals, the impact of certain technological approaches, breeding influence and other external organized factors on the consolidation of pigs groups on certain grounds should be evaluated. Breeding consolidation is a desirable breeding process that is realized through more motivated consolidation of intra-breeding structural units for maintaining a significant level of intergroup differentiation and variability. If the issue relates to the rearing young animals that are introduced into the herd, this is the most urgent issue that needs to be monitored. The purpose of the research is to determine the consociality of the main signs of reproductive ability of the gilts, which are checked at different rates of artificial insemination of sows of the main herd. The research was carried out at the Shubs`ke farm in the Bogoduhivsky District of Kharkiv Oblast at the pig farm for the pure breeding of the Welsh breed pigs (breeding reproductive status from 2014). In order to evaluate the optimal multiplicity (from single to triple), a gilts with a total of 30 heads was selected. The main indicators of reproductive ability of gilts (multiplicity, weight of nest at birth and excommunication and keeping piglets before weaning on day 28) were evaluated. Recalculation on the weight of the litter at weaning at the weight of the nest at extermination in 60 days was carried out in accordance with the current instruction on the boning of pigs. The results of researches were worked out according to traditional methods by the method of variation statistics. Consolidation of individual indicators of reproductive capacity of gilts was calculated to the total number of evaluated animals. In the previous stage of the research, it was found that the use of multiple insemination of gilts compared to single insemination is positively reflected at the level of their reproductive ability. A decrease in the percentage of non-productive inseminants in animal groups has been established. Triple insemination of gilts allows for 1.14 piglets to be obtained more compared to single insemination of the same pigs (p < 0.01). Also, for three times insemination of gilts, in comparison with single insemination, larger nest for weaning were obtained (by 14.24 kg, converted to 60th day p < 0.01). At the same time, the reduction in the keeping of piglets to weaning for increase frequency of insemination of gilts. According to the multiplicity of gilts, the most consolidated level of symptoms per group was obtained for single insemination. Increasing the multiplicity of insemination negatively affected the consolidation of the multiplicity of the piglets (as for determining the coefficients of phenotypic consolidation due to the mean square deviation, so, and for determining the coefficient of variability). The least consolidated in terms of multiplicity were uterus for double insemination. It should also be noted that there is little difference, in general, on the indicators of the theonotypical consolidation of the multiplicity of piglets between different groups of animals. So this difference between the most contrasting groups was 0.447 points for determining the coefficients due to the mean square deviation and 0.397 points for the determination due to the coefficient of variability, respectively. By weight of the same litters at birth, the most consolidated group was gilts, which was inseminated twice. The least consolidated are trimmed three times, respectively. The difference as a whole, according to the indicators of the theonotype consolidation of the mass of the litter’s piglets at birth, between different groups of pigs was even smaller. The difference between the most contrasting groups was 0.270 points for determining the coefficients due to the mean square deviation and 0.260 points for the determination due to the coefficient of variability, respectively. On the basis of the mass of the litter at weaning, the most consolidated level of symptoms was obtained in the group of gilts for triple insemination. The least consolidated group, respectively, was gilts for single insemination. At the same time, on the basis of the weight of the litter at weaning, the slightest differences were obtained after the consolidation of the signs between different groups of pigs. The difference between the most contrasting groups was 0.173 points for determining the coefficients due to the mean square deviation and 0.248 points for the determination due to the coefficient of variation, respectively. At different rates of insemination of gilts, there are no significant differences between the groups between the groups in terms of the consolidation of signs of reproductive ability. Also, there was no clear effect on increasing the multiplicity of insemination of gilts to the consolidation of their signs of reproductive qualities.


2019 ◽  
Vol 27 (2) ◽  
pp. 230949901986122
Author(s):  
Ali Sahin ◽  
Mehmet Emin Simsek ◽  
Safa Gursoy ◽  
Mustafa Akkaya ◽  
Cetin Isik ◽  
...  

Background: This study aimed to evaluate the effect of total hip arthroplasty (THA) on sagittal pelvic parameters and to evaluate the effect of sagittal pelvic parameters on acetabular cup orientation. Methods: The study included 86 patients who underwent THA for a diagnosis of unilateral coxarthrosis between 2011 and 2015. Measurements were taken of the preoperative and postoperative acetabular cup inclination (ACI), anteversion, and sagittal pelvic parameters. The effect of THA on sagittal pelvic parameters and the effects of the sagittal pelvic parameters on acetabular cup orientation were investigated. Results: The sagittal pelvic tilt values calculated were mean 9.7° ± 6.3° (2°; 23°) preoperatively and 11.0° ± 6.1° (2°; 25°) postoperatively. The increase in postoperative pelvic incidence (PI) values was determined to be statistically significant ( p < 0.05). The preoperative PI values had no significant effect on ACI, but in cases with high preoperative PI values, a tendency to high anteversion values was determined. The mean inclination values were found to be 40.2° ± 11.0° in the low PI group, 41.7° ± 7.4° in the normal PI group, and 44.1° ± 8.3° in the high PI group. As no increase in inclination values was observed with an increase in PI values, no statistical correlation was determined ( p = 0.343). Average of anteversion values in the low PI group was 9.2° ± 13.7°, in the normal PI group 19.3° ± 10.5°, and in the high PI group 21.1° ± 12.5°. The difference between the groups was statistically significant ( p = 0.001). Conclusion: Evaluating the results of this study, it can be concluded that varying PI values do affect the acetabular cup anterversion in THA. So, preoperative assessment of PI values is important in preventing postoperative acetabular cup malposition.


2020 ◽  
Vol 22 (4) ◽  
Author(s):  
Bernard Nowakowski ◽  
Gerhard Ströhmer

AbstractWe investigate the existence and regularity of solutions to the stationary Stokes system and non-stationary Navier–Stokes equations in three dimensional bounded domains with in- and out-lets. We assume that on the in- and out-flow parts of the boundary the pressure is prescribed and the tangential component of the velocity field is zero, whereas on the lateral part of the boundary the fluid is at rest.


Author(s):  
Ravon Venters ◽  
Brian Helenbrook ◽  
Goodarz Ahmadi

Abstract Turbulent flow in an elbow has been numerically investigated. The flow was modeled using two approaches; Reynolds Averaged Navier-Stokes (RANS) and Direct Numerical Simulation (DNS) methods. The DNS allows for all the scales of turbulence to be evaluated, providing a detailed depiction of the flow. The RANS simulation, which is typically used in industry, evaluates time-averaged components of the flow. The numerical results are accompanied by experimental data, which was used to validate the two methods. Profiles of the mean and root-mean-square (RMS) fluctuating components were compared at various points along the midplane of the elbow. Upstream of the elbow, the predicted mean and RMS velocities from the RANS and DNS simulations compared well with the experiment, differing slightly near the walls. However, downstream of the elbow, the RANS deviated from the experiment and DNS, showing a longer region of flow re-circulation. This caused the mean and RMS velocities to significantly differ. Examining the cross-section flow field, secondary motion was clearly present. Upstream secondary motion of the first kind was observed which is caused by anisotropy of the reynolds stresses in the turbulent flow. Downstream of the bend, the flow transitions to secondary motion of the second kind which is caused by streamline curvature. Qualitatively, the RANS and DNS showed similar results upstream of the bend, however downstream, the magnitude of the secondary motion differed significantly.


2019 ◽  
Vol 2019 (11) ◽  
Author(s):  
Haruki Kurasawa ◽  
Toshio Suzuki

Abstract The relativistic expression for the $n$th-order moment of the nuclear charge density is presented. For the mean square radius (msr) of the nuclear charge density, the non-relativistic expression, which is equivalent to the relativistic one, is also derived consistently up to $1/M^2$ with use of the Foldy–Wouthuysen transformation. The difference between the relativistic and non-relativistic expressions for the msr of the point proton density is also discussed. The $n(\ge 4)$th-order moment of the nuclear charge density depends on the point neutron density. The fourth-order moment yields useful information on the msr of the point neutron density, and is expected to play an important role in electron scattering off neutron-rich nuclei.


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