scholarly journals Representation of the kinematics of the natural trihedral of a spiral-helix trajectory by quaternion matrices

2021 ◽  
Vol 9 (4) ◽  
pp. 18-29
Author(s):  
Anatolii Alpatov ◽  
Victor Kravets ◽  
Volodymyr Kravets ◽  
Erik Lapkhanov
Keyword(s):  
Computational Experiment ◽  
Nonlinear Problems ◽  
Unit Vector ◽  
Frame Of Reference ◽  
Mathematical Apparatus ◽  
Dynamic Design ◽  
Quaternion Matrices ◽  
Transport Vehicle ◽  
Stationary Frame ◽  
Curvature And Torsion

The spiral-helix trajectory of the transport vehicle programmed motion in the form of a hodograph in the stationary frame of reference is considered. A relative frame of reference associated with the natural trihedral of the trajectory is introduced. The formulas of curvature and torsion of the trajectory, the unit vector of the natural trihedral, the components of the angular velocity of rotation of the natural trihedral in the proper axes and in the stationary frame of reference are set in the quaternionic matrices. The results are verified using the Frenet-Serret formulas. The mathematical apparatus of quaternion matrices is tested with the aim of adapting spatial, nonlinear problems of dynamic design of transport vehicles to a computational experiment.

Turbomachinery Flow Measurements Using Long-Nose Probes

2003 ◽  
Author(s):  
A. Doukelis ◽  
K. Mathioudakis
Keyword(s):  
Flow Field ◽  
Field Measurements ◽  
Laser Doppler Anemometer ◽  
Frame Of Reference ◽  
Measuring Technique ◽  
Flow Measurements ◽  
Pneumatic Measuring ◽  
Stationary Frame ◽  
Annular Cascade ◽  
Long Nose

The present work provides a detailed account of a pneumatic measuring technique appropriate for flow field measurements in turbomachinery configurations, making use of long-nose 5-hole probes. The way of obtaining flow quantities in a frame of reference on the sensing head of the probe is first addressed. Transformation of velocity co-ordinates from the probe frame to a stationary frame, customary for turbomachinery flows, is then discussed. Sources of error are also discussed, with particular attention on those that can be introduced by the nose geometry and the co-ordinate transformations. The potential of the measuring technique is demonstrated by presenting the application of the technique for measurements in an annular cascade facility. The results are compared to results obtained by a 3-D Laser-Doppler Anemometer.

Simulation of a Rotor Flux Oriented Induction Motor Drive

2012 ◽  
Vol 516-517 ◽  
pp. 1632-1635
Author(s):  
Xiao Jie Chen
Keyword(s):  
Unit Vector ◽  
Motor Drive ◽  
Current Loop ◽  
Induction Motor Drive ◽  
Stator Current ◽  
Rotor Flux ◽  
Stationary Frame ◽  
Stator Flux ◽  
Vector Signal ◽  
Electro Motive Force

The synchronously rotating vector components of the stator current isq and isd are controlled independently to control the torque and the rotor flux, respectively. It can be shown that rotor flux orientation in contrast to stator flux orientation tends to give true decoupling control. Within the synchronous current, the respective counter EMF (Electro Motive Force) signals can be added (or subtracted) to enhance the current loop response. The unit vector signal thetas that transforms the synchronously rotating stator voltage into stationary frame signals has been generated from the speed signal and slip signal which is a function of isq.

scholarly journals Experimental Investigation of Steady and Unsteady Flow Field Downstream of an Automotive Torque Converter Turbine and Stator

1995 ◽  
Vol 2 (2) ◽  
pp. 67-84 ◽  
Author(s):  
B. V. Marathe ◽  
B. Lakshminarayana
Keyword(s):  
Experimental Data ◽  
Flow Field ◽  
Unsteady Flow ◽  
Torque Converter ◽  
Mean Value ◽  
Frame Of Reference ◽  
Secondary Flows ◽  
Flow Properties ◽  
The Core ◽  
Stationary Frame

The objective of this investigation is to understand the steady and the unsteady flow field at the exit of an automotive torque converter turbine and stator with a view towards improving it's performance. A high frequency response five-hole probe was designed and built to measure the three-dimensional steady and unsteady flow fields. The measurements were conducted in a stationary frame of reference and the data were processed to derive the flow properties in the relative (turbine) frame of reference. The experimental data were processed in the frequency domain by spectrum analysis and in temporal-spatial domain by ensemble averaging technique. The data show that the flow field is highly unsteady with high unresolved unsteadiness (approx. 17-21% of mean value) and significant blade-to-blade periodic component approx. 6% of mean value). The unresolved unsteadiness and periodic unsteadiness increase with an increase in the radius from the shell to the core whereas the aperiodic unsteadiness does not show any systematic variation with the radius. The experimental data reveal the presence of a low momentum region near the core due to possible flow separation and reattachment inside the turbine passage. Data also show the presence of strong secondary flow near the core and weak secondary flow near the shell at the exit of the turbine. These secondary flows generate high levels of turbulence. A comparison of the flow properties upstream and downstream of the stator in the stationary frame of reference indicate the presence of high losses near the core due to high turbulence levels and large secondary flows, and high losses near the shell due to possible corner separation near the shell suction surface inside the stator blade passage. The unsteadiness in the flow properties upstream of the stator is high. The rms value of the unsteady total velocity is approx. 20% of the steady state value. Periodic and aperiodic unsteadiness were also found significant.

scholarly journals Comparison of the characteristics of the genetic algorithm and the method of coordinates search for optimization of temperature modes indoor areas

2019 ◽  
pp. 260-270
Author(s):  
A P Shuravin ◽  
S V Vologdin
Keyword(s):  
Artificial Intelligence ◽  
Genetic Algorithm ◽  
Computational Experiment ◽  
Mathematical Formulation ◽  
Computational Cost ◽  
Optimization Methods ◽  
Search Method ◽  
Mathematical Apparatus ◽  
Temperature Mode ◽  
Project Smart

The article substantiates the relevance of optimization algorithms research for solving various applied problems and for the science of artificial intelligence. The need to solve problems of optimizing the thermal-hydraulic modes of buildings (as part of the project "Smart City") is explained. The paper presents a mathematical formulation of the problem of optimizing the temperature mode of rooms using adjustable devices. Existing work provides two methods for solving the posed problem. They are the coordinates search method and the genetic algorithm. The article contains the description of the above mentioned algorithms (including the mathematical apparatus used). The results of the computational experiment (for the considered optimization methods) are presented. These experimental results show that the genetic algorithm provides better optimization results than the coordinates search method, but it has a large computational cost. The hypothesis was confirmed that in order to increase the efficiency of solving the considered class of problems it is necessary to combine the genetic algorithm and the coordinates search method.

scholarly journals Numerical Calculation of Secondary Flow in Pump Volute and Circular Casings using 3D Viscous Flow Techniques

2000 ◽  
Vol 6 (4) ◽  
pp. 245-252 ◽  
Author(s):  
K. Majidi ◽  
H. E. Siekmann
Keyword(s):  
Flow Field ◽  
Static Pressure ◽  
Frame Of Reference ◽  
Centrifugal Impeller ◽  
Pressure Gradients ◽  
Cross Sectional ◽  
Stationary Frame ◽  
Multiple Frame ◽  
Secondary Velocity ◽  
Flow Techniques

The flow field in volute and circular casings interacting with a centrifugal impeller is obtained by numerical analysis. In the present study, effects of the volute and circular casings on the flow pattern have been investigated by successively combining a volute casing and a circular casing with a single centrifugal impeller. The numerical calculations are carried out with a multiple frame of reference to predict the flow field inside the entire impeller and casings. The impeller flow field is solved in a rotating frame and the flow field in the casings in a stationary frame. The static pressure and velocity in the casing and impeller, and the static pressures and secondary velocity vectors at several cross-sectional planes of the casings are calculated. The calculations show that the curvature of the casings creates pressure gradients that cause vortices at cross-sectional planes of the casings.

scholarly journals Inductance Measurement of Interior Permanent Magnet Synchronous Motor in Stationary Frame of Reference

2011 ◽  
Vol 16 (4) ◽  
pp. 391-397 ◽  
Author(s):  
Geun-Ho Lee ◽  
Woong-chul Choi ◽  
Byeong-Hwa Lee ◽  
Jae-Woo Jung ◽  
Jung-Pyo Hong
Keyword(s):  
Permanent Magnet ◽  
Permanent Magnet Synchronous Motor ◽  
Synchronous Motor ◽  
Frame Of Reference ◽  
Interior Permanent Magnet ◽  
Stationary Frame
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