scholarly journals A semi-empirical model for streamwise vortex intensification

2019 ◽  
Vol 233 (12) ◽  
pp. 4396-4409
Author(s):  
Grant McLelland ◽  
David MacManus ◽  
Chris Sheaf
Keyword(s):  
Empirical Model ◽  
Vortex Core ◽  
Axial Strain ◽  
Empirical Relationship ◽  
Tangential Velocity ◽  
Streamwise Vortex ◽  
Stereoscopic Particle Image Velocimetry ◽  
Wide Range ◽  
Semi Empirical ◽  
Vortex Intensification

Vortex intensification plays an important role in a wide range of flows of engineering interest. One scenario of interest is when a streamwise vortex passes through the contracting streamtube of an aircraft intake. There is, however, limited experimental data of flows of this type to reveal the dominant flow physics and to guide the development of vortex models. To this end, the evolution of wing-tip vortices inside a range of streamtube contractions has been measured using stereoscopic particle image velocimetry. A semi-empirical model has been applied to provide new insight on the role of vorticity diffusion during the intensification process. The analysis demonstrates that for mild flow contractions, vorticity diffusion has a negligible influence due to the low rates of diffusion in the vortex flow prior to intensification and the short convective times associated with the streamtube contraction. As the contraction levels increase, there is a substantial increase in the rates of diffusion which is driven by the greater levels of vorticity in the vortex core. A new semi-empirical relationship, as a function of the local streamtube contraction levels and vortex Reynolds number, has been developed. The model comprises a simple correction to vortex filament theory and provides a significant improvement in the estimation of vortex characteristics in contracting flows. For the range of contractions investigated, errors in the estimation of vortex core radius, peak tangential velocity and vorticity are reduced by an order of magnitude. The model can be applied to estimate the change in vortex characteristics for a range of flows with intense axial strain, such as contracting intake streamtubes and swirling flows in turbomachinery.

scholarly journals Computational simulation of flocculent sedimentation based on experimental results

2012 ◽  
Vol 65 (6) ◽  
pp. 1007-1013 ◽  
Author(s):  
Mafeni S. Ramatsoma ◽  
Evans M. N. Chirwa
Keyword(s):  
Empirical Model ◽  
Mechanistic Model ◽  
Computational Simulation ◽  
Data Sets ◽  
Random Errors ◽  
Wide Range ◽  
Model Predictions ◽  
Sedimentation Basins ◽  
Semi Empirical ◽  
Better Than

Computerised interpolation algorithms as well as the empirical model for analysing the flocculent settling data were developed. A mechanistic semi-empirical model developed from fundamental physical principles of a falling particle in a viscous fluid was tested against actual flocculation column data. The accuracy of the mechanistic model was evaluated using the sum of the squared errors between the interpolated values (real values) and the model predictions. Its fitting capabilities were compared with Özer's model using nine flocculent data sets of which four were obtained from literature and the rest were actual data from the performed experiments. The developed model consistently simulated the flocculation behaviour of particles in settling columns better than Özer's model in eight of the nine data sets considered. It is recommended that the model's performance be further compared with other models like the Rule based and San's model. The errors due to the use of interpolated values when determining the performance of the empirical models need to be investigated. Furthermore, a three-way rather than two-way interpolation should now be achievable using the interpolation algorithm developed in this study thereby reducing the effects of interpolation bias. The above work opens the way to full automation of design of flocculation sedimentation basins and other gravitational particle separation systems which at present are designed manually and are susceptible to a wide range of human and random errors.

Transient Lift on a Blade During Orthogonal Vortex Cutting

2017 ◽  
Author(s):  
D. Curtis Saunders ◽  
Jeffrey S. Marshall
Keyword(s):  
Vortex Core ◽  
Lift Force ◽  
Lift Coefficient ◽  
Orthogonal Cutting ◽  
Axial Flow ◽  
Leading Edge ◽  
Streamwise Vortex ◽  
Navier Stokes ◽  
Wide Range ◽  
The Impact

Vortex cutting imposes significant forces on blades in applications such as wind turbines operating in the wake of upstream turbines, helicopter rotor vortex impingement on the tail rotor, intake vortex interaction with a pump impellor, and streamwise vortex ingestion into a submarine propeller. The transient lift on a blade during orthogonal cutting of a vortex with non-zero axial flow was examined in the current paper using a combination of scaling theory, an analytical solution for instantaneous cutting and full Navier-Stokes simulations. The paper focuses on two distinct forces that occur during vortex cutting — the transient lift force that occurs during penetration of the blade leading edge into the vortex core and the steady-state lift force associated with the difference in vortex core radius over the blade surface. We show that the maximum value of the lift coefficient for the transient blade penetration force is proportional to the impact parameter and inversely proportional to the axial flow parameter. This observation is used to collapse predictions of the full Navier-Stokes simulations for lift coefficient over a wide range of values of the governing dimensionless parameters.

scholarly journals A Semi-Empirical Model for Predicting Frost Properties

Processes ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 412
Author(s):  
Shao-Ming Li ◽  
Kai-Shing Yang ◽  
Chi-Chuan Wang
Keyword(s):  
Thermal Conductivity ◽  
Linear Programming ◽  
Numerical Model ◽  
Empirical Model ◽  
Quantitative Method ◽  
Predictive Ability ◽  
Dimensionless Temperature ◽  
Crystal Shape ◽  
Proposed Model ◽  
Semi Empirical

In this study, a quantitative method for classifying the frost geometry is first proposed to substantiate a numerical model in predicting frost properties like density, thickness, and thermal conductivity. This method can recognize the crystal shape via linear programming of the existing map for frost morphology. By using this method, the frost conditions can be taken into account in a model to obtain the corresponding frost properties like thermal conductivity, frost thickness, and density for specific frost crystal. It is found that the developed model can predict the frost properties more accurately than the existing correlations. Specifically, the proposed model can identify the corresponding frost shape by a dimensionless temperature and the surface temperature. Moreover, by adopting the frost identification into the numerical model, the frost thickness can also be predicted satisfactorily. The proposed calculation method not only shows better predictive ability with thermal conductivities, but also gives good predictions for density and is especially accurate when the frost density is lower than 125 kg/m3. Yet, the predictive ability for frost density is improved by 24% when compared to the most accurate correlation available.

scholarly journals Extrapolability and limitations of a semi-empirical model for the simulation of volumetric expanders

2017 ◽  
Vol 129 ◽  
pp. 315-322 ◽  
Author(s):  
Olivier Dumont ◽  
Rémi Dickes ◽  
Vincent Lemort
Keyword(s):  
Empirical Model ◽  
Semi Empirical

scholarly journals DFT calculation and assignment of vibrational spectra of aryl and alkyl chlorophosphates

2014 ◽  
Vol 12 (2) ◽  
pp. 153-163
Author(s):  
Viktor Anishchenko ◽  
Vladimir Rybachenko ◽  
Konstantin Chotiy ◽  
Andrey Redko
Keyword(s):  
Vibrational Spectra ◽  
Basis Sets ◽  
Heavy Atoms ◽  
Wide Range ◽  
Complete Assignment ◽  
Key Factor ◽  
Polarization Functions ◽  
Experimental Values ◽  
Semi Empirical ◽  
Good Agreement

AbstractDFT calculations of vibrational spectra of chlorophosphates using wide range of basis sets and hybrid functionals were performed. Good agreement between calculated and experimental vibrational spectra was reached by the combination of non-empirical functional PBE0 with both middle and large basis sets. The frequencies of the stretching vibrations of the phosphate group calculated using semi-empirical functional B3LYP for all basis sets deviate significantly from the experimental values. The number of polarization functions on heavy atoms was shown to be a key factor for the calculation of vibrational frequencies of organophosphates. The importance of consideration of all the stable rotamers for a complete assignment of fundamental modes was shown.

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