DEVELOPMENT OF A MATHEMATICAL MODEL FOR PERFORMANCE PREDICTION OF PLANING CATAMARAN IN CALM WATER

2021 ◽  
Vol 161 (A2) ◽  
Author(s):  
A Ghassemzadeh ◽  
A Dashtimanesh ◽  
M Habibiasl ◽  
P Sahoo
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Performance Prediction ◽  
Data Evaluation ◽  
Empirical Equations ◽  
Calm Water ◽  
Semi Empirical ◽  
The Mathematical Model ◽  
Comparison With Experimental Data

In this paper, an attempt has been made to predict the performance of a planing catamaran using a mathematical model. Catamarans subjected to a common hydrodynamic lift, have an extra lift between the two asymmetric half bodies. In order to develop a mathematical model for performance prediction of planing catamarans, existing formulas for hydrodynamic lift calculation must be modified. Existing empirical and semi-empirical equations in the literature have been implemented and compared against available experimental data. Evaluation of lift in comparison with experimental data has been documented. Parameters influencing the interaction between demi-hulls and separation effects have been analyzed. The mathematical model for planing catamarans has been developed based on Savitsky’s method and results have been compared against experimental data. Finally, the effects of variation in hull geometry such as deadrise angle and distance between two half bodies on equilibrium trim angle, resistance and wetted surface have been examined.

Development of a Mathematical Model for Performance Prediction of Planing Catamaran in Calm Water

2019 ◽  
Vol 161 (A2) ◽  
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Performance Prediction ◽  
Data Evaluation ◽  
Empirical Equations ◽  
Calm Water ◽  
Semi Empirical ◽  
The Mathematical Model ◽  
Comparison With Experimental Data

In this paper, an attempt has been made to predict the performance of a planing catamaran using a mathematical model. Catamarans subjected to a common hydrodynamic lift, have an extra lift between the two asymmetric half bodies. In order to develop a mathematical model for performance prediction of planing catamarans, existing formulas for hydrodynamic lift calculation must be modified. Existing empirical and semi-empirical equations in the literature have been implemented and compared against available experimental data. Evaluation of lift in comparison with experimental data has been documented. Parameters influencing the interaction between demi-hulls and separation effects have been analyzed. The mathematical model for planing catamarans has been developed based on Savitsky’s method and results have been compared against experimental data. Finally, the effects of variation in hull geometry such as deadrise angle and distance between two half bodies on equilibrium trim angle, resistance and wetted surface have been examined.

Development of a 2D+T theory for performance prediction of double-stepped planing hulls in calm water

2018 ◽  
Vol 233 (3) ◽  
pp. 886-904 ◽  
Author(s):  
Rasul Niazmand Bilandi ◽  
Abbas Dashtimanesh ◽  
Sasan Tavakoli
Keyword(s):  
Mathematical Model ◽  
Performance Prediction ◽  
Empirical Models ◽  
Two Dimensional ◽  
Reasonable Accuracy ◽  
Future Studies ◽  
Normal Forces ◽  
Calm Water ◽  
The Mean ◽  
The Mathematical Model

In this article, a mathematical model based on the 2D+T theory has been developed to predict the performance of two-stepped planing hulls in calm water. It has been attempted to develop a mathematical model without using regression formulas. It leads to development of a computational model with no common limitations related to empirical models which have an individual range of applicability. For this purpose, theoretical solution of water entry of a two-dimensional wedge section has been implemented to compute the pressure distribution over wedge section entering water, and then normal forces acting on the two-dimensional sections are computed. Bottom of the boat has been divided into three different planing surfaces including fore, middle and aft bodies. Computations are performed for each of these surfaces. By integrating the two-dimensional sectional normal forces over the entire wetted length of the vessel, the trim angle, wetted surface and resistance have been obtained. To evaluate the accuracy of the presented method, the obtained results are compared against experimental data and a previous empirical-based method developed by authors. The comparison suggests that the proposed method predicted dynamic trim angle, wetted surface and resistance of double stepped boats with reasonable accuracy. The mean errors in prediction of trim angle, wetted surface and resistance are, respectively, 13%, 16% and 8%. It should also be noted that although computation of running attitudes and resistance of double-stepped planing boats are targeted in this article, the mathematical model has been developed in such a way that it has the potential to model transverse and vertical motions of two-stepped planing hulls in future studies.

scholarly journals DETERMINING OF OPERATIONAL PARAMETERS FOR TRAWL SYSTEM TAKING INTO ACCOUNT EXPERIMENTAL DATA ON SHAPE OF THE ROPE-NET SHELL OF MIDWATER TRAWLS

2020 ◽  
Vol 200 ◽  
pp. 193-209
Author(s):  
O. N. Kruchinin ◽  
E. A. Zakharov ◽  
D. L. Shabelsky
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Empirical Equations ◽  
Okhotsk Sea ◽  
Operational Parameters ◽  
Midwater Trawl ◽  
Biological Resources ◽  
Hydroacoustic Measurements ◽  
Model Equations ◽  
The Mathematical Model

Calculating of horizontal opening for a trawl mouth using the mathematical model of midwater trawl system developed by V.I. Gabryuk gives the errors 25.4 and 32.9 %, on average, for the trawls RT 57/360 m and RT 80/396 m, respectively. The significant errors cause doubts about correctness of this model equations application for calculation of the catch zone that is necessary for assessment of abundance and biomass of marine biological resources. New empirical equations are proposed on the basis of experimental data on shape of the rope-net shell of a midwater trawl, which allow to calculate the horizontal opening for its certain sections. The errors of the horizontal opening calculation with these new equations are 13.7 and 6.1 %, on average, for the trawls RT 57/360 m and RT 80/396 m, respectively, that is satisfactory for using them for calculating operational parameters of a midwater trawl system. The operational parameters of the midwater trawls RT 57/360 m and RT 80/396 m are calculated using Baranov’s approach with these new empirical equations, and their good adequacy is shown in the experiment with hydroacoustic measurements of the trawls mouth horizontal opening and the distance between the trawl doors conducted aboard RV TINRO and RV Professor Kaganovsky in the Okhotsk Sea in 2012–2015.

scholarly journals Calm Water Performance of Hard-Chine Vessels in Semi-Planing and Planing Regimes

2016 ◽  
Vol 23 (4) ◽  
pp. 23-45 ◽  
Author(s):  
Parviz Ghadimi ◽  
Sasan Tavakoli ◽  
Abbas Dashtimanesh
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Iterative Method ◽  
Performance Prediction ◽  
Equilibrium Equations ◽  
Frictional Drag ◽  
Pressure Distributions ◽  
Induced Drag ◽  
Proposed Model ◽  
Calm Water

Abstract In the current paper, a mathematical model is developed for performance prediction of hard-chin boats which can be used in both semi-planing and planing regimes. The proposed model bases on the 2D+T theory and implements pressure distributions over the length of the hull in order to compute the forces. To determine the forces in the semi-planing range, a function is proposed for the non-dimensional length at which the transom effect appears. Three drag components, which are: frictional drag, induced drag, and spray drag, are considered in the computations performed using an iterative method to satisfy two equilibrium equations. The validity of the proposed method is verified by comparing the predicted trim angle and resistance against the available experimental data. Based on this comparison, it is observed that the proposed method reveals satisfying accuracy in both semi-planing and planing regimes. The method is then used to study variation of hydrodynamic and hydrostatic forces as the hull makes a transition from the semi-planing regime to the planing regime. In addition, different components of the resistance are analyzed.

Effect of Freestream Radial Velocity Component on Hydrodynamic Analysis of Propellers

1983 ◽  
Vol 27 (02) ◽  
pp. 131-134
Author(s):  
Terry Brockett
Keyword(s):  
Mathematical Model ◽  
Radial Velocity ◽  
Performance Prediction ◽  
Velocity Component ◽  
Additional Term ◽  
Radial Component ◽  
Radial Velocity Component ◽  
Hydrodynamic Analysis ◽  
The Mathematical Model ◽  
Wake Fields

For wake fields with circumferential averages that include a small radial component, an additional termarises in the mathematical model used for design or performance prediction of propellers that has been previously overlooked. This term arises from the boundary condition that the blade is impenetrable and is a function of only geometry and the inflow radial velocity component. This simple additional term is shown to be important for the example considered, leading to a variable change in camber and a pitch reduction.

Application of a Bubble-Induced Turbulence Model to Subcooled Boiling in a Vertical Pipe

1999 ◽  
Author(s):  
Mahmut D. Mat ◽  
Yüksel Kaplan ◽  
Olusegun J. Ilegbusi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Liquid Phase ◽  
Turbulence Model ◽  
Transport Equations ◽  
Subcooled Boiling ◽  
Vertical Pipe ◽  
Void Fractions ◽  
Turbulence Production ◽  
The Mathematical Model

Abstract Subcooled boiling of water in a vertical pipe is numerically investigated. The mathematical model involves solution of transport equations for vapor and liquid phase separately. Turbulence model considers the turbulence production and dissipation by the motion of the bubbles. The radial and axial void fractions, temperature and velocity profiles in the pipe are calculated. The estimated results are compared to experimental data available in the literature. It is found that while present study satisfactorily agrees with experimental data in the literature, it improves the prediction at lower void fractions.

Analytical Study of Hydro-Pneumatic Processes for Gorlov's Power System

1994 ◽  
Vol 208 (1) ◽  
pp. 67-70
Author(s):  
A I Ryazanov
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Power System ◽  
Analytical Study ◽  
Model Tests ◽  
Air Pressure ◽  
Pneumatic Power ◽  
Time Required ◽  
The Mathematical Model

This paper describes the aerohydrodvnamics of processes in chambers of Gorlov's hydro-pneumatic power system. The mathematical model is developed to determine the main parameters of the processes: water and air velocities, air pressure in the chamber, the periods of time required to fill and empty the chambers and the output of energy during the cycle. The results obtained are in agreement with experimental data and model tests.

scholarly journals MATHEMATICAL MODELING OF LEACHING PROCESS OF RED MUD IN ORDER TO OBTAIN THE KINETICS PARAMETERS

2015 ◽  
Vol 14 (2) ◽  
pp. 90 ◽  
Author(s):  
K. L. M. Dos Passos ◽  
B. M. Viegas ◽  
E. N. Macêdo ◽  
J. A. S. Souza ◽  
E. M. Magalhães
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Red Mud ◽  
Mineralogical Composition ◽  
Raw Material ◽  
Data Conversion ◽  
Kinetics Parameters ◽  
Leaching Process ◽  
Iron Leaching ◽  
The Mathematical Model

The use of the waste of the Bayer process, red mud, is due to its chemical and mineralogical composition that shows a material rich in oxides of iron, titanium and aluminum. Some studies conducted show that this waste can be applied as a source of alternative raw material for concentration and subsequent recovery of titanium compounds from an iron leaching process, which is present in higher amounts, about 30% by weight. To obtain a greater understanding about the leaching kinetics, the information of the kinetic data of this process is very important. In this context, the main objective of this work is the development of a mathematical model that is able to fit the experimental data (conversion / extraction iron, titanium and aluminum) of the leaching process by which is possible to obtain the main kinetic parameters such as the activation energy and the velocity of chemical reactions as well as the controlling step of the process. The development of the mathematical model was based on the model of core decreasing. The obtained model system of ordinary differential equations was able to fit the experimental data obtained from the leaching process, enabling the determination of the controlling step, the rate constants and the activation energies of the leaching process.

scholarly journals Belt conveyor failure simulation at the design stage with transverse displacements of the belt

2020 ◽  
Vol 168 ◽  
pp. 00056
Author(s):  
Vitalii Monastyrskyi ◽  
Serhii Monastyrskyi ◽  
Denis Nomerovskyi ◽  
Borys Mostovyi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Fourier Transform ◽  
Adaptive Control ◽  
Design Stage ◽  
Belt Conveyor ◽  
Failure Simulation ◽  
The Fourier Transform ◽  
External Forces ◽  
The Mathematical Model

To find possible conveyor failures at the design stage means to determine a transverse belt displacement and compare the obtained data with the permissible ones. The dynamic problem of the belt movement on the conveyor has been defined. Resistance and external forces, limits of the belt displacement have been determined. The transverse belt displacement can be described by partial differential equations. To solve the problem, the Fourier transform has been used. Change patterns in the transverse belt conveyor displacement dependent on conveyor’s parameters, type of load, and skewing of the idlers along the conveyor have been obtained. The results agree with experimental data. The method of adaptive control of the transverse belt displacement has been described. The essence of this method is to adapt the model of the moving belt in the conveying trough to changed conditions and to reveal the uncertainty of the control with the known parameters of the mathematical model.

scholarly journals Mathematical modelling of trastuzumab-induced immune response in an in vivo murine model of HER2+ breast cancer

2018 ◽  
Vol 36 (3) ◽  
pp. 381-410 ◽  
Author(s):  
Angela M Jarrett ◽  
Meghan J Bloom ◽  
Wesley Godfrey ◽  
Anum K Syed ◽  
David A Ekrut ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Experimental Data ◽  
Mathematical Model ◽  
Immune Response ◽  
Immune System ◽  
Murine Model ◽  
Tumour Growth ◽  
Experimental Approach ◽  
Her2 Breast Cancer ◽  
The Mathematical Model

Abstract The goal of this study is to develop an integrated, mathematical–experimental approach for understanding the interactions between the immune system and the effects of trastuzumab on breast cancer that overexpresses the human epidermal growth factor receptor 2 (HER2+). A system of coupled, ordinary differential equations was constructed to describe the temporal changes in tumour growth, along with intratumoural changes in the immune response, vascularity, necrosis and hypoxia. The mathematical model is calibrated with serially acquired experimental data of tumour volume, vascularity, necrosis and hypoxia obtained from either imaging or histology from a murine model of HER2+ breast cancer. Sensitivity analysis shows that model components are sensitive for 12 of 13 parameters, but accounting for uncertainty in the parameter values, model simulations still agree with the experimental data. Given theinitial conditions, the mathematical model predicts an increase in the immune infiltrates over time in the treated animals. Immunofluorescent staining results are presented that validate this prediction by showing an increased co-staining of CD11c and F4/80 (proteins expressed by dendritic cells and/or macrophages) in the total tissue for the treated tumours compared to the controls ($p < 0.03$). We posit that the proposed mathematical–experimental approach can be used to elucidate driving interactions between the trastuzumab-induced responses in the tumour and the immune system that drive the stabilization of vasculature while simultaneously decreasing tumour growth—conclusions revealed by the mathematical model that were not deducible from the experimental data alone.

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