Spars Effect on the Stress Reduction in the Multi-box Airfoils

Toufik Yahiaoui,Walid Hamaidia,Toufik Zebbiche 한국항공우주학회 2024 International Journal of Aeronautical and Space Sc Vol.25 No.1

The aim of this paper is to develop a new numerical program aiming to calculate the stress effect of the successive addition of the vertical spars on the reduction of the maximum tangential and normal stress due to the various internal forces, in multi-box thin-walled airfoils sections. The comparison is made with the single box airfoil without spar. The airfoil is given by tabulated values. An interpolation by cubic spline is necessary to obtain an analytical function for the upper and the lower surfaces. The calculation is based on the computation of the geometrical characteristics of the thin-walled section with different spars number. The method consists of scanning the position of the first spar along the airfoil chord, and calculating the maximum of the tangential and the normal stress, giving at the end the optimal spar position with the smallest stress values. The calculation is be repeated for the second spar based on the first optimal spar position. The insertion of a third spar is made on the optimum position of the first two spars. The calculation will be repeated each time an additional spar is inserted. The optimum spars position is not the same for the two types of torsional and normal stress. The diagrams of the internal forces are necessary to locate the dangerous section stressed by the maximum internal forces. The application is made up to five spars as an improvement to the current applications for 1 and 2 spars. Six airfoils are used for comparison.

Numerical Quadrature for the Prandtl Meyer Function at High Temperature with Application for Air

Toufik Zebbiche 한국항공우주학회 2008 International Journal of Aeronautical and Space Sc Vol.9 No.2

When the stagnation temperature of the combustion chamber or ambient air increases, the specific heats and their ratio do not remain constant any more, and start to vary with this temperature. The gas remains perfect, except, it will be calorically imperfect and thermally perfect. A new generalized form of the Prandtl Meyer function is developed, by adding the effect of variation of this temperature, lower than the threshold of dissociation. The new relation is presented in the form of integral of a complex analytical function, having an infinite derivative at the critical temperature. A robust numerical integration quadrature is presented in this context. The classical form of the Prandtl Meyer function of a perfect gas becomes a particular case of the developed form. The comparison is made with the perfect gas model for aim to present a limit of its application. The application is for air.

Effect of Stagnation Temperature on the Supersonic Flow Parameters with Application for Air in Nozzles

Toufik Zebbiche,ZineEddine Youbi 한국항공우주학회 2006 International Journal of Aeronautical and Space Sc Vol.7 No.1

When the stagnation temperature of a perfect gas increases, the specific heat for constant pressure and ratio of the specefic heats do not remain constant any more and start to vary with this temperature. The gas remains perfect: its state equation remains always valid, with exception that it will be named by calorically imperfect gas. The aim of this research is to develop the relations of the necessary thermodynamics and geometrical ratios. and to study the supersonic flow at high temperature. lower than the threshold of dissociation. The results are found by the resolution of nonlinear algebraic equations and integration of complex analytical functions where the exact calculation is impossible. The dichotomy method is used to solve the nonlinear equation. and the Simpson algorithm for the numerical integration of the found integrals. A condensation of the nodes is used. Since. the functions to be integrated have a high gradient at the extremity of the interval of integration. The comparison is made with the calorifcally perfect gas to determine the error made by this last. The application is made for the air in a supersonic nozzle.

Supersonic Plug Nozzle Design and Comparison to the Minimum Length Nozzle Configuration

Toufik Zebbiche,ZineEddine Youbi 한국항공우주학회 2006 International Journal of Aeronautical and Space Sc Vol.7 No.1

A method to design the contour and conception of a plug nozzle of arbitrary shape, but specified exit flow conditions is presented. Severals shapes can be obtained for exit Mach number by changing the specific heats ratio. The characteristics of the nozzle in terms of length, weight and pressure force exerted on the wall are compared to the Minimum Length Nozzle and found to be better. Our field of study is limited to the supersonic mode to not to have the dissociation of the molecules. The design method is based on the use of the Prandtl Meyer function of a perfect gas. The flow is not axial at the throat, which may be advantageous for many propulsion applications. The performance benefits of the plug nozzle compared to the Minimum Length Nozzle are also presented.

Modified Apostol-type polynomials arising from umbral calculus

Toufik Mansour,Hacer Ozden,Yilmaz Simsek 장전수학회 2014 Advanced Studies in Contemporary Mathematics Vol.24 No.2

In this paper, by using the orthogonality type as defined in the umbral calculus, we derive an explicit formula for several well-known polynomials as a linear combination of the modified Apostol-type polynomials.

Sensorless Fault-Tolerant Control of an Induction Motor Based Electric Vehicle

Toufik Roubache,Souad Chaouch,Med Said Nait Said 대한전기학회 2016 Journal of Electrical Engineering & Technology Vol.11 No.5

This paper describes a sensorless fault-tolerant control (FTC) for a high-performance induction motor drive that propels an electric-vehicle (EV). The effect of the fault on the induction motor (IM) can be modeled by an exogenous signal from a stable autonomous system. An additive term is added to the nominal offset and serves to control the effect of the defect (FTC aspect). The proposed sensorless FTC for IM is realized in presence of both rotor and stator electrical faults. Consequently, the extended kalman filter (EKF) is proposed to estimate the rotor flux and the rotor speed using the measured stator currents and voltages. Therefore, a classical EV traction system is studied using an induction motor drive. Indeed, the induction motor based powertrain is coupled to DC machine-based load torque emulator taking into account the electric vehicle mechanics and aerodynamics. Simulation and experimental results confirm widely the feasibility and the effectiveness of the proposed FTC of IM based SMC in the electric vehicle application.

Effect of the Stagnation Temperature on the Normal Shock Wave

Toufik Zebbiche 한국항공우주학회 2009 International Journal of Aeronautical and Space Sc Vol.10 No.1

When the stagnation temperature increases, the specific heat does not remain constant and start to vary with this temperature. The gas is perfect, it's state equation remains always valid, except, it was called by gas calorically imperfect or gas at high temperatures. The purpose of this work is to develop a mathematical model for a normal shock wave normal at high temperature when the stagnation temperature is taken into account, less than the dissociation of the molecules as a generalisation model of perfect for constant heat specific. A study on the error given by the perfect gas model compared to our model is presented in order to find a limit of application of the perfect gas model. The application is for air.

Supersonic Dual Bell Axisymmetric Minimum Length Nozzle Conception for High Propulsion Thrust

Toufik Zebbiche 한국항공우주학회 2019 International Journal of Aeronautical and Space Sc Vol.20 No.3

The aim of this work is to develop a new numerical computing program to design a new form of a dual bell axisymmetric supersonic minimum length nozzle contour, adapted to two different altitudes, usually at sea level and space, giving a supersonic uniform and parallel flow to the exit section. The first bell has a uniform and parallel sonic inlet and a low-altitude adaptation, with a reduced supersonic Mach number, while the second bell has a supersonic inlet and uniform and parallel flow and high altitude adaptation with high supersonic Mach number. The two bells are attached to an inflection point at the exit of the first bell. The passage from low altitude to high altitude is done without any mechanical activation. The purpose of this type of nozzle is the possibility of supersonic flight in two different regimes adapted into two different altitudes, under the assumption of a calorically and thermally perfect gas. This type of nozzle has an inflection point at the attachment point of the second bell to the first bell. The design is done using the method of characteristics. Solving the equations is done numerically by the predictor corrector algorithm. The validation of the results is controlled by the convergence of the critical sections ratio, calculated numerically, to that given by the theory. In this case, all the design parameters automatically converge towards the desired solution.

Supersonic Axisymmetric Minimum Length Nozzle Conception at High Temperature with Application for Air

Toufik Zebbiche 한국항공우주학회 2008 International Journal of Aeronautical and Space Sc Vol.9 No.1

When the stagnation temperature of a perfect gas increases, the specific heats and their ratio do not remain constant any more and start to vary with this temperature. The gas remains perfect; its state equation remains always valid, except, it is named in more by calorically imperfect gas. The aim of this work is to trace the profiles of the supersonic axisymmetric Minimum Length Nozzle to have a uniform and parallel flow at the exit section, when the stagnation temperature is taken into account, lower than the dissociation threshold of the molecules, and to have for each exit Mach number and stagnation temperature shape of nozzle. The method of characteristics is used with the algorithm of the second order finite differences method. The form of the nozzle has a point of deflection and an initial angle of expansion. The comparison is made with the calorically perfect gas. The application is for air.

Effect of the Stagnation Temperature on the Normal Shock Wave

Zebbiche, Toufik The Korean Society for Aeronautical and Space Scie 2009 International Journal of Aeronautical and Space Sc Vol.10 No.1

When the stagnation temperature increases, the specific heat does not remain constant and start to vary with this temperature. The gas is perfect, it's state equation remains always valid, except, it was called by gas calorically imperfect or gas at high temperatures. The purpose of this work is to develop a mathematical model for a normal shock wave normal at high temperature when the stagnation temperature is taken into account, less than the dissociation of the molecules as a generalisation model of perfect for constant heat specific. A study on the error given by the perfect gas model compared to our model is presented in order to find a limit of application of the perfect gas model. The application is for air.