The linear stability analysis of a Poiseuille flow running over a porous slab is considered in th... more The linear stability analysis of a Poiseuille flow running over a porous slab is considered in the case where the suction , due to a cross flow, is present through both the channel and the slab. At the interface between the two regions proper matching conditions are to be satisfied. An analytic solution is found for the basic flow in the entire field whereas the stability analysis is carried out by numerically solving the eigenvalues problem for the flow channel only. The influence of the main parameters which govern the perturbed flow field is fully discussed.
In this work, a receptivity analysis of the boundary layer evolving along a NACA-0012 wing profil... more In this work, a receptivity analysis of the boundary layer evolving along a NACA-0012 wing profile with suction at wall surface is considered. The environmental perturbations that arrive from the free stream and enter the boundary layer, such as acoustic or vortical waves, do not have the correct wave parameters (i.e., the frequency and the wavelength) to excite the instability wave. Thus, a wave-modulation mechanism is needed in order to create the modal instability. The interaction between the external disturbance and the perturbation induced in the boundary layer by suction at the wing surface can activate this mechanism. In the model proposed here, the Navier-Stokes equations that govern the problem are linearized around a basic flow which is determined by the boundary-layer equations. Besides, considering that the boundary layer evolves with two different length scales, the theory of multiple scales is employed to solve the receptivity problem. A solvability condition, given by the orthogonality relation between the adjoint eigenfunction (solution of the adjoint eigenvalue problem) and the non-homogeneous term of the receptivity differential equation, allows the solution of the non-homogeneous problem. After imposing the solvability condition, a first-order differential equation with variable coefficients is obtained. The analytical expression of this equation gives the solution of the complex multiplicative coefficient that allows the wave-amplitude estimation as well as the obtention of the here-denominated receptivity function which gives an estimation of how receptive is the airfoil boundary layer to the considered disturbances.
Publisher Summary This chapter presents the numerical experimentation results of a new double-mul... more Publisher Summary This chapter presents the numerical experimentation results of a new double-multiple stream tube model. This model was developed for the aerodynamic analysis of a nonconventional new vertical axis wind turbine. Frequently, in the conventional Darrieus turbines, blades move in a circular trajectory been rigidly related to the central axis by structural elements. The results presented in this chapter belong to different oval-trajectory rotors with a high number of blades. The equivalent power coefficient gives an idea of the efficiency of the wind-mechanical energy conversion, and the trajectory efficiency is a kind of technical economical index. Their results are shown in this chapter for different CF values.
Publisher Summary This chapter discusses the new double-multiple streamtube model that can simula... more Publisher Summary This chapter discusses the new double-multiple streamtube model that can simulate either conventional Darrieus rotors or new oval-trajectory variable-geometry. This capability allows it to treat more general cases and expands the spectrum of analysis for Darrieus turbines design. This model allows the prediction of the aerodynamic performance of noncircular trajectory Darrieus turbines with variable blade-positioning angle. This model was developed to predict the aerodynamic performance of a new-concept turbine whose most remarked characteristics are high number of blades and low rotational speed. The new double-multiple streamtube model can simulate either conventional Darrieus rotors or new oval-trajectory variable-geometry ones. Based on these characteristics, a double-multiple steamtube model was developed. This model includes variable blade-positioning angle β, the trajectory-shape coefficient CF, and the wind orientation angle φ. The new reference frame is the length of the trajectory.
Publisher Summary This chapter discusses the new double-multiple streamtube model that can simula... more Publisher Summary This chapter discusses the new double-multiple streamtube model that can simulate either conventional Darrieus rotors or new oval-trajectory variable-geometry. This capability allows it to treat more general cases and expands the spectrum of analysis for Darrieus turbines design. This model allows the prediction of the aerodynamic performance of noncircular trajectory Darrieus turbines with variable blade-positioning angle. This model was developed to predict the aerodynamic performance of a new-concept turbine whose most remarked characteristics are high number of blades and low rotational speed. The new double-multiple streamtube model can simulate either conventional Darrieus rotors or new oval-trajectory variable-geometry ones. Based on these characteristics, a double-multiple steamtube model was developed. This model includes variable blade-positioning angle β, the trajectory-shape coefficient CF, and the wind orientation angle φ. The new reference frame is the length of the trajectory.
Publisher Summary This chapter presents the numerical experimentation results of a new double-mul... more Publisher Summary This chapter presents the numerical experimentation results of a new double-multiple stream tube model. This model was developed for the aerodynamic analysis of a nonconventional new vertical axis wind turbine. Frequently, in the conventional Darrieus turbines, blades move in a circular trajectory been rigidly related to the central axis by structural elements. The results presented in this chapter belong to different oval-trajectory rotors with a high number of blades. The equivalent power coefficient gives an idea of the efficiency of the wind-mechanical energy conversion, and the trajectory efficiency is a kind of technical economical index. Their results are shown in this chapter for different CF values.
In this work, a receptivity analysis of the boundary layer evolving along a NACA-0012 wing profil... more In this work, a receptivity analysis of the boundary layer evolving along a NACA-0012 wing profile with suction at wall surface is considered. The environmental perturbations that arrive from the free stream and enter the boundary layer, such as acoustic or vortical waves, do not have the correct wave parameters (i.e., the frequency and the wavelength) to excite the instability wave. Thus, a wavemodulation mechanism is needed in order to create the modal instability. The interaction between the external disturbance and the perturbation induced in the boundary layer by suction at the wing surface can activate this mechanism. In the model proposed here, the Navier-Stokes equations that govern the problem are linearized around a basic flow which is determined by the boundary-layer equations. Besides, considering that the boundary layer evolves with two different length scales, the theory of multiple scales is employed to solve the receptivity problem. A solvability condition, given by ...
The stability and the admittance analysis are considered for a Poiseuille flow running over a per... more The stability and the admittance analysis are considered for a Poiseuille flow running over a permeable slab. The case where a suction, due to a cross flow, is present through both the channel and the porous slab is also dealt with. An analytic solution is found for the basic flow in the entire field whereas the stability analysis and the evaluation of the admittance at the interface are numerically carried out. The errors made in the usually simplified analyses are fully discussed.
The linear stability analysis of a Poiseuille flow running over a porous slab is considered in th... more The linear stability analysis of a Poiseuille flow running over a porous slab is considered in the case where the suction , due to a cross flow, is present through both the channel and the slab. At the interface between the two regions proper matching conditions are to be satisfied. An analytic solution is found for the basic flow in the entire field whereas the stability analysis is carried out by numerically solving the eigenvalues problem for the flow channel only. The influence of the main parameters which govern the perturbed flow field is fully discussed.
In this work, a receptivity analysis of the boundary layer evolving along a NACA-0012 wing profil... more In this work, a receptivity analysis of the boundary layer evolving along a NACA-0012 wing profile with suction at wall surface is considered. The environmental perturbations that arrive from the free stream and enter the boundary layer, such as acoustic or vortical waves, do not have the correct wave parameters (i.e., the frequency and the wavelength) to excite the instability wave. Thus, a wave-modulation mechanism is needed in order to create the modal instability. The interaction between the external disturbance and the perturbation induced in the boundary layer by suction at the wing surface can activate this mechanism. In the model proposed here, the Navier-Stokes equations that govern the problem are linearized around a basic flow which is determined by the boundary-layer equations. Besides, considering that the boundary layer evolves with two different length scales, the theory of multiple scales is employed to solve the receptivity problem. A solvability condition, given by the orthogonality relation between the adjoint eigenfunction (solution of the adjoint eigenvalue problem) and the non-homogeneous term of the receptivity differential equation, allows the solution of the non-homogeneous problem. After imposing the solvability condition, a first-order differential equation with variable coefficients is obtained. The analytical expression of this equation gives the solution of the complex multiplicative coefficient that allows the wave-amplitude estimation as well as the obtention of the here-denominated receptivity function which gives an estimation of how receptive is the airfoil boundary layer to the considered disturbances.
Publisher Summary This chapter presents the numerical experimentation results of a new double-mul... more Publisher Summary This chapter presents the numerical experimentation results of a new double-multiple stream tube model. This model was developed for the aerodynamic analysis of a nonconventional new vertical axis wind turbine. Frequently, in the conventional Darrieus turbines, blades move in a circular trajectory been rigidly related to the central axis by structural elements. The results presented in this chapter belong to different oval-trajectory rotors with a high number of blades. The equivalent power coefficient gives an idea of the efficiency of the wind-mechanical energy conversion, and the trajectory efficiency is a kind of technical economical index. Their results are shown in this chapter for different CF values.
Publisher Summary This chapter discusses the new double-multiple streamtube model that can simula... more Publisher Summary This chapter discusses the new double-multiple streamtube model that can simulate either conventional Darrieus rotors or new oval-trajectory variable-geometry. This capability allows it to treat more general cases and expands the spectrum of analysis for Darrieus turbines design. This model allows the prediction of the aerodynamic performance of noncircular trajectory Darrieus turbines with variable blade-positioning angle. This model was developed to predict the aerodynamic performance of a new-concept turbine whose most remarked characteristics are high number of blades and low rotational speed. The new double-multiple streamtube model can simulate either conventional Darrieus rotors or new oval-trajectory variable-geometry ones. Based on these characteristics, a double-multiple steamtube model was developed. This model includes variable blade-positioning angle β, the trajectory-shape coefficient CF, and the wind orientation angle φ. The new reference frame is the length of the trajectory.
Publisher Summary This chapter discusses the new double-multiple streamtube model that can simula... more Publisher Summary This chapter discusses the new double-multiple streamtube model that can simulate either conventional Darrieus rotors or new oval-trajectory variable-geometry. This capability allows it to treat more general cases and expands the spectrum of analysis for Darrieus turbines design. This model allows the prediction of the aerodynamic performance of noncircular trajectory Darrieus turbines with variable blade-positioning angle. This model was developed to predict the aerodynamic performance of a new-concept turbine whose most remarked characteristics are high number of blades and low rotational speed. The new double-multiple streamtube model can simulate either conventional Darrieus rotors or new oval-trajectory variable-geometry ones. Based on these characteristics, a double-multiple steamtube model was developed. This model includes variable blade-positioning angle β, the trajectory-shape coefficient CF, and the wind orientation angle φ. The new reference frame is the length of the trajectory.
Publisher Summary This chapter presents the numerical experimentation results of a new double-mul... more Publisher Summary This chapter presents the numerical experimentation results of a new double-multiple stream tube model. This model was developed for the aerodynamic analysis of a nonconventional new vertical axis wind turbine. Frequently, in the conventional Darrieus turbines, blades move in a circular trajectory been rigidly related to the central axis by structural elements. The results presented in this chapter belong to different oval-trajectory rotors with a high number of blades. The equivalent power coefficient gives an idea of the efficiency of the wind-mechanical energy conversion, and the trajectory efficiency is a kind of technical economical index. Their results are shown in this chapter for different CF values.
In this work, a receptivity analysis of the boundary layer evolving along a NACA-0012 wing profil... more In this work, a receptivity analysis of the boundary layer evolving along a NACA-0012 wing profile with suction at wall surface is considered. The environmental perturbations that arrive from the free stream and enter the boundary layer, such as acoustic or vortical waves, do not have the correct wave parameters (i.e., the frequency and the wavelength) to excite the instability wave. Thus, a wavemodulation mechanism is needed in order to create the modal instability. The interaction between the external disturbance and the perturbation induced in the boundary layer by suction at the wing surface can activate this mechanism. In the model proposed here, the Navier-Stokes equations that govern the problem are linearized around a basic flow which is determined by the boundary-layer equations. Besides, considering that the boundary layer evolves with two different length scales, the theory of multiple scales is employed to solve the receptivity problem. A solvability condition, given by ...
The stability and the admittance analysis are considered for a Poiseuille flow running over a per... more The stability and the admittance analysis are considered for a Poiseuille flow running over a permeable slab. The case where a suction, due to a cross flow, is present through both the channel and the porous slab is also dealt with. An analytic solution is found for the basic flow in the entire field whereas the stability analysis and the evaluation of the admittance at the interface are numerically carried out. The errors made in the usually simplified analyses are fully discussed.
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