# Source code for fluids.filters

    # -*- coding: utf-8 -*-
    '''Chemical Engineering Design Library (ChEDL). Utilities for process modeling.
    Copyright (C) 2016, Caleb Bell <Caleb.Andrew.Bell@gmail.com>

    Permission is hereby granted, free of charge, to any person obtaining a copy
    of this software and associated documentation files (the "Software"), to deal
    in the Software without restriction, including without limitation the rights
    to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
    copies of the Software, and to permit persons to whom the Software is
    furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be included in all
    copies or substantial portions of the Software.

    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
    AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
    LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
    OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
    SOFTWARE.'''

    from __future__ import division
    from math import radians, cos
    from fluids.numerics import interp, implementation_optimize_tck, splev

    __all__ = ['round_edge_screen', 'round_edge_open_mesh', 'square_edge_screen',
    'square_edge_grill', 'round_edge_grill']

    round_Res = [20.0, 30.0, 40.0, 60.0, 80.0, 100.0, 200.0, 400.0]
    round_betas = [1.3, 1.1, 0.95, 0.83, 0.75, 0.7, 0.6, 0.52]
    '''Quadratic interpolation with no smoothing, constant value extremities
    returned when outside table limits'''

    round_thetas = [0.0, 10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 70.0, 80.0, 85.0]
    round_gammas = [1.0, 0.97, 0.88, 0.75, 0.59, 0.45, 0.3, 0.23, 0.15, 0.09]
    '''Quadratic interpolation with no smoothing, constant value extremities
    returned when outside table limits'''

    '''Quadratic interpolation with no smoothing, constant value extremities
    returned when outside table limits. Last actual value in the original table is
    K=1000 at alpha=0.05; the rest are extrapolated.'''
    square_alphas = [0.0015625, 0.003125, 0.00625, 0.0125, 0.025, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 1.]
    square_Ks = [1024000., 256000, 64000, 16000, 4000, 1000., 250., 85., 52., 30., 17., 11., 7.7, 5.5, 3.8, 2.8, 2, 1.5, 1.1, 0.78, 0.53, 0.35, 0.08, 0.]

    grills_rounded_alphas = [0.3, 0.4, 0.5, 0.6, 0.7]
    grills_rounded_Ks = [2.0, 1.0, 0.6, 0.4, 0.2]
    '''Cubic interpolation with no smoothing, constant value extremities
    returned when outside table limits'''
    grills_rounded_tck = implementation_optimize_tck([[0.3, 0.3, 0.3, 0.45, 0.55, 0.7, 0.7, 0.7],
                                                      [2.0, 1.0014285714285716, 0.5799999999999998,
                                                       0.3585714285714287, 0.2, 0.0, 0.0, 0.0],
                                                       2])

    def round_edge_screen(alpha, Re, angle=0):
        r'''Returns the loss coefficient for a round edged wire screen or bar
        screen, as shown in [1]_. Angle of inclination may be specified as well.

        Parameters
        ----------
        alpha : float
            Fraction of screen open to flow [-]
        Re : float
            Reynolds number of flow through screen with D = space between rods, []
        angle : float, optional
            Angle of inclination, with 0 being straight and 90 being parallel to
            flow [degrees]

        Returns
        -------
        K : float
            Loss coefficient [-]

        Notes
        -----
        Linear interpolation between a table of values. Re table extends
        from 20 to 400, with constant values outside of the table. This behavior
        should be adequate.
        alpha should be between 0.05 and 0.8.
        If angle is over 85 degrees, the value at 85 degrees is used.

        The velocity the loss coefficient relates to is the approach velocity
        before the screen.

        Examples
        --------
        >>> round_edge_screen(0.5, 100)
        2.0999999999999996
        >>> round_edge_screen(0.5, 100, 45)
        1.05

        References
        ----------
        .. [1] Blevins, Robert D. Applied Fluid Dynamics Handbook. New York, N.Y.:
           Van Nostrand Reinhold Co., 1984.
        '''
        beta = interp(Re, round_Res, round_betas)
        alpha2 = alpha*alpha
        K = beta*(1.0 - alpha2)/alpha2
        if angle:
            if angle <= 45:
                K *= cos(radians(angle))**2
            else:
                K *= interp(angle, round_thetas, round_gammas)
        return K

    def round_edge_open_mesh(alpha, subtype='diamond pattern wire', angle=0):
        r'''Returns the loss coefficient for a round edged open net/screen
        made of one of the following patterns, according to [1]_:

        'round bar screen':

        .. math::
            K = 0.95(1-\alpha) + 0.2(1-\alpha)^2

        'diamond pattern wire':

        .. math::
            K = 0.67(1-\alpha) + 1.3(1-\alpha)^2

        'knotted net':

        .. math::
            K = 0.70(1-\alpha) + 4.9(1-\alpha)^2

        'knotless net':

        .. math::
            K = 0.72(1-\alpha) + 2.1(1-\alpha)^2

        Parameters
        ----------
        alpha : float
            Fraction of net/screen open to flow [-]
        subtype : str
            One of 'round bar screen', 'diamond pattern wire', 'knotted net' or
            'knotless net'.
        angle : float, optional
            Angle of inclination, with 0 being straight and 90 being parallel to
            flow [degrees]

        Returns
        -------
        K : float
            Loss coefficient [-]

        Notes
        -----
        `alpha` should be between 0.85 and 1 for these correlations.
        Flow should be turbulent, with Re > 500.

        The velocity the loss coefficient relates to is the approach velocity
        before the mesh.

        Examples
        --------
        >>> round_edge_open_mesh(0.96, angle=33.)
        0.02031327712601458

        References
        ----------
        .. [1] Blevins, Robert D. Applied Fluid Dynamics Handbook. New York, N.Y.:
           Van Nostrand Reinhold Co., 1984.
        '''
        if subtype == 'round bar screen':
            K = 0.95*(1-alpha) + 0.2*(1-alpha)**2
        elif subtype == 'diamond pattern wire':
            K = 0.67*(1-alpha) + 1.3*(1-alpha)**2
        elif subtype == 'knotted net':
            K = 0.70*(1-alpha) + 4.9*(1-alpha)**2
        elif subtype == 'knotless net':
            K = 0.72*(1-alpha) + 2.1*(1-alpha)**2
        else:
            raise Exception('Subtype not recognized')
        if angle:
            if angle < 45:
                K *= cos(radians(angle))**2
            else:
                K *= interp(angle, round_thetas, round_gammas)
        return K

    def square_edge_screen(alpha):
        r'''Returns the loss coefficient for a square wire screen or square bar
        screen or perforated plate with squared edges, as shown in [1]_.

        Parameters
        ----------
        alpha : float
            Fraction of screen open to flow [-]

        Returns
        -------
        K : float
            Loss coefficient [-]

        Notes
        -----
        Linear interpolation between a table of values.
        The velocity the loss coefficient relates to is the approach velocity
        before the screen.

        Examples
        --------
        >>> square_edge_screen(0.99)
        0.008000000000000007

        References
        ----------
        .. [1] Blevins, Robert D. Applied Fluid Dynamics Handbook. New York, N.Y.:
           Van Nostrand Reinhold Co., 1984.
        '''
        return interp(alpha, square_alphas, square_Ks)

    def square_edge_grill(alpha, l=None, Dh=None, fd=None):
        r'''Returns the loss coefficient for a square grill or square bar
        screen or perforated plate with squared edges of thickness l, as shown in
        [1]_.

        for Dh < l < 50D

        .. math::
            K = \frac{0.5(1-\alpha) + (1-\alpha^2)}{\alpha^2}

        else:

        .. math::
            K = \frac{0.5(1-\alpha) + (1-\alpha^2) + f{l}/D}{\alpha^2}

        Parameters
        ----------
        alpha : float
            Fraction of grill open to flow [-]
        l : float, optional
            Thickness of the grill or plate [m]
        Dh : float, optional
            Hydraulic diameter of gap in grill, [m]
        fd : float, optional
            Darcy friction factor [-]

        Returns
        -------
        K : float
            Loss coefficient [-]

        Notes
        -----
        If l, Dh, or fd is not provided, the first expression is used instead.
        The alteration of the expression to include friction factor is there
        if the grill is long enough to have considerable friction along the
        surface of the grill.

        The velocity the loss coefficient relates to is the approach velocity
        before the grill.

        Examples
        --------
        >>> square_edge_grill(.45)
        5.296296296296296
        >>> square_edge_grill(.45, l=.15, Dh=.002, fd=.0185)
        12.148148148148147

        References
        ----------
        .. [1] Blevins, Robert D. Applied Fluid Dynamics Handbook. New York, N.Y.:
           Van Nostrand Reinhold Co., 1984.
        '''
        if Dh and l and fd and l > 50*Dh:
            return (0.5*(1-alpha) + (1-alpha**2) + fd*l/Dh)/alpha**2
        else:
            return (0.5*(1-alpha) + (1-alpha**2))/alpha**2

    def round_edge_grill(alpha, l=None, Dh=None, fd=None):
        r'''Returns the loss coefficient for a rounded square grill or square bar
        screen or perforated plate with rounded edges of thickness l, as shown in
        [1]_.

        for Dh < l < 50D

        .. math::
            K = lookup(alpha)

        else:

        .. math::
            K = lookup(alpha) + \frac{fl}{\alpha^2D}

        Parameters
        ----------
        alpha : float
            Fraction of grill open to flow [-]
        l : float, optional
            Thickness of the grill or plate [m]
        Dh : float, optional
            Hydraulic diameter of gap in grill, [m]
        fd : float, optional
            Darcy friction factor [-]

        Returns
        -------
        K : float
            Loss coefficient [-]

        Notes
        -----
        If l, Dh, or fd is not provided, the first expression is used instead.
        The alteration of the expression to include friction factor is there
        if the grill is long enough to have considerable friction along the
        surface of the grill.
        alpha must be between 0.3 and 0.7.

        The velocity the loss coefficient relates to is the approach velocity
        before the grill.

        Examples
        --------
        >>> round_edge_grill(.4)
        1.0
        >>> round_edge_grill(.4, l=.15, Dh=.002, fd=.0185)
        2.3874999999999997

        References
        ----------
        .. [1] Blevins, Robert D. Applied Fluid Dynamics Handbook. New York, N.Y.:
           Van Nostrand Reinhold Co., 1984.
        '''
        t1 = float(splev(alpha, grills_rounded_tck))
        if Dh and l and fd and l > 50*Dh:
            return t1 + fd*l/Dh
        else:
            return t1