Пример #1
0
def h_Briggs_Young(m, A, A_min, A_increase, A_fin, A_tube_showing,
                   tube_diameter, fin_diameter, fin_thickness, bare_length,
                   rho, Cp, mu, k, k_fin):
    r'''Calculates the air side heat transfer coefficient for an air cooler
    or other finned tube bundle with the formulas of Briggs and Young [1], [2]_
    [3]_.
    
    .. math::
        Nu = 0.134Re^{0.681} Pr^{0.33}\left(\frac{S}{h}\right)^{0.2}
        \left(\frac{S}{b}\right)^{0.1134}
        
    Parameters
    ----------
    m : float
        Mass flow rate of air across the tube bank, [kg/s]
    A : float
        Surface area of combined finned and non-finned area exposed for heat
        transfer, [m^2]
    A_min : float
        Minimum air flow area, [m^2]
    A_increase : float
        Ratio of actual surface area to bare tube surface area
        :math:`A_{increase} = \frac{A_{tube}}{A_{bare, total/tube}}`, [-]
    A_fin : float
        Surface area of all fins in the bundle, [m^2]
    A_tube_showing : float
        Area of the bare tube which is exposed in the bundle, [m^2]
    tube_diameter : float
        Diameter of the bare tube, [m]
    fin_diameter : float
        Outer diameter of each tube after including the fin on both sides,
        [m]
    fin_thickness : float
        Thickness of the fins, [m]
    bare_length : float
        Length of bare tube between two fins 
        :math:`\text{bare length} = \text{fin interval} - t_{fin}`, [m]
    rho : float
        Average (bulk) density of air across the tube bank, [kg/m^3]
    Cp : float
        Average (bulk) heat capacity of air across the tube bank, [J/kg/K]
    mu : float
        Average (bulk) viscosity of air across the tube bank, [Pa*s]
    k : float
        Average (bulk) thermal conductivity of air across the tube bank, 
        [W/m/K]
    k_fin : float
        Thermal conductivity of the fin, [W/m/K]
        
    Returns
    -------
    h_bare_tube_basis : float
        Air side heat transfer coefficient on a bare-tube surface area as if 
        there were no fins present basis, [W/K/m^2]

    Notes
    -----
    The limits on this equation are :math:`1000 < Re < `8000`, 
    11.13 mm :math:`< D_o < ` 40.89 mm, 1.42 mm < fin height < 16.57 mm,
    0.33 mm < fin thickness < 2.02 mm, 1.30 mm < fin pitch < 4.06 mm, and 
    24.49 mm < normal pitch < 111 mm.
    
    Examples
    --------
    >>> AC = AirCooledExchanger(tube_rows=4, tube_passes=4, tubes_per_row=20, tube_length=3, 
    ... tube_diameter=1*inch, fin_thickness=0.000406, fin_density=1/0.002309,
    ... pitch_normal=.06033, pitch_parallel=.05207,
    ... fin_height=0.0159, tube_thickness=(.0254-.0186)/2,
    ... bundles_per_bay=1, parallel_bays=1, corbels=True)
    
    >>> h_Briggs_Young(m=21.56, A=AC.A, A_min=AC.A_min, A_increase=AC.A_increase, A_fin=AC.A_fin,
    ... A_tube_showing=AC.A_tube_showing, tube_diameter=AC.tube_diameter,
    ... fin_diameter=AC.fin_diameter, bare_length=AC.bare_length,
    ... fin_thickness=AC.fin_thickness,
    ... rho=1.161, Cp=1007., mu=1.85E-5, k=0.0263, k_fin=205)
    1422.8722403237716

    References
    ----------
    .. [1] Briggs, D.E., and Young, E.H., 1963, "Convection Heat Transfer and
       Pressure Drop of Air Flowing across Triangular Banks of Finned Tubes",
       Chemical Engineering Progress Symp., Series 41, No. 59. Chem. Eng. Prog.
       Symp. Series No. 41, "Heat Transfer - Houston".
    .. [2] Mukherjee, R., and Geoffrey Hewitt. Practical Thermal Design of 
       Air-Cooled Heat Exchangers. New York: Begell House Publishers Inc.,U.S.,
       2007.
    .. [3] Kroger, Detlev. Air-Cooled Heat Exchangers and Cooling Towers: 
       Thermal-Flow Performance Evaluation and Design, Vol. 1. Tulsa, Okl:
       PennWell Corp., 2004.
    '''
    fin_height = 0.5 * (fin_diameter - tube_diameter)

    V_max = m / (A_min * rho)

    Re = Reynolds(V=V_max, D=tube_diameter, rho=rho, mu=mu)
    Pr = Prandtl(Cp=Cp, mu=mu, k=k)

    Nu = 0.134 * Re**0.681 * Pr**(1 / 3.) * (bare_length / fin_height)**0.2 * (
        bare_length / fin_thickness)**0.1134

    h = k / tube_diameter * Nu
    efficiency = fin_efficiency_Kern_Kraus(Do=tube_diameter,
                                           D_fin=fin_diameter,
                                           t_fin=fin_thickness,
                                           k_fin=k_fin,
                                           h=h)
    h_total_area_basis = (efficiency * A_fin + A_tube_showing) / A * h
    h_bare_tube_basis = h_total_area_basis * A_increase

    return h_bare_tube_basis
Пример #2
0
def h_ESDU_high_fin(m,
                    A,
                    A_min,
                    A_increase,
                    A_fin,
                    A_tube_showing,
                    tube_diameter,
                    fin_diameter,
                    fin_thickness,
                    bare_length,
                    pitch_parallel,
                    pitch_normal,
                    tube_rows,
                    rho,
                    Cp,
                    mu,
                    k,
                    k_fin,
                    Pr_wall=None):
    r'''Calculates the air side heat transfer coefficient for an air cooler
    or other finned tube bundle with the formulas of [2]_ as presented in [1]_.

    .. math::
        Nu = 0.242 Re^{0.658} \left(\frac{\text{bare length}}
        {\text{fin height}}\right)^{0.297}
        \left(\frac{P_1}{P_2}\right)^{-0.091} P_r^{1/3}\cdot F_1\cdot F_2
                
    .. math::
        h_{A,total} = \frac{\eta A_{fin} + A_{bare, showing}}{A_{total}} h
        
    .. math::
        h_{bare,total} = A_{increase} h_{A,total}

    Parameters
    ----------
    m : float
        Mass flow rate of air across the tube bank, [kg/s]
    A : float
        Surface area of combined finned and non-finned area exposed for heat
        transfer, [m^2]
    A_min : float
        Minimum air flow area, [m^2]
    A_increase : float
        Ratio of actual surface area to bare tube surface area
        :math:`A_{increase} = \frac{A_{tube}}{A_{bare, total/tube}}`, [-]
    A_fin : float
        Surface area of all fins in the bundle, [m^2]
    A_tube_showing : float
        Area of the bare tube which is exposed in the bundle, [m^2]
    tube_diameter : float
        Diameter of the bare tube, [m]
    fin_diameter : float
        Outer diameter of each tube after including the fin on both sides,
        [m]
    fin_thickness : float
        Thickness of the fins, [m]
    bare_length : float
        Length of bare tube between two fins 
        :math:`\text{bare length} = \text{fin interval} - t_{fin}`, [m]
    pitch_parallel : float
        Distance between tube center along a line parallel to the flow;
        has been called `longitudinal` pitch, `pp`, `s2`, `SL`, and `p2`, [m]
    pitch_normal : float
        Distance between tube centers in a line 90° to the line of flow;
        has been called the `transverse` pitch, `pn`, `s1`, `ST`, and `p1`, [m]
    tube_rows : int
        Number of tube rows per bundle, [-]
    rho : float
        Average (bulk) density of air across the tube bank, [kg/m^3]
    Cp : float
        Average (bulk) heat capacity of air across the tube bank, [J/kg/K]
    mu : float
        Average (bulk) viscosity of air across the tube bank, [Pa*s]
    k : float
        Average (bulk) thermal conductivity of air across the tube bank, 
        [W/m/K]
    k_fin : float
        Thermal conductivity of the fin, [W/m/K]
    Pr_wall : float, optional
        Prandtl number at the wall temperature; provide if a correction with  
        the defaults parameters is desired; otherwise apply the correction
        elsewhere, [-]

    Returns
    -------
    h_bare_tube_basis : float
        Air side heat transfer coefficient on a bare-tube surface area as if 
        there were no fins present basis, [W/K/m^2]

    Notes
    -----
    The tube-row count correction factor is 1 for four or more rows, 0.92 for
    three rows, 0.84 for two rows, and 0.76 for one row according to [1]_.
    
    The property correction factor can be disabled by not specifying
    `Pr_wall`. A Prandtl number exponent of 0.26 is recommended in [1]_ for 
    heating and cooling for both liquids and gases.
    
    Examples
    --------
    >>> AC = AirCooledExchanger(tube_rows=4, tube_passes=4, tubes_per_row=20, tube_length=3, 
    ... tube_diameter=1*inch, fin_thickness=0.000406, fin_density=1/0.002309,
    ... pitch_normal=.06033, pitch_parallel=.05207,
    ... fin_height=0.0159, tube_thickness=(.0254-.0186)/2,
    ... bundles_per_bay=1, parallel_bays=1, corbels=True)
    
    >>> h_ESDU_high_fin(m=21.56, A=AC.A, A_min=AC.A_min, A_increase=AC.A_increase, A_fin=AC.A_fin,
    ... A_tube_showing=AC.A_tube_showing, tube_diameter=AC.tube_diameter,
    ... fin_diameter=AC.fin_diameter, bare_length=AC.bare_length,
    ... fin_thickness=AC.fin_thickness, tube_rows=AC.tube_rows,
    ... pitch_normal=AC.pitch_normal, pitch_parallel=AC.pitch_parallel, 
    ... rho=1.161, Cp=1007., mu=1.85E-5, k=0.0263, k_fin=205)
    1390.888918049757

    References
    ----------
    .. [1] Hewitt, G. L. Shires, T. Reg Bott G. F., George L. Shires, and T.
       R. Bott. Process Heat Transfer. 1st edition. Boca Raton: CRC Press, 
       1994.
    .. [2] "High-Fin Staggered Tube Banks: Heat Transfer and Pressure Drop for
       Turbulent Single Phase Gas Flow." ESDU 86022 (October 1, 1986). 
    .. [3] Rabas, T. J., and J. Taborek. "Survey of Turbulent Forced-Convection
       Heat Transfer and Pressure Drop Characteristics of Low-Finned Tube Banks
       in Cross Flow."  Heat Transfer Engineering 8, no. 2 (January 1987): 
       49-62.
    '''
    fin_height = 0.5 * (fin_diameter - tube_diameter)

    V_max = m / (A_min * rho)
    Re = Reynolds(V=V_max, D=tube_diameter, rho=rho, mu=mu)
    Pr = Prandtl(Cp=Cp, mu=mu, k=k)
    Nu = 0.242 * Re**0.658 * (bare_length / fin_height)**0.297 * (
        pitch_normal / pitch_parallel)**-0.091 * Pr**(1 / 3.)

    if tube_rows < 2:
        F2 = 0.76
    elif tube_rows < 3:
        F2 = 0.84
    elif tube_rows < 4:
        F2 = 0.92
    else:
        F2 = 1.0

    Nu *= F2
    if Pr_wall is not None:
        F1 = wall_factor(Pr=Pr,
                         Pr_wall=Pr_wall,
                         Pr_heating_coeff=0.26,
                         Pr_cooling_coeff=0.26,
                         property_option=WALL_FACTOR_PRANDTL)
        Nu *= F1

    h = k / tube_diameter * Nu
    efficiency = fin_efficiency_Kern_Kraus(Do=tube_diameter,
                                           D_fin=fin_diameter,
                                           t_fin=fin_thickness,
                                           k_fin=k_fin,
                                           h=h)

    h_total_area_basis = (efficiency * A_fin + A_tube_showing) / A * h
    h_bare_tube_basis = h_total_area_basis * A_increase
    return h_bare_tube_basis
Пример #3
0
def h_boiling_Huang_Sheer(rhol,
                          rhog,
                          mul,
                          kl,
                          Hvap,
                          sigma,
                          Cpl,
                          q,
                          Tsat,
                          angle=35.):
    r'''Calculates the two-phase boiling heat transfer coefficient of a
    liquid and gas flowing inside a plate and frame heat exchanger, as
    developed in [1]_ and again in the thesis [2]_. Depends on the properties
    of the fluid and not the heat exchanger's geometry.

    .. math::
        h = 1.87\times10^{-3}\left(\frac{k_l}{d_o}\right)\left(\frac{q d_o}
        {k_l T_{sat}}\right)^{0.56}
        \left(\frac{H_{vap} d_o^2}{\alpha_l^2}\right)^{0.31} Pr_l^{0.33}

    .. math::
        d_o = 0.0146\theta\left[\frac{2\sigma}{g(\rho_l-\rho_g)}\right]^{0.5}\\
        \theta =  35^\circ

    Note that this model depends on the specific heat flux involved and
    the saturation temperature of the fluid.

    Parameters
    ----------
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]
    mul : float
        Viscosity of the liquid [Pa*s]
    kl : float
        Thermal conductivity of liquid [W/m/K]
    Hvap : float
        Heat of vaporization of the fluid at the system pressure, [J/kg]
    sigma : float
        Surface tension of liquid [N/m]
    Cpl : float
        Heat capacity of liquid [J/kg/K]
    q : float
        Heat flux, [W/m^2]
    Tsat : float
        Actual saturation temperature of the fluid at the system pressure, [K]
    angle : float, optional
        Contact angle of the bubbles with the wall, assumed 35 for refrigerants
        in the development of the correlation [degrees]

    Returns
    -------
    h : float
        Boiling heat transfer coefficient [W/m^2/K]

    Notes
    -----
    Developed with 222 data points for R134a and R507A with only two of them
    for ammonia and R12. Chevron angles ranged from 28 to 60 degrees, heat
    fluxes from 1.85 kW/m^2 to 10.75 kW/m^2, mass fluxes 5.6 to 52.25 kg/m^2/s,
    qualities from 0.21 to 0.95, and saturation temperatures in degrees Celcius
    of 1.9 to 13.04.

    The inclusion of the saturation temperature makes this correlation have
    limited predictive power for other fluids whose saturation tempratures
    might be much higher or lower than those used in the development of the
    correlation. For this reason it should be regarded with caution.

    As first published in [1]_ a power of two was missing in the correlation
    for bubble diameter in the dimensionless group with a power of 0.31. That
    made the correlation non-dimensional.

    A second variant of this correlation was also published in [2]_ but with
    less accuracy because it was designed to mimick the standard pool boiling
    curve.

    The correlation is reviewed in [3]_, but without the corrected power. It
    was also changed there to use hydraulic diameter, not bubble diameter.
    It still ranked as one of the more accurate correlations reviewed.
    [4]_ also reviewed it without the corrected power but found it predicted
    the lowest results of those surveyed.

    Examples
    --------
    >>> h_boiling_Huang_Sheer(rhol=567., rhog=18.09, kl=0.086, mul=156E-6,
    ... Hvap=9E5, sigma=0.02, Cpl=2200, q=1E4, Tsat=279.15)
    4401.055635078054

    References
    ----------
    .. [1] Huang, Jianchang, Thomas J. Sheer, and Michael Bailey-McEwan. "Heat
       Transfer and Pressure Drop in Plate Heat Exchanger Refrigerant
       Evaporators." International Journal of Refrigeration 35, no. 2 (March
       2012): 325-35. doi:10.1016/j.ijrefrig.2011.11.002.
    .. [2] Huang, Jianchang. "Performance Analysis of Plate Heat Exchangers
       Used as Refrigerant Evaporators," 2011. Thesis.
       http://wiredspace.wits.ac.za/handle/10539/9779
    .. [3] Amalfi, Raffaele L., Farzad Vakili-Farahani, and John R. Thome.
       "Flow Boiling and Frictional Pressure Gradients in Plate Heat Exchangers.
       Part 1: Review and Experimental Database." International Journal of
       Refrigeration 61 (January 2016): 166-84.
       doi:10.1016/j.ijrefrig.2015.07.010.
    .. [4] Eldeeb, Radia, Vikrant Aute, and Reinhard Radermacher. "A Survey of
       Correlations for Heat Transfer and Pressure Drop for Evaporation and
       Condensation in Plate Heat Exchangers." International Journal of
       Refrigeration 65 (May 2016): 12-26. doi:10.1016/j.ijrefrig.2015.11.013.
    '''
    do = 0.0146 * angle * (2. * sigma / (g * (rhol - rhog)))**0.5
    Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
    alpha_l = thermal_diffusivity(k=kl, rho=rhol, Cp=Cpl)
    h = 1.87E-3 * (kl / do) * (q * do / (kl * Tsat))**0.56 * (
        Hvap * do**2 / alpha_l**2)**0.31 * Prl**0.33
    return h
Пример #4
0
def h_boiling_Yan_Lin(m, x, Dh, rhol, rhog, mul, kl, Hvap, Cpl, q,
                      A_channel_flow):
    r'''Calculates the two-phase boiling heat transfer coefficient of a
    liquid and gas flowing inside a plate and frame heat exchanger, as
    developed in [1]_. Reviewed in [2]_, [3]_, [4]_, and [5]_.

    .. math::
        h = 1.926\left(\frac{k_l}{D_h}\right) Re_{eq} Pr_l^{1/3} Bo_{eq}^{0.3}
        Re^{-0.5}

    .. math::
        Re_{eq} = \frac{G_{eq} D_h}{\mu_l}

    .. math::
        Bo_{eq} = \frac{q}{G_{eq} H_{vap}}

    .. math::
        G_{eq} = \frac{m}{A_{flow}}\left[1 - x + x\left(\frac{\rho_l}{\rho_g}
        \right)^{1/2}\right]

    .. math::
        Re = \frac{G D_h}{\mu_l}

    Claimed to be valid for :math:`2000 < Re_{eq} < 10000`.

    Parameters
    ----------
    m : float
        Mass flow rate [kg/s]
    x : float
        Quality at the specific point in the plate exchanger []
    Dh : float
        Hydraulic diameter of the plate, :math:`D_h = \frac{4\lambda}{\phi}` [m]
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]
    mul : float
        Viscosity of the liquid [Pa*s]
    kl : float
        Thermal conductivity of liquid [W/m/K]
    Hvap : float
        Heat of vaporization of the fluid at the system pressure, [J/kg]
    Cpl : float
        Heat capacity of liquid [J/kg/K]
    q : float
        Heat flux, [W/m^2]
    A_channel_flow : float
        The flow area for the fluid, calculated as
        :math:`A_{ch} = 2\cdot \text{width} \cdot \text{amplitude}` [m]

    Returns
    -------
    h : float
        Boiling heat transfer coefficient [W/m^2/K]

    Notes
    -----
    Developed with R134a as the refrigerant in a PHD with 2 channels, chevron
    angle 60 degrees, quality from 0.1 to 0.8, heat flux 11-15 kW/m^2, and mass
    fluxes of 55 and 70 kg/m^2/s.

    Examples
    --------
    >>> h_boiling_Yan_Lin(m=3E-5, x=.4, Dh=0.002, rhol=567., rhog=18.09,
    ... kl=0.086, Cpl=2200, mul=156E-6, Hvap=9E5, q=1E5, A_channel_flow=0.0003)
    318.7228565961241

    References
    ----------
    .. [1] Yan, Y.-Y., and T.-F. Lin. "Evaporation Heat Transfer and Pressure
       Drop of Refrigerant R-134a in a Plate Heat Exchanger." Journal of Heat
       Transfer 121, no. 1 (February 1, 1999): 118-27. doi:10.1115/1.2825924.
    .. [2] Amalfi, Raffaele L., Farzad Vakili-Farahani, and John R. Thome.
       "Flow Boiling and Frictional Pressure Gradients in Plate Heat Exchangers.
       Part 1: Review and Experimental Database." International Journal of
       Refrigeration 61 (January 2016): 166-84.
       doi:10.1016/j.ijrefrig.2015.07.010.
    .. [3] Eldeeb, Radia, Vikrant Aute, and Reinhard Radermacher. "A Survey of
       Correlations for Heat Transfer and Pressure Drop for Evaporation and
       Condensation in Plate Heat Exchangers." International Journal of
       Refrigeration 65 (May 2016): 12-26. doi:10.1016/j.ijrefrig.2015.11.013.
    .. [4] García-Cascales, J. R., F. Vera-García, J. M. Corberán-Salvador, and
       J. Gonzálvez-Maciá. "Assessment of Boiling and Condensation Heat
       Transfer Correlations in the Modelling of Plate Heat Exchangers."
       International Journal of Refrigeration 30, no. 6 (September 2007):
       1029-41. doi:10.1016/j.ijrefrig.2007.01.004.
    .. [5] Huang, Jianchang. "Performance Analysis of Plate Heat Exchangers
       Used as Refrigerant Evaporators," 2011. Thesis.
       http://wiredspace.wits.ac.za/handle/10539/9779
    '''
    G = m / A_channel_flow
    G_eq = G * ((1. - x) + x * (rhol / rhog)**0.5)
    Re_eq = G_eq * Dh / mul
    Re = G * Dh / mul  #  Not actually specified clearly but it is in another paper by them
    Bo_eq = q / (G_eq * Hvap)
    Pr_l = Prandtl(Cp=Cpl, k=kl, mu=mul)
    return 1.926 * (kl / Dh) * Re_eq * Pr_l**(1 / 3.) * Bo_eq**0.3 * Re**-0.5
Пример #5
0
def Chen_Bennett(m, x, D, rhol, rhog, mul, mug, kl, Cpl, Hvap, sigma,
                   dPsat, Te):
    r'''Calculates heat transfer coefficient for film boiling of saturated
    fluid in any orientation of flow. Correlation
    is developed in [1]_ and [2]_, and reviewed in [3]_. This model is one of
    the most often used, and replaces the `Chen_Edelstein` correlation. It uses
    the Dittus-Boelter correlation for turbulent convection and the
    Forster-Zuber correlation for pool boiling, and combines them with two
    factors `F` and `S`.

    .. math::
        h_{tp} = S\cdot h_{nb} + F \cdot h_{sp,l}

    .. math::
       h_{sp,l} = 0.023 Re_l^{0.8} Pr_l^{0.4} k_l/D

    .. math::
       Re_l = \frac{DG(1-x)}{\mu_l}

    .. math::
       h_{nb} = 0.00122\left( \frac{\lambda_l^{0.79} c_{p,l}^{0.45}
        \rho_l^{0.49}}{\sigma^{0.5} \mu^{0.29} H_{vap}^{0.24} \rho_g^{0.24}}
        \right)\Delta T_{sat}^{0.24} \Delta p_{sat}^{0.75}

    .. math::
       F = \left(\frac{Pr_1+1}{2}\right)^{0.444}\cdot (1+X_{tt}^{-0.5})^{1.78}

    .. math::
       S = \frac{1-\exp(-F\cdot h_{conv} \cdot X_0/k_l)}
        {F\cdot h_{conv}\cdot X_0/k_l}

    .. math::
       X_{tt} = \left( \frac{1-x}{x}\right)^{0.9} \left(\frac{\rho_g}{\rho_l}
        \right)^{0.5}\left( \frac{\mu_l}{\mu_g}\right)^{0.1}

    .. math::
       X_0 = 0.041 \left(\frac{\sigma}{g \cdot (\rho_l-\rho_v)}\right)^{0.5}

    Parameters
    ----------
    m : float
        Mass flow rate [kg/s]
    x : float
        Quality at the specific tube interval []
    D : float
        Diameter of the tube [m]
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]
    mul : float
        Viscosity of liquid [Pa*s]
    mug : float
        Viscosity of gas [Pa*s]
    kl : float
        Thermal conductivity of liquid [W/m/K]
    Cpl : float
        Heat capacity of liquid [J/kg/K]
    Hvap : float
        Heat of vaporization of liquid [J/kg]
    sigma : float
        Surface tension of liquid [N/m]
    dPsat : float
        Difference in Saturation pressure of fluid at Te and T, [Pa]
    Te : float
        Excess temperature of wall, [K]

    Returns
    -------
    h : float
        Heat transfer coefficient [W/m^2/K]

    Notes
    -----
    [1]_ and [2]_ have been reviewed, but the model is only put together in
    the review of [3]_. Many other forms of this equation exist with different
    functions for `F` and `S`.

    Examples
    --------
    >>> Chen_Bennett(m=0.106, x=0.2, D=0.0212, rhol=567, rhog=18.09,
    ... mul=156E-6, mug=7.11E-6, kl=0.086, Cpl=2730, Hvap=2E5, sigma=0.02,
    ... dPsat=1E5, Te=3)
    4938.275351219369

    See Also
    --------
    Chen_Edelstein
    turbulent_Dittus_Boelter
    Forster_Zuber

    References
    ----------
    .. [1] Bennett, Douglas L., and John C. Chen. "Forced Convective Boiling in
       Vertical Tubes for Saturated Pure Components and Binary Mixtures."
       AIChE Journal 26, no. 3 (May 1, 1980): 454-61. doi:10.1002/aic.690260317.
    .. [2] Bennett, Douglas L., M.W. Davies and B.L. Hertzler, The Suppression
       of Saturated Nucleate Boiling by Forced Convective Flow, American
       Institute of Chemical Engineers Symposium Series, vol. 76, no. 199.
       91-103, 1980.
    .. [3] Bertsch, Stefan S., Eckhard A. Groll, and Suresh V. Garimella.
       "Review and Comparative Analysis of Studies on Saturated Flow Boiling in
       Small Channels." Nanoscale and Microscale Thermophysical Engineering 12,
       no. 3 (September 4, 2008): 187-227. doi:10.1080/15567260802317357.
    '''
    G = m/(pi/4*D**2)
    Rel = D*G*(1-x)/mul
    Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
    hl = turbulent_Dittus_Boelter(Re=Rel, Pr=Prl)*kl/D
    Xtt = Lockhart_Martinelli_Xtt(x=x, rhol=rhol, rhog=rhog, mul=mul, mug=mug)
    F = ((Prl+1)/2.)**0.444*(1 + Xtt**-0.5)**1.78
    X0 = 0.041*(sigma/(g*(rhol-rhog)))**0.5
    S = (1 - exp(-F*hl*X0/kl))/(F*hl*X0/kl)

    hnb = Forster_Zuber(Te=Te, dPsat=dPsat, Cpl=Cpl, kl=kl, mul=mul, sigma=sigma,
                       Hvap=Hvap, rhol=rhol, rhog=rhog)
    return hnb*S + hl*F
Пример #6
0
def Shah(m, x, D, rhol, mul, kl, Cpl, P, Pc):
    r'''Calculates heat transfer coefficient for condensation
    of a fluid inside a tube, as presented in [1]_ and again by the same
    author in [2]_; also given in [3]_. Requires no properties of the gas.
    Uses the Dittus-Boelter correlation for single phase heat transfer
    coefficient, with a Reynolds number assuming all the flow is liquid.

    .. math::
        h_{TP} = h_L\left[(1-x)^{0.8} +\frac{3.8x^{0.76}(1-x)^{0.04}}
        {P_r^{0.38}}\right]

    Parameters
    ----------
    m : float
        Mass flow rate [kg/s]
    x : float
        Quality at the specific interval [-]
    D : float
        Diameter of the channel [m]
    rhol : float
        Density of the liquid [kg/m^3]
    mul : float
        Viscosity of liquid [Pa*s]
    kl : float
        Thermal conductivity of liquid [W/m/K]
    Cpl : float
        Constant-pressure heat capacity of liquid [J/kg/K]
    P : float
        Pressure of the fluid, [Pa]
    Pc : float
        Critical pressure of the fluid, [Pa]

    Returns
    -------
    h : float
        Heat transfer coefficient [W/m^2/K]

    Notes
    -----
    [1]_ is well written an unambiguous as to how to apply this equation.

    Examples
    --------
    >>> Shah(m=1, x=0.4, D=.3, rhol=800, mul=1E-5, kl=0.6, Cpl=2300, P=1E6, Pc=2E7)
    2561.2593415479214

    References
    ----------
    .. [1] Shah, M. M. "A General Correlation for Heat Transfer during Film
       Condensation inside Pipes." International Journal of Heat and Mass
       Transfer 22, no. 4 (April 1, 1979): 547-56.
       doi:10.1016/0017-9310(79)90058-9.
    .. [2] Shah, M. M., Heat Transfer During Film Condensation in Tubes and
       Annuli: A Review of the Literature, ASHRAE Transactions, vol. 87, no.
       3, pp. 1086-1100, 1981.
    .. [3] Kakaç, Sadik, ed. Boilers, Evaporators, and Condensers. 1st.
       Wiley-Interscience, 1991.
    '''
    VL = m / (rhol * pi / 4 * D**2)
    ReL = Reynolds(V=VL, D=D, rho=rhol, mu=mul)
    Prl = Prandtl(Cp=Cpl, k=kl, mu=mul)
    hL = turbulent_Dittus_Boelter(ReL, Prl) * kl / D
    Pr = P / Pc
    return hL * ((1 - x)**0.8 + 3.8 * x**0.76 * (1 - x)**0.04 / Pr**0.38)
Пример #7
0
def Ravipudi_Godbold(m, x, D, rhol, rhog, Cpl, kl, mug, mu_b, mu_w=None):
    r'''Calculates the two-phase non-boiling heat transfer coefficient of a
    liquid and gas flowing inside a tube of any inclination, as in [1]_ and
    reviewed in [2]_.

    .. math::
        Nu = \frac{h_{TP} D}{k_l} = 0.56 \left(\frac{V_{gs}}{V_{ls}}
        \right)^{0.3}\left(\frac{\mu_g}{\mu_l}\right)^{0.2} Re_{ls}^{0.6}
        Pr_l^{1/3}\left(\frac{\mu_b}{\mu_w}\right)^{0.14}

    Parameters
    ----------
    m : float
        Mass flow rate [kg/s]
    x : float
        Quality at the specific tube interval [-]
    D : float
        Diameter of the tube [m]
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]
    Cpl : float
        Constant-pressure heat capacity of liquid [J/kg/K]
    kl : float
        Thermal conductivity of liquid [W/m/K]
    mug : float
        Viscosity of gas [Pa*s]
    mu_b : float
        Viscosity of liquid at bulk conditions (average of inlet/outlet
        temperature) [Pa*s]
    mu_w : float, optional
        Viscosity of liquid at wall temperature [Pa*s]

    Returns
    -------
    h : float
        Heat transfer coefficient [W/m^2/K]

    Notes
    -----
    If the viscosity at the wall temperature is not given, the liquid viscosity
    correction is not applied.

    Developed with a vertical pipe, superficial gas/liquid velocity ratios of
    1-90, in the froth regime, and for fluid mixtures of air and water,
    toluene, benzene, and methanol.

    Examples
    --------
    >>> Ravipudi_Godbold(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6, mug=1E-5, mu_b=1E-3, mu_w=1.2E-3)
    299.3796286459285

    References
    ----------
    .. [1] Ravipudi, S., and Godbold, T., The Effect of Mass Transfer on Heat
       Transfer Rates for Two-Phase Flow in a Vertical Pipe, Proceedings 6th
       International Heat Transfer Conference, Toronto, V. 1, p. 505-510, 1978.
    .. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
       Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
       Seven Sets of Experimental Data, Including Flow Pattern and Tube
       Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
       1999): 15-40. doi:10.1080/014576399271691.
    '''
    Vgs = m*x/(rhog*pi/4*D**2)
    Vls = m*(1-x)/(rhol*pi/4*D**2)
    Prl = Prandtl(Cp=Cpl, mu=mu_b, k=kl)
    Rels = D*Vls*rhol/mu_b
    Nu = 0.56*(Vgs/Vls)**0.3*(mug/mu_b)**0.2*Rels**0.6*Prl**(1/3.)
    if mu_w is not None:
        Nu *= (mu_b/mu_w)**0.14
    return Nu*kl/D
Пример #8
0
def Thome(m, x, D, rhol, rhog, mul, mug, kl, kg, Cpl, Cpg, Hvap, sigma, Psat,
          Pc, q=None, Te=None):
    r'''Calculates heat transfer coefficient for film boiling of saturated
    fluid in any orientation of flow. Correlation
    is as developed in [1]_ and [2]_, and also reviewed [3]_. This is a
    complicated model, but expected to have more accuracy as a result.

    Either the heat flux or excess temperature is required for the calculation
    of heat transfer coefficient. The solution for a specified excess
    temperature is solved numerically, making it slow.

    .. math::
        h(z) = \frac{t_l}{\tau} h_l(z) +\frac{t_{film}}{\tau} h_{film}(z)
        +  \frac{t_{dry}}{\tau} h_{g}(z)

    .. math::
        h_{l/g}(z) = (Nu_{lam}^4 + Nu_{trans}^4)^{1/4} k/D

    .. math::
        Nu_{laminar} = 0.91 {Pr}^{1/3} \sqrt{ReD/L(z)}

    .. math::
        Nu_{trans} = \frac{ (f/8) (Re-1000)Pr}{1+12.7 (f/8)^{1/2} (Pr^{2/3}-1)}
        \left[ 1 + \left( \frac{D}{L(z)}\right)^{2/3}\right]

    .. math::
        f = (1.82 \log_{10} Re - 1.64 )^{-2}

    .. math::
        L_l = \frac{\tau G_{tp}}{\rho_l}(1-x)

    .. math::
        L_{dry} = v_p t_{dry}

    .. math::
        t_l = \frac{\tau}{1 + \frac{\rho_l}{\rho_g}\frac{x}{1-x}}

    .. math::
        t_v = \frac{\tau}{1 + \frac{\rho_g}{\rho_l}\frac{1-x}{x}}

    .. math::
        \tau = \frac{1}{f_{opt}}

    .. math::
        f_{opt} = \left(\frac{q}{q_{ref}}\right)^{n_f}

    .. math::
        q_{ref} = 3328\left(\frac{P_{sat}}{P_c}\right)^{-0.5}

    .. math::
        t_{dry,film} = \frac{\rho_l \Delta H_{vap}}{q}[\delta_0(z) -
        \delta_{min}]

    .. math::
        \frac{\delta_0}{D} = C_{\delta 0}\left(3\sqrt{\frac{\nu_l}{v_p D}}
        \right)^{0.84}\left[(0.07Bo^{0.41})^{-8} + 0.1^{-8}\right]^{-1/8}

    .. math::
        Bo = \frac{\rho_l D}{\sigma} v_p^2

    .. math::
        v_p = G_{tp} \left[\frac{x}{\rho_g} + \frac{1-x}{\rho_l}\right]

    .. math::
        h_{film}(z) = \frac{2 k_l}{\delta_0(z) + \delta_{min}(z)}

    .. math::
        \delta_{min} = 0.3\cdot 10^{-6} \text{m}

    .. math::
        C_{\delta,0} = 0.29

    .. math::
        n_f = 1.74

    if t dry film > tv:

    .. math::
        \delta_{end}(x) = \delta(z, t_v)

    .. math::
        t_{film} = t_v

    .. math::
        t_{dry} = 0

    Otherwise:

    .. math::
        \delta_{end}(z) = \delta_{min}

    .. math::
        t_{film} = t_{dry,film}

    .. math::
        t_{dry} = t_v - t_{film}

    Parameters
    ----------
    m : float
        Mass flow rate [kg/s]
    x : float
        Quality at the specific tube interval []
    D : float
        Diameter of the tube [m]
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]
    mul : float
        Viscosity of liquid [Pa*s]
    mug : float
        Viscosity of gas [Pa*s]
    kl : float
        Thermal conductivity of liquid [W/m/K]
    kg : float
        Thermal conductivity of gas [W/m/K]
    Cpl : float
        Heat capacity of liquid [J/kg/K]
    Cpg : float
        Heat capacity of gas [J/kg/K]
    Hvap : float
        Heat of vaporization of liquid [J/kg]
    sigma : float
        Surface tension of liquid [N/m]
    Psat : float
        Vapor pressure of fluid, [Pa]
    Pc : float
        Critical pressure of fluid, [Pa]
    q : float, optional
        Heat flux to wall [W/m^2]
    Te : float, optional
        Excess temperature of wall, [K]

    Returns
    -------
    h : float
        Heat transfer coefficient [W/m^2/K]

    Notes
    -----
    [1]_ and [2]_ have been reviewed, and are accurately reproduced in [3]_.

    [1]_ used data from 7 studies, covering 7 fluids and Dh from 0.7-3.1 mm,
    heat flux from 0.5-17.8 W/cm^2, x from 0.01-0.99, and G from 50-564
    kg/m^2/s.

    Liquid and/or gas slugs are both considered, and are hydrodynamically
    developing. `Ll` is the calculated length of liquid slugs, and `L_dry`
    is the same for vapor slugs.

    Because of the complexity of the model and that there is some logic in this
    function, `Te` as an input may lead to a different solution that the
    calculated `q` will in return.

    Examples
    --------
    >>> Thome(m=1, x=0.4, D=0.3, rhol=567., rhog=18.09, kl=0.086, kg=0.2,
    ... mul=156E-6, mug=1E-5, Cpl=2300, Cpg=1400, sigma=0.02, Hvap=9E5,
    ... Psat=1E5, Pc=22E6, q=1E5)
    1633.008836502032

    References
    ----------
    .. [1] Thome, J. R., V. Dupont, and A. M. Jacobi. "Heat Transfer Model for
       Evaporation in Microchannels. Part I: Presentation of the Model."
       International Journal of Heat and Mass Transfer 47, no. 14-16 (July
       2004): 3375-85. doi:10.1016/j.ijheatmasstransfer.2004.01.006.
    .. [2] Dupont, V., J. R. Thome, and A. M. Jacobi. "Heat Transfer Model for
       Evaporation in Microchannels. Part II: Comparison with the Database."
       International Journal of Heat and Mass Transfer 47, no. 14-16 (July
       2004): 3387-3401. doi:10.1016/j.ijheatmasstransfer.2004.01.007.
    .. [3] Bertsch, Stefan S., Eckhard A. Groll, and Suresh V. Garimella.
       "Review and Comparative Analysis of Studies on Saturated Flow Boiling in
       Small Channels." Nanoscale and Microscale Thermophysical Engineering 12,
       no. 3 (September 4, 2008): 187-227. doi:10.1080/15567260802317357.
    '''
    if q is None and Te is not None:
        q = secant(to_solve_q_Thome, 1E4, args=( m, x, D, rhol, rhog, kl, kg, mul, mug, Cpl, Cpg, sigma, Hvap, Psat, Pc, Te))
        return Thome(m=m, x=x, D=D, rhol=rhol, rhog=rhog, kl=kl, kg=kg, mul=mul, mug=mug, Cpl=Cpl, Cpg=Cpg, sigma=sigma, Hvap=Hvap, Psat=Psat, Pc=Pc, q=q)
    elif q is None and Te is None:
        raise ValueError('Either q or Te is needed for this correlation')
    C_delta0 = 0.3E-6
    G = m/(pi/4*D**2)
    Rel = G*D*(1-x)/mul
    Reg = G*D*x/mug
    qref = 3328*(Psat/Pc)**-0.5
    if q is None: q = 1e4 # Make numba happy, their bug, never gets ran
    fopt = (q/qref)**1.74
    tau = 1./fopt

    vp = G*(x/rhog + (1-x)/rhol)
    Bo = rhol*D/sigma*vp**2 # Not standard definition
    nul = mul/rhol
    delta0 = D*0.29*(3*(nul/vp/D)**0.5)**0.84*((0.07*Bo**0.41)**-8 + 0.1**-8)**(-1/8.)

    tl = tau/(1 + rhol/rhog*(x/(1.-x)))
    tv = tau/(1 ++ rhog/rhol*((1.-x)/x))

    t_dry_film = rhol*Hvap/q*(delta0 - C_delta0)
    if t_dry_film > tv:
        t_film = tv
        delta_end = delta0 - q/rhol/Hvap*tv # what could time possibly be?
        t_dry = 0
    else:
        t_film = t_dry_film
        delta_end = C_delta0
        t_dry = tv-t_film
    Ll = tau*G/rhol*(1-x)
    Ldry = t_dry*vp


    Prg = Prandtl(Cp=Cpg, k=kg, mu=mug)
    Prl = Prandtl(Cp=Cpl, k=kl, mu=mul)
    fg = (1.82*log10(Reg) - 1.64)**-2
    fl = (1.82*log10(Rel) - 1.64)**-2

    Nu_lam_Zl = 2*0.455*(Prl)**(1/3.)*(D*Rel/Ll)**0.5
    Nu_trans_Zl = turbulent_Gnielinski(Re=Rel, Pr=Prl, fd=fl)*(1 + (D/Ll)**(2/3.))
    if Ldry == 0:
        Nu_lam_Zg, Nu_trans_Zg = 0, 0
    else:
        Nu_lam_Zg = 2*0.455*(Prg)**(1/3.)*(D*Reg/Ldry)**0.5
        Nu_trans_Zg = turbulent_Gnielinski(Re=Reg, Pr=Prg, fd=fg)*(1 + (D/Ldry)**(2/3.))

    h_Zg = kg/D*(Nu_lam_Zg**4 + Nu_trans_Zg**4)**0.25
    h_Zl = kl/D*(Nu_lam_Zl**4 + Nu_trans_Zl**4)**0.25

    h_film = 2*kl/(delta0 + C_delta0)
    return tl/tau*h_Zl + t_film/tau*h_film + t_dry/tau*h_Zg
Пример #9
0
def Kudirka_Grosh_McFadden(m, x, D, rhol, rhog, Cpl, kl, mug, mu_b, mu_w=None):
    r'''Calculates the two-phase non-boiling heat transfer coefficient of a
    liquid and gas flowing inside a tube of any inclination, as in [1]_ and
    reviewed in [2]_.

    .. math::
        Nu = \frac{h_{TP} D}{k_l} = 125 \left(\frac{V_{gs}}{V_{ls}}
        \right)^{0.125}\left(\frac{\mu_g}{\mu_l}\right)^{0.6} Re_{ls}^{0.25}
        Pr_l^{1/3}\left(\frac{\mu_b}{\mu_w}\right)^{0.14}

    Parameters
    ----------
    m : float
        Mass flow rate [kg/s]
    x : float
        Quality at the specific tube interval [-]
    D : float
        Diameter of the tube [m]
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]
    Cpl : float
        Constant-pressure heat capacity of liquid [J/kg/K]
    kl : float
        Thermal conductivity of liquid [W/m/K]
    mug : float
        Viscosity of gas [Pa*s]
    mu_b : float
        Viscosity of liquid at bulk conditions (average of inlet/outlet
        temperature) [Pa*s]
    mu_w : float, optional
        Viscosity of liquid at wall temperature [Pa*s]

    Returns
    -------
    h : float
        Heat transfer coefficient [W/m^2/K]

    Notes
    -----
    If the viscosity at the wall temperature is not given, the liquid viscosity
    correction is not applied.

    Developed for air-water and air-ethylene glycol systems with a L/D of 17.6
    and at low gas-liquid ratios. The flow regimes studied were bubble, slug,
    and froth flow.

    Examples
    --------
    >>> Kudirka_Grosh_McFadden(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300,
    ... kl=.6, mug=1E-5, mu_b=1E-3, mu_w=1.2E-3)
    303.9941255903587

    References
    ----------
    .. [1] Kudirka, A. A., R. J. Grosh, and P. W. McFadden. "Heat Transfer in
       Two-Phase Flow of Gas-Liquid Mixtures." Industrial & Engineering
       Chemistry Fundamentals 4, no. 3 (August 1, 1965): 339-44.
       doi:10.1021/i160015a018.
    .. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
       Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
       Seven Sets of Experimental Data, Including Flow Pattern and Tube
       Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
       1999): 15-40. doi:10.1080/014576399271691.
    '''
    Vgs = m*x/(rhog*pi/4*D**2)
    Vls = m*(1-x)/(rhol*pi/4*D**2)
    Prl = Prandtl(Cp=Cpl, mu=mu_b, k=kl)
    Rels = D*Vls*rhol/mu_b
    Nu = 125*(Vgs/Vls)**0.125*(mug/mu_b)**0.6*Rels**0.25*Prl**(1/3.)
    if mu_w:
        Nu *= (mu_b/mu_w)**0.14
    return Nu*kl/D
Пример #10
0
def Martin_Sims(m, x, D, rhol, rhog, hl=None,
                Cpl=None, kl=None, mu_b=None, mu_w=None, L=None):
    r'''Calculates the two-phase non-boiling heat transfer coefficient of a
    liquid and gas flowing inside a tube of any inclination, as in [1]_ and
    reviewed in [2]_.

    .. math::
        \frac{h_{TP}}{h_l} = 1 + 0.64\sqrt{\frac{V_{gs}}{V_{ls}}}

    Parameters
    ----------
    m : float
        Mass flow rate [kg/s]
    x : float
        Quality at the specific tube interval []
    D : float
        Diameter of the tube [m]
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]
    hl : float, optional
        Liquid-phase heat transfer coefficient as described below, [W/m^2/K]
    Cpl : float, optional
        Constant-pressure heat capacity of liquid [J/kg/K]
    kl : float, optional
        Thermal conductivity of liquid [W/m/K]
    mu_b : float, optional
        Viscosity of liquid at bulk conditions (average of inlet/outlet
        temperature) [Pa*s]
    mu_w : float, optional
        Viscosity of liquid at wall temperature [Pa*s]
    L : float, optional
        Length of the tube [m]

    Returns
    -------
    h : float
        Heat transfer coefficient [W/m^2/K]

    Notes
    -----
    No specific suggestion for how to calculate the liquid-phase heat transfer
    coefficient is given in [1]_; [2]_ suggests to use the same procedure as
    in `Knott`.

    Examples
    --------
    >>> Martin_Sims(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, hl=141.2)
    5563.280000000001
    >>> Martin_Sims(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6,
    ... mu_b=1E-3, mu_w=1.2E-3, L=24)
    5977.505465781747

    References
    ----------
    .. [1] Martin, B. W, and G. E Sims. "Forced Convection Heat Transfer to
       Water with Air Injection in a Rectangular Duct." International Journal
       of Heat and Mass Transfer 14, no. 8 (August 1, 1971): 1115-34.
       doi:10.1016/0017-9310(71)90208-0.
    .. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
       Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
       Seven Sets of Experimental Data, Including Flow Pattern and Tube
       Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
       1999): 15-40. doi:10.1080/014576399271691.
    '''
    Vgs = m*x/(rhog*pi/4*D**2)
    Vls = m*(1-x)/(rhol*pi/4*D**2)
    if hl is None:
        V = Vgs + Vls # Net velocity
        Re = Reynolds(V=V, D=D, rho=rhol, mu=mu_b)
        Pr = Prandtl(Cp=Cpl, k=kl, mu=mu_b)
        Nul = laminar_entry_Seider_Tate(Re=Re, Pr=Pr, L=L, Di=D, mu=mu_b, mu_w=mu_w)
        hl = Nul*kl/D
    return hl*(1.0 + 0.64*(Vgs/Vls)**0.5)
Пример #11
0
def Knott(m, x, D, rhol, rhog, Cpl=None, kl=None, mu_b=None, mu_w=None, L=None,
          hl=None):
    r'''Calculates the two-phase non-boiling heat transfer coefficient of a
    liquid and gas flowing inside a tube of any inclination, as in [1]_ and
    reviewed in [2]_.

    Either a specified `hl` is required, or `Cpl`, `kl`, `mu_b`, `mu_w` and
    `L` are required to calculate `hl`.

    .. math::
        \frac{h_{TP}}{h_l} = \left(1 + \frac{V_{gs}}{V_{ls}}\right)^{1/3}

    Parameters
    ----------
    m : float
        Mass flow rate [kg/s]
    x : float
        Quality at the specific tube interval [-]
    D : float
        Diameter of the tube [m]
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]
    Cpl : float, optional
        Constant-pressure heat capacity of liquid [J/kg/K]
    kl : float, optional
        Thermal conductivity of liquid [W/m/K]
    mu_b : float, optional
        Viscosity of liquid at bulk conditions (average of inlet/outlet
        temperature) [Pa*s]
    mu_w : float, optional
        Viscosity of liquid at wall temperature [Pa*s]
    L : float, optional
        Length of the tube [m]
    hl : float, optional
        Liquid-phase heat transfer coefficient as described below, [W/m^2/K]

    Returns
    -------
    h : float
        Heat transfer coefficient [W/m^2/K]

    Notes
    -----
    The liquid-only heat transfer coefficient will be calculated with the
    `laminar_entry_Seider_Tate` correlation, should it not be provided as an
    input. Many of the arguments to this function are optional and are only
    used if `hl` is not provided.

    `hl` should be calculated with a velocity equal to that determined with
    a combined volumetric flow of both the liquid and the gas. All other
    parameters used in calculating the heat transfer coefficient are those
    of the liquid. If the viscosity at the wall temperature is not given, the
    liquid viscosity correction in `laminar_entry_Seider_Tate` is not applied.

    Examples
    --------
    >>> Knott(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6, mu_b=1E-3,
    ... mu_w=1.2E-3, L=4)
    4225.536758045839

    References
    ----------
    .. [1] Knott, R. F., R. N. Anderson, Andreas. Acrivos, and E. E. Petersen.
       "An Experimental Study of Heat Transfer to Nitrogen-Oil Mixtures."
       Industrial & Engineering Chemistry 51, no. 11 (November 1, 1959):
       1369-72. doi:10.1021/ie50599a032.
    .. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
       Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
       Seven Sets of Experimental Data, Including Flow Pattern and Tube
       Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
       1999): 15-40. doi:10.1080/014576399271691.
    '''
    Vgs = m*x/(rhog*pi/4*D**2)
    Vls = m*(1-x)/(rhol*pi/4*D**2)
    if not hl:
        V = Vgs + Vls # Net velocity
        Re = Reynolds(V=V, D=D, rho=rhol, mu=mu_b)
        Pr = Prandtl(Cp=Cpl, k=kl, mu=mu_b)
        Nul = laminar_entry_Seider_Tate(Re=Re, Pr=Pr, L=L, Di=D, mu=mu_b, mu_w=mu_w)
        hl = Nul*kl/D
    return hl*(1 + Vgs/Vls)**(1/3.)
Пример #12
0
def Davis_David(m, x, D, rhol, rhog, Cpl, kl, mul):
    r'''Calculates the two-phase non-boiling heat transfer coefficient of a
    liquid and gas flowing inside a tube of any inclination, as in [1]_ and
    reviewed in [2]_.

    .. math::
        \frac{h_{TP} D}{k_l} = 0.060\left(\frac{\rho_L}{\rho_G}\right)^{0.28}
        \left(\frac{DG_{TP} x}{\mu_L}\right)^{0.87}
        \left(\frac{C_{p,L} \mu_L}{k_L}\right)^{0.4}

    Parameters
    ----------
    m : float
        Mass flow rate [kg/s]
    x : float
        Quality at the specific tube interval [-]
    D : float
        Diameter of the tube [m]
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]
    Cpl : float
        Constant-pressure heat capacity of liquid [J/kg/K]
    kl : float
        Thermal conductivity of liquid [W/m/K]
    mul : float
        Viscosity of liquid [Pa*s]

    Returns
    -------
    h : float
        Heat transfer coefficient [W/m^2/K]

    Notes
    -----
    Developed for both vertical and horizontal flow, and flow patters of
    annular or mist annular flow. Steam-water and air-water were the only
    considered fluid combinations. Quality ranged from 0.1 to 1 in their data.
    [1]_ claimed an AAE of 17%.

    Examples
    --------
    >>> Davis_David(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6,
    ... mul=1E-3)
    1437.3282869955121

    References
    ----------
    .. [1] Davis, E. J., and M. M. David. "Two-Phase Gas-Liquid Convection Heat
       Transfer. A Correlation." Industrial & Engineering Chemistry
       Fundamentals 3, no. 2 (May 1, 1964): 111-18. doi:10.1021/i160010a005.
    .. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
       Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
       Seven Sets of Experimental Data, Including Flow Pattern and Tube
       Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
       1999): 15-40. doi:10.1080/014576399271691.
    '''
    G = m/(pi/4*D**2)
    Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
    Nu_TP = 0.060*(rhol/rhog)**0.28*(D*G*x/mul)**0.87*Prl**0.4
    return Nu_TP*kl/D
Пример #13
0
def Groothuis_Hendal(m, x, D, rhol, rhog, Cpl, kl, mug, mu_b, mu_w=None,
                     water=False):
    r'''Calculates the two-phase non-boiling heat transfer coefficient of a
    liquid and gas flowing inside a tube of any inclination, as in [1]_ and
    reviewed in [2]_.

    .. math::
        Re_M = \frac{D V_{ls} \rho_l}{\mu_l} + \frac{D V_{gs} \rho_g}{\mu_g}

    For the air-water system:

    .. math::
        \frac{h_{TP} D}{k_L} = 0.029 Re_M^{0.87}Pr^{1/3}_l (\mu_b/\mu_w)^{0.14}

    For gas/air-oil systems (default):

    .. math::
        \frac{h_{TP} D}{k_L} = 2.6 Re_M^{0.39}Pr^{1/3}_l (\mu_b/\mu_w)^{0.14}

    Parameters
    ----------
    m : float
        Mass flow rate [kg/s]
    x : float
        Quality at the specific tube interval [-]
    D : float
        Diameter of the tube [m]
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]
    Cpl : float
        Constant-pressure heat capacity of liquid [J/kg/K]
    kl : float
        Thermal conductivity of liquid [W/m/K]
    mug : float
        Viscosity of gas [Pa*s]
    mu_b : float
        Viscosity of liquid at bulk conditions (average of inlet/outlet
        temperature) [Pa*s]
    mu_w : float, optional
        Viscosity of liquid at wall temperature [Pa*s]
    water : bool, optional
        Whether to use the water-air correlation or the gas/air-oil correlation

    Returns
    -------
    h : float
        Heat transfer coefficient [W/m^2/K]

    Notes
    -----
    If the viscosity at the wall temperature is not given, the liquid viscosity
    correction is not applied.

    Developed for vertical pipes, with superficial velocity ratios of 0.6-250.
    Tested fluids were air-water, and gas/air-oil.

    Examples
    --------
    >>> Groothuis_Hendal(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300, kl=.6,
    ... mug=1E-5, mu_b=1E-3, mu_w=1.2E-3)
    1192.9543445455754

    References
    ----------
    .. [1] Groothuis, H., and W. P. Hendal. "Heat Transfer in Two-Phase Flow.:
       Chemical Engineering Science 11, no. 3 (November 1, 1959): 212-20.
       doi:10.1016/0009-2509(59)80089-0.
    .. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
       Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
       Seven Sets of Experimental Data, Including Flow Pattern and Tube
       Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
       1999): 15-40. doi:10.1080/014576399271691.
    '''
    Vg = m*x/(rhog*pi/4*D**2)
    Vl = m*(1-x)/(rhol*pi/4*D**2)

    Prl = Prandtl(Cp=Cpl, mu=mu_b, k=kl)
    ReM = D*Vl*rhol/mu_b + D*Vg*rhog/mug

    if water:
        Nu_TP = 0.029*(ReM)**0.87*(Prl)**(1/3.)
    else:
        Nu_TP = 2.6*ReM**0.39*Prl**(1/3.)
    if mu_w:
        Nu_TP *= (mu_b/mu_w)**0.14
    return Nu_TP*kl/D
Пример #14
0
def h_ESDU_low_fin(m,
                   A,
                   A_min,
                   A_increase,
                   A_fin,
                   A_tube_showing,
                   tube_diameter,
                   fin_diameter,
                   fin_thickness,
                   bare_length,
                   pitch_parallel,
                   pitch_normal,
                   tube_rows,
                   rho,
                   Cp,
                   mu,
                   k,
                   k_fin,
                   Pr_wall=None):
    r'''Calculates the air side heat transfer coefficient for an air cooler
    or other finned tube bundle with low fins using the formulas of [1]_ as
    presented in [2]_ (and also [3]_).
    
    .. math::
        Nu = 0.183Re^{0.7} \left(\frac{\text{bare length}}{\text{fin height}}
        \right)^{0.36}\left(\frac{p_1}{D_{o}}\right)^{0.06}
        \left(\frac{\text{fin height}}{D_o}\right)^{0.11}
        Pr^{0.36} \cdot F_1\cdot F_2
        
    .. math::
        h_{A,total} = \frac{\eta A_{fin} + A_{bare, showing}}{A_{total}} h
        
    .. math::
        h_{bare,total} = A_{increase} h_{A,total}
        
    Parameters
    ----------
    m : float
        Mass flow rate of air across the tube bank, [kg/s]
    A : float
        Surface area of combined finned and non-finned area exposed for heat
        transfer, [m^2]
    A_min : float
        Minimum air flow area, [m^2]
    A_increase : float
        Ratio of actual surface area to bare tube surface area
        :math:`A_{increase} = \frac{A_{tube}}{A_{bare, total/tube}}`, [-]
    A_fin : float
        Surface area of all fins in the bundle, [m^2]
    A_tube_showing : float
        Area of the bare tube which is exposed in the bundle, [m^2]
    tube_diameter : float
        Diameter of the bare tube, [m]
    fin_diameter : float
        Outer diameter of each tube after including the fin on both sides,
        [m]
    fin_thickness : float
        Thickness of the fins, [m]
    bare_length : float
        Length of bare tube between two fins 
        :math:`\text{bare length} = \text{fin interval} - t_{fin}`, [m]
    pitch_parallel : float
        Distance between tube center along a line parallel to the flow;
        has been called `longitudinal` pitch, `pp`, `s2`, `SL`, and `p2`, [m]
    pitch_normal : float
        Distance between tube centers in a line 90° to the line of flow;
        has been called the `transverse` pitch, `pn`, `s1`, `ST`, and `p1`, [m]
    tube_rows : int
        Number of tube rows per bundle, [-]
    rho : float
        Average (bulk) density of air across the tube bank, [kg/m^3]
    Cp : float
        Average (bulk) heat capacity of air across the tube bank, [J/kg/K]
    mu : float
        Average (bulk) viscosity of air across the tube bank, [Pa*s]
    k : float
        Average (bulk) thermal conductivity of air across the tube bank, 
        [W/m/K]
    k_fin : float
        Thermal conductivity of the fin, [W/m/K]
    Pr_wall : float, optional
        Prandtl number at the wall temperature; provide if a correction with  
        the defaults parameters is desired; otherwise apply the correction
        elsewhere, [-]
        
    Returns
    -------
    h_bare_tube_basis : float
        Air side heat transfer coefficient on a bare-tube surface area as if 
        there were no fins present basis, [W/K/m^2]

    Notes
    -----
    The tube-row count correction factor `F2` can be disabled by setting `tube_rows`
    to 10. The property correction factor `F1` can be disabled by not specifying
    `Pr_wall`. A Prandtl number exponent of 0.26 is recommended in [1]_ for 
    heating and cooling for both liquids and gases.
    
    There is a third correction factor in [1]_ for tube angles not 30, 45, or
    60 degrees, but it is not fully explained and it is not shown in [2]_. 
    Another correction factor is in [2]_ for flow at an angle; however it would
    not make sense to apply it to finned tube banks due to the blockage by the
    fins.
    
    Examples
    --------
    >>> AC = AirCooledExchanger(tube_rows=4, tube_passes=4, tubes_per_row=8, tube_length=0.5, 
    ... tube_diameter=0.0164, fin_thickness=0.001, fin_density=1/0.003,
    ... pitch_normal=0.0313, pitch_parallel=0.0271, fin_height=0.0041, corbels=True)
    
    >>> h_ESDU_low_fin(m=0.914, A=AC.A, A_min=AC.A_min, A_increase=AC.A_increase, A_fin=AC.A_fin,
    ... A_tube_showing=AC.A_tube_showing, tube_diameter=AC.tube_diameter,
    ... fin_diameter=AC.fin_diameter, bare_length=AC.bare_length,
    ... fin_thickness=AC.fin_thickness, tube_rows=AC.tube_rows,
    ... pitch_normal=AC.pitch_normal, pitch_parallel=AC.pitch_parallel, 
    ... rho=1.217, Cp=1007., mu=1.8E-5, k=0.0253, k_fin=15)
    553.853836470948

    References
    ----------
    .. [1] Hewitt, G. L. Shires, T. Reg Bott G. F., George L. Shires, and T.
       R. Bott. Process Heat Transfer. 1st edition. Boca Raton: CRC Press, 
       1994.
    .. [2] "High-Fin Staggered Tube Banks: Heat Transfer and Pressure Drop for
       Turbulent Single Phase Gas Flow." ESDU 86022 (October 1, 1986). 
    .. [3] Rabas, T. J., and J. Taborek. "Survey of Turbulent Forced-Convection
       Heat Transfer and Pressure Drop Characteristics of Low-Finned Tube Banks
       in Cross Flow."  Heat Transfer Engineering 8, no. 2 (January 1987): 
       49-62.
    '''
    fin_height = 0.5 * (fin_diameter - tube_diameter)

    V_max = m / (A_min * rho)
    Re = Reynolds(V=V_max, D=tube_diameter, rho=rho, mu=mu)
    Pr = Prandtl(Cp=Cp, mu=mu, k=k)
    Nu = (0.183 * Re**0.7 * (bare_length / fin_height)**0.36 *
          (pitch_normal / fin_diameter)**0.06 *
          (fin_height / fin_diameter)**0.11 * Pr**0.36)

    staggered = abs(1 - pitch_normal / pitch_parallel) > 0.05
    F2 = ESDU_tube_row_correction(tube_rows=tube_rows, staggered=staggered)
    Nu *= F2
    if Pr_wall is not None:
        F1 = wall_factor(Pr=Pr,
                         Pr_wall=Pr_wall,
                         Pr_heating_coeff=0.26,
                         Pr_cooling_coeff=0.26,
                         property_option=WALL_FACTOR_PRANDTL)
        Nu *= F1

    h = k / tube_diameter * Nu
    efficiency = fin_efficiency_Kern_Kraus(Do=tube_diameter,
                                           D_fin=fin_diameter,
                                           t_fin=fin_thickness,
                                           k_fin=k_fin,
                                           h=h)
    h_total_area_basis = (efficiency * A_fin + A_tube_showing) / A * h
    h_bare_tube_basis = h_total_area_basis * A_increase
    return h_bare_tube_basis
Пример #15
0
def Aggour(m, x, alpha, D, rhol, Cpl, kl, mu_b, mu_w=None, L=None,
           turbulent=None):
    r'''Calculates the two-phase non-boiling laminar heat transfer coefficient
    of a liquid and gas flowing inside a tube of any inclination, as in [1]_
    and reviewed in [2]_.

    Laminar for Rel <= 2000:

    .. math::
        h_{TP} = 1.615\frac{k_l}{D}\left(\frac{Re_l Pr_l D}{L}\right)^{1/3}
        \left(\frac{\mu_b}{\mu_w}\right)^{0.14}

    Turbulent for Rel > 2000:

    .. math::
        h_{TP} = 0.0155\frac{k_l}{D} Pr_l^{0.5} Re_l^{0.83}

    .. math::
        Re_l = \frac{\rho_l v_l D}{\mu_l}

    .. math::
        V_l = \frac{V_{ls}}{1-\alpha}

    Parameters
    ----------
    m : float
        Mass flow rate [kg/s]
    x : float
        Quality at the specific tube interval [-]
    alpha : float
        Void fraction in the tube, [-]
    D : float
        Diameter of the tube [m]
    rhol : float
        Density of the liquid [kg/m^3]
    Cpl : float
        Constant-pressure heat capacity of liquid [J/kg/K]
    kl : float
        Thermal conductivity of liquid [W/m/K]
    mu_b : float
        Viscosity of liquid at bulk conditions (average of inlet/outlet
        temperature) [Pa*s]
    mu_w : float, optional
        Viscosity of liquid at wall temperature [Pa*s]
    L : float, optional
        Length of the tube, [m]
    turbulent : bool or None, optional
        Whether or not to force the correlation to return the turbulent
        result; will return the laminar regime if False

    Returns
    -------
    h : float
        Heat transfer coefficient [W/m^2/K]

    Notes
    -----
    Developed with mixtures of air-water, helium-water, and freon-12-water and
    vertical tests. Studied flow patterns were bubbly, slug, annular,
    bubbly-slug, and slug-annular regimes. Superficial velocity ratios ranged
    from 0.02 to 470.

    A viscosity correction is only suggested for the laminar regime.
    If the viscosity at the wall temperature is not given, the liquid viscosity
    correction is not applied.

    Examples
    --------
    >>> Aggour(m=1, x=.9, D=.3, alpha=.9, rhol=1000, Cpl=2300, kl=.6, mu_b=1E-3)
    420.9347146885667

    References
    ----------
    .. [1] Aggour, Mohamed A. Hydrodynamics and Heat Transfer in Two-Phase
       Two-Component Flows, Ph.D. Thesis, University of Manutoba, Canada
       (1978). http://mspace.lib.umanitoba.ca/xmlui/handle/1993/14171.
    .. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
       Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
       Seven Sets of Experimental Data, Including Flow Pattern and Tube
       Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
       1999): 15-40. doi:10.1080/014576399271691.
    '''
    Vls = m*(1-x)/(rhol*pi/4*D**2)
    Vl = Vls/(1.-alpha)

    Prl = Prandtl(Cp=Cpl, k=kl, mu=mu_b)
    Rel = Reynolds(V=Vl, D=D, rho=rhol, mu=mu_b)

    if turbulent or (Rel > 2000.0 and turbulent is None):
        hl = 0.0155*(kl/D)*Rel**0.83*Prl**0.5
        return hl*(1-alpha)**-0.83
    else:
        hl = 1.615*(kl/D)*(Rel*Prl*D/L)**(1/3.)
        if mu_w:
            hl *= (mu_b/mu_w)**0.14
        return hl*(1.0 - alpha)**(-1/3.)
Пример #16
0
def h_Ganguli_VDI(m, A, A_min, A_increase, A_fin, A_tube_showing,
                  tube_diameter, fin_diameter, fin_thickness, bare_length,
                  pitch_parallel, pitch_normal, tube_rows, rho, Cp, mu, k,
                  k_fin):
    r'''Calculates the air side heat transfer coefficient for an air cooler
    or other finned tube bundle with the formulas of [1]_ as modified in [2]_.
    
    Inline:
        
    .. math::
        Nu_d = 0.22Re_d^{0.6}\left(\frac{A}{A_{tube,only}}\right)^{-0.15}Pr^{1/3}
        
    Staggered:
        
    .. math::
        Nu_d = 0.38 Re_d^{0.6}\left(\frac{A}{A_{tube,only}}\right)^{-0.15}Pr^{1/3}
            
    Parameters
    ----------
    m : float
        Mass flow rate of air across the tube bank, [kg/s]
    A : float
        Surface area of combined finned and non-finned area exposed for heat
        transfer, [m^2]
    A_min : float
        Minimum air flow area, [m^2]
    A_increase : float
        Ratio of actual surface area to bare tube surface area
        :math:`A_{increase} = \frac{A_{tube}}{A_{bare, total/tube}}`, [-]
    A_fin : float
        Surface area of all fins in the bundle, [m^2]
    A_tube_showing : float
        Area of the bare tube which is exposed in the bundle, [m^2]
    tube_diameter : float
        Diameter of the bare tube, [m]
    fin_diameter : float
        Outer diameter of each tube after including the fin on both sides,
        [m]
    fin_thickness : float
        Thickness of the fins, [m]
    bare_length : float
        Length of bare tube between two fins 
        :math:`\text{bare length} = \text{fin interval} - t_{fin}`, [m]
    pitch_parallel : float
        Distance between tube center along a line parallel to the flow;
        has been called `longitudinal` pitch, `pp`, `s2`, `SL`, and `p2`, [m]
    pitch_normal : float
        Distance between tube centers in a line 90° to the line of flow;
        has been called the `transverse` pitch, `pn`, `s1`, `ST`, and `p1`, [m]
    tube_rows : int
        Number of tube rows per bundle, [-]
    rho : float
        Average (bulk) density of air across the tube bank, [kg/m^3]
    Cp : float
        Average (bulk) heat capacity of air across the tube bank, [J/kg/K]
    mu : float
        Average (bulk) viscosity of air across the tube bank, [Pa*s]
    k : float
        Average (bulk) thermal conductivity of air across the tube bank, 
        [W/m/K]
    k_fin : float
        Thermal conductivity of the fin, [W/m/K]
        
    Returns
    -------
    h_bare_tube_basis : float
        Air side heat transfer coefficient on a bare-tube surface area as if 
        there were no fins present basis, [W/K/m^2]

    Notes
    -----
    The VDI modifications were developed in comparison with HTFS and HTRI data
    according to [2]_.
    
    For cases where the tube row count is less than four, the coefficients are
    modified in [2]_. For the inline case, 0.2 replaces 0.22. For the stagered
    cases, the coefficient is 0.2, 0.33, 0.36 for 1, 2, or 3 tube rows 
    respectively.
    
    The model is also showin in [4]_.
    
    Examples
    --------
    Example 12.1 in [3]_:
    
    >>> AC = AirCooledExchanger(tube_rows=4, tube_passes=4, tubes_per_row=56, tube_length=36*foot, 
    ... tube_diameter=1*inch, fin_thickness=0.013*inch, fin_density=10/inch,
    ... angle=30, pitch_normal=2.5*inch, fin_height=0.625*inch, corbels=True)

    >>> h_Ganguli_VDI(m=130.70315, A=AC.A, A_min=AC.A_min, A_increase=AC.A_increase, A_fin=AC.A_fin,
    ... A_tube_showing=AC.A_tube_showing, tube_diameter=AC.tube_diameter,
    ... fin_diameter=AC.fin_diameter, bare_length=AC.bare_length,
    ... fin_thickness=AC.fin_thickness, tube_rows=AC.tube_rows,
    ... pitch_parallel=AC.pitch_parallel, pitch_normal=AC.pitch_normal,
    ... rho=1.2013848, Cp=1009.0188, mu=1.9304793e-05, k=0.027864828, k_fin=238)
    969.2850818578595
    
    References
    ----------
    .. [1] Ganguli, A., S. S. Tung, and J. Taborek. "Parametric Study of
       Air-Cooled Heat Exchanger Finned Tube Geometry." In AIChE Symposium 
       Series, 81:122-28, 1985.
    .. [2] Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition.
       Berlin; New York:: Springer, 2010.
    .. [3] Serth, Robert W., and Thomas Lestina. Process Heat Transfer: 
       Principles, Applications and Rules of Thumb. Academic Press, 2014.
    .. [4] Kroger, Detlev. Air-Cooled Heat Exchangers and Cooling Towers: 
       Thermal-Flow Performance Evaluation and Design, Vol. 1. Tulsa, Okl:
       PennWell Corp., 2004.
    '''
    V_max = m / (A_min * rho)

    Re = Reynolds(V=V_max, D=tube_diameter, rho=rho, mu=mu)
    Pr = Prandtl(Cp=Cp, mu=mu, k=k)

    if abs(1 - pitch_normal / pitch_parallel
           ) < 0.05:  # in-line, with a tolerance of 0.05 proximity
        if tube_rows < 4:
            coeff = 0.2
        else:
            coeff = 0.22
    else:  # staggered
        if tube_rows == 1:
            coeff = 0.2
        elif tube_rows == 2:
            coeff = 0.33
        elif tube_rows == 3:
            coeff = 0.36
        else:
            coeff = 0.38

    # VDI example shows the ratio is of the total area, to the original bare tube area
    # Serth example would match Nu = 47.22 except for lazy rounding
    Nu = coeff * Re**0.6 * Pr**(1 / 3.) * (A_increase)**-0.15
    h = k / tube_diameter * Nu
    efficiency = fin_efficiency_Kern_Kraus(Do=tube_diameter,
                                           D_fin=fin_diameter,
                                           t_fin=fin_thickness,
                                           k_fin=k_fin,
                                           h=h)
    h_total_area_basis = (efficiency * A_fin + A_tube_showing) / A * h
    h_bare_tube_basis = h_total_area_basis * A_increase
    return h_bare_tube_basis
Пример #17
0
def Elamvaluthi_Srinivas(m, x, D, rhol, rhog, Cpl, kl, mug, mu_b, mu_w=None):
    r'''Calculates the two-phase non-boiling heat transfer coefficient of a
    liquid and gas flowing inside a tube of any inclination, as in [1]_ and
    reviewed in [2]_.

    .. math::
        \frac{h_{TP} D}{k_L} = 0.5\left(\frac{\mu_G}{\mu_L}\right)^{0.25}
        Re_M^{0.7} Pr^{1/3}_L (\mu_b/\mu_w)^{0.14}

    .. math::
        Re_M = \frac{D V_L \rho_L}{\mu_L} + \frac{D V_g \rho_g}{\mu_g}

    Parameters
    ----------
    m : float
        Mass flow rate [kg/s]
    x : float
        Quality at the specific tube interval [-]
    D : float
        Diameter of the tube [m]
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]
    Cpl : float
        Constant-pressure heat capacity of liquid [J/kg/K]
    kl : float
        Thermal conductivity of liquid [W/m/K]
    mug : float
        Viscosity of gas [Pa*s]
    mu_b : float
        Viscosity of liquid at bulk conditions (average of inlet/outlet
        temperature) [Pa*s]
    mu_w : float, optional
        Viscosity of liquid at wall temperature [Pa*s]

    Returns
    -------
    h : float
        Heat transfer coefficient [W/m^2/K]

    Notes
    -----
    If the viscosity at the wall temperature is not given, the liquid viscosity
    correction is not applied.

    Developed for vertical flow, and flow patters of bubbly and slug.
    Gas/liquid superficial velocity ratios from 0.3 to 4.6, liquid mass fluxes
    from 200 to 1600 kg/m^2/s, and the fluids tested were air-water and
    air-aqueous glycerine solutions. The tube inner diameter was 1 cm, and the
    L/D ratio was 86.

    Examples
    --------
    >>> Elamvaluthi_Srinivas(m=1, x=.9, D=.3, rhol=1000, rhog=2.5, Cpl=2300,
    ... kl=.6, mug=1E-5, mu_b=1E-3, mu_w=1.2E-3)
    3901.2134471578584

    References
    ----------
    .. [1] Elamvaluthi, G., and N. S. Srinivas. "Two-Phase Heat Transfer in Two
       Component Vertical Flows." International Journal of Multiphase Flow 10,
       no. 2 (April 1, 1984): 237-42. doi:10.1016/0301-9322(84)90021-1.
    .. [2] Dongwoo Kim, Venkata K. Ryali, Afshin J. Ghajar, Ronald L.
       Dougherty. "Comparison of 20 Two-Phase Heat Transfer Correlations with
       Seven Sets of Experimental Data, Including Flow Pattern and Tube
       Inclination Effects." Heat Transfer Engineering 20, no. 1 (February 1,
       1999): 15-40. doi:10.1080/014576399271691.
    '''
    Vg = m*x/(rhog*pi/4*D**2)
    Vl = m*(1-x)/(rhol*pi/4*D**2)

    Prl = Prandtl(Cp=Cpl, mu=mu_b, k=kl)
    ReM = D*Vl*rhol/mu_b + D*Vg*rhog/mug
    Nu_TP = 0.5*(mug/mu_b)**0.25*ReM**0.7*Prl**(1/3.)
    if mu_w:
        Nu_TP *= (mu_b/mu_w)**0.14
    return Nu_TP*kl/D
Пример #18
0
def Chen_Edelstein(m, x, D, rhol, rhog, mul, mug, kl, Cpl, Hvap, sigma,
                   dPsat, Te):
    r'''Calculates heat transfer coefficient for film boiling of saturated
    fluid in any orientation of flow. Correlation
    is developed in [1]_ and [2]_, and reviewed in [3]_. This model is one of
    the most often used. It uses the Dittus-Boelter correlation for turbulent
    convection and the Forster-Zuber correlation for pool boiling, and
    combines them with two factors `F` and `S`.


    .. math::
        h_{tp} = S\cdot h_{nb} + F \cdot h_{sp,l}

    .. math::
        h_{sp,l} = 0.023 Re_l^{0.8} Pr_l^{0.4} k_l/D

    .. math::
        Re_l = \frac{DG(1-x)}{\mu_l}

    .. math::
        h_{nb} = 0.00122\left( \frac{\lambda_l^{0.79} c_{p,l}^{0.45}
        \rho_l^{0.49}}{\sigma^{0.5} \mu^{0.29} H_{vap}^{0.24} \rho_g^{0.24}}
        \right)\Delta T_{sat}^{0.24} \Delta p_{sat}^{0.75}

    .. math::
        F = (1 + X_{tt}^{-0.5})^{1.78}

    .. math::
        X_{tt} = \left( \frac{1-x}{x}\right)^{0.9} \left(\frac{\rho_g}{\rho_l}
        \right)^{0.5}\left( \frac{\mu_l}{\mu_g}\right)^{0.1}

    .. math::
        S = 0.9622 - 0.5822\left(\tan^{-1}\left(\frac{Re_L\cdot F^{1.25}}
        {6.18\cdot 10^4}\right)\right)

    Parameters
    ----------
    m : float
        Mass flow rate [kg/s]
    x : float
        Quality at the specific tube interval []
    D : float
        Diameter of the tube [m]
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]
    mul : float
        Viscosity of liquid [Pa*s]
    mug : float
        Viscosity of gas [Pa*s]
    kl : float
        Thermal conductivity of liquid [W/m/K]
    Cpl : float
        Heat capacity of liquid [J/kg/K]
    Hvap : float
        Heat of vaporization of liquid [J/kg]
    sigma : float
        Surface tension of liquid [N/m]
    dPsat : float
        Difference in Saturation pressure of fluid at Te and T, [Pa]
    Te : float
        Excess temperature of wall, [K]

    Returns
    -------
    h : float
        Heat transfer coefficient [W/m^2/K]

    Notes
    -----
    [1]_ and [2]_ have been reviewed, but the model is only put together in
    the review of [3]_. Many other forms of this equation exist with different
    functions for `F` and `S`.

    Examples
    --------
    >>> Chen_Edelstein(m=0.106, x=0.2, D=0.0212, rhol=567, rhog=18.09,
    ... mul=156E-6, mug=7.11E-6, kl=0.086, Cpl=2730, Hvap=2E5, sigma=0.02,
    ... dPsat=1E5, Te=3)
    3289.058731974052

    See Also
    --------
    turbulent_Dittus_Boelter
    Forster_Zuber

    References
    ----------
    .. [1] Chen, J. C. "Correlation for Boiling Heat Transfer to Saturated
       Fluids in Convective Flow." Industrial & Engineering Chemistry Process
       Design and Development 5, no. 3 (July 1, 1966): 322-29.
       doi:10.1021/i260019a023.
    .. [2] Edelstein, Sergio, A. J. Pérez, and J. C. Chen. "Analytic
       Representation of Convective Boiling Functions." AIChE Journal 30, no.
       5 (September 1, 1984): 840-41. doi:10.1002/aic.690300528.
    .. [3] Bertsch, Stefan S., Eckhard A. Groll, and Suresh V. Garimella.
       "Review and Comparative Analysis of Studies on Saturated Flow Boiling in
       Small Channels." Nanoscale and Microscale Thermophysical Engineering 12,
       no. 3 (September 4, 2008): 187-227. doi:10.1080/15567260802317357.
    '''
    G = m/(pi/4*D**2)
    Rel = D*G*(1-x)/mul
    Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
    hl = turbulent_Dittus_Boelter(Re=Rel, Pr=Prl)*kl/D

    Xtt = Lockhart_Martinelli_Xtt(x=x, rhol=rhol, rhog=rhog, mul=mul, mug=mug)
    F = (1 + Xtt**-0.5)**1.78
    Re = Rel*F**1.25
    S = 0.9622 - 0.5822*atan(Re/6.18E4)
    hnb = Forster_Zuber(Te=Te, dPsat=dPsat, Cpl=Cpl, kl=kl, mul=mul, sigma=sigma,
                       Hvap=Hvap, rhol=rhol, rhog=rhog)
    return hnb*S + hl*F
Пример #19
0
def h_boiling_Han_Lee_Kim(m,
                          x,
                          Dh,
                          rhol,
                          rhog,
                          mul,
                          kl,
                          Hvap,
                          Cpl,
                          q,
                          A_channel_flow,
                          wavelength,
                          chevron_angle=45.0):
    r'''Calculates the two-phase boiling heat transfer coefficient of a
    liquid and gas flowing inside a plate and frame heat exchanger, as
    developed in [1]_ from experiments with three plate exchangers and the
    working fluids R410A and R22. A well-documented and tested correlation,
    reviewed in [2]_, [3]_, [4]_, [5]_, and [6]_.

    .. math::
        h = Ge_1\left(\frac{k_l}{D_h}\right)Re_{eq}^{Ge_2} Pr^{0.4} Bo_{eq}^{0.3}

    .. math::
        Ge_1 = 2.81\left(\frac{\lambda}{D_h}\right)^{-0.041}\left(\frac{\pi}{2}
        -\beta\right)^{-2.83}

    .. math::
        Ge_2 = 0.746\left(\frac{\lambda}{D_h}\right)^{-0.082}\left(\frac{\pi}
        {2}-\beta\right)^{0.61}

    .. math::
        Re_{eq} = \frac{G_{eq} D_h}{\mu_l}

    .. math::
        Bo_{eq} = \frac{q}{G_{eq} H_{vap}}

    .. math::
        G_{eq} = \frac{m}{A_{flow}}\left[1 - x + x\left(\frac{\rho_l}{\rho_g}
        \right)^{1/2}\right]

    In the above equations, lambda is the wavelength of the corrugations, and
    the flow area is specified to be (twice the corrugation amplitude times the
    width of the plate. The mass flow is that per channel. Radians is used in
    degrees, and the formulas are for the  inclination angle not the
    chevron angle (it is converted internally).
    Note that this model depends on the specific heat flux involved.

    Parameters
    ----------
    m : float
        Mass flow rate [kg/s]
    x : float
        Quality at the specific point in the plate exchanger []
    Dh : float
        Hydraulic diameter of the plate, :math:`D_h = \frac{4\lambda}{\phi}` [m]
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]
    mul : float
        Viscosity of the liquid [Pa*s]
    kl : float
        Thermal conductivity of liquid [W/m/K]
    Hvap : float
        Heat of vaporization of the fluid at the system pressure, [J/kg]
    Cpl : float
        Heat capacity of liquid [J/kg/K]
    q : float
        Heat flux, [W/m^2]
    A_channel_flow : float
        The flow area for the fluid, calculated as
        :math:`A_{ch} = 2\cdot \text{width} \cdot \text{amplitude}` [m]
    wavelength : float
        Distance between the bottoms of two of the ridges (sometimes called
        pitch), [m]
    chevron_angle : float, optional
        Angle of the plate corrugations with respect to the vertical axis
        (the direction of flow if the plates were straight), between 0 and
        90. For exchangers with two angles, use the average value. [degrees]

    Returns
    -------
    h : float
        Boiling heat transfer coefficient [W/m^2/K]

    Notes
    -----
    Date regression was with the log mean temperature difference, uncorrected
    for geometry. Developed with three plate heat exchangers with angles of 45,
    35, and 20 degrees. Mass fluxes ranged from 13 to 34 kg/m^2/s; evaporating
    temperatures of 5, 10, and 15 degrees, vapor quality 0.9 to 0.15, heat
    fluxes of 2.5-8.5 kW/m^2.

    Examples
    --------
    >>> h_boiling_Han_Lee_Kim(m=3E-5, x=.4, Dh=0.002, rhol=567., rhog=18.09,
    ... kl=0.086, mul=156E-6,  Hvap=9E5, Cpl=2200, q=1E5, A_channel_flow=0.0003,
    ... wavelength=3.7E-3, chevron_angle=45)
    675.7322255419421

    References
    ----------
    .. [1] Han, Dong-Hyouck, Kyu-Jung Lee, and Yoon-Ho Kim. "Experiments on the
       Characteristics of Evaporation of R410A in Brazed Plate Heat Exchangers
       with Different Geometric Configurations." Applied Thermal Engineering 23,
       no. 10 (July 2003): 1209-25. doi:10.1016/S1359-4311(03)00061-9.
    .. [2] Amalfi, Raffaele L., Farzad Vakili-Farahani, and John R. Thome.
       "Flow Boiling and Frictional Pressure Gradients in Plate Heat Exchangers.
       Part 1: Review and Experimental Database." International Journal of
       Refrigeration 61 (January 2016): 166-84.
       doi:10.1016/j.ijrefrig.2015.07.010.
    .. [3] Eldeeb, Radia, Vikrant Aute, and Reinhard Radermacher. "A Survey of
       Correlations for Heat Transfer and Pressure Drop for Evaporation and
       Condensation in Plate Heat Exchangers." International Journal of
       Refrigeration 65 (May 2016): 12-26. doi:10.1016/j.ijrefrig.2015.11.013.
    .. [4] Solotych, Valentin, Donghyeon Lee, Jungho Kim, Raffaele L. Amalfi,
       and John R. Thome. "Boiling Heat Transfer and Two-Phase Pressure Drops
       within Compact Plate Heat Exchangers: Experiments and Flow
       Visualizations." International Journal of Heat and Mass Transfer 94
       (March 2016): 239-253. doi:10.1016/j.ijheatmasstransfer.2015.11.037.
    .. [5] García-Cascales, J. R., F. Vera-García, J. M. Corberán-Salvador, and
       J. Gonzálvez-Maciá. "Assessment of Boiling and Condensation Heat
       Transfer Correlations in the Modelling of Plate Heat Exchangers."
       International Journal of Refrigeration 30, no. 6 (September 2007):
       1029-41. doi:10.1016/j.ijrefrig.2007.01.004.
    .. [6] Huang, Jianchang. "Performance Analysis of Plate Heat Exchangers
       Used as Refrigerant Evaporators," 2011. Thesis.
       http://wiredspace.wits.ac.za/handle/10539/9779
    '''
    chevron_angle = radians(chevron_angle)
    G = m / A_channel_flow  # For once, clearly defined in the publication
    G_eq = G * ((1. - x) + x * (rhol / rhog)**0.5)
    Re_eq = G_eq * Dh / mul
    Bo_eq = q / (G_eq * Hvap)
    Pr = Prandtl(Cp=Cpl, k=kl, mu=mul)
    Ge1 = 2.81 * (wavelength / Dh)**-0.041 * chevron_angle**-2.83
    Ge2 = 0.746 * (wavelength / Dh)**-0.082 * chevron_angle**0.61
    return Ge1 * kl / Dh * Re_eq**Ge2 * Bo_eq**0.3 * Pr**0.4
Пример #20
0
def Liu_Winterton(m, x, D, rhol, rhog, mul, kl, Cpl, MW, P,  Pc, Te):
    r'''Calculates heat transfer coefficient for film boiling of saturated
    fluid in any orientation of flow. Correlation
    is as developed in [1]_, also reviewed in [2]_ and [3]_.

    Excess wall temperature is required to use this correlation.

    .. math::
        h_{tp} = \sqrt{ (F\cdot h_l)^2 + (S\cdot h_{nb})^2}

    .. math::
       S = \left( 1+0.055F^{0.1} Re_{L}^{0.16}\right)^{-1}

    .. math::
       h_{l} = 0.023 Re_L^{0.8} Pr_l^{0.4} k_l/D

    .. math::
       Re_L = \frac{GD}{\mu_l}

    .. math::
       F = \left[ 1+ xPr_{l}(\rho_l/\rho_g-1)\right]^{0.35}

    .. math::
       h_{nb} = \left(55\Delta Te^{0.67} \frac{P}{P_c}^{(0.12 - 0.2\log_{10}
         R_p)}(-\log_{10} \frac{P}{P_c})^{-0.55} MW^{-0.5}\right)^{1/0.33}

    Parameters
    ----------
    m : float
        Mass flow rate [kg/s]
    x : float
        Quality at the specific tube interval []
    D : float
        Diameter of the tube [m]
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]
    mul : float
        Viscosity of liquid [Pa*s]
    kl : float
        Thermal conductivity of liquid [W/m/K]
    Cpl : float
        Heat capacity of liquid [J/kg/K]
    MW : float
        Molecular weight of the fluid, [g/mol]
    P : float
        Pressure of fluid, [Pa]
    Pc : float
        Critical pressure of fluid, [Pa]
    Te : float, optional
        Excess temperature of wall, [K]

    Returns
    -------
    h : float
        Heat transfer coefficient [W/m^2/K]

    Notes
    -----
    [1]_ has been reviewed, and is accurately reproduced in [3]_.

    Uses the `Cooper` and `turbulent_Dittus_Boelter` correlations.

    A correction for horizontal flow at low Froude numbers is available in
    [1]_ but has not been implemented and is not recommended in several
    sources.

    Examples
    --------
    >>> Liu_Winterton(m=1, x=0.4, D=0.3, rhol=567., rhog=18.09, kl=0.086,
    ... mul=156E-6, Cpl=2300, P=1E6, Pc=22E6, MW=44.02, Te=7)
    4747.749477190532

    References
    ----------
    .. [1] Liu, Z., and R. H. S. Winterton. "A General Correlation for
       Saturated and Subcooled Flow Boiling in Tubes and Annuli, Based on a
       Nucleate Pool Boiling Equation." International Journal of Heat and Mass
       Transfer 34, no. 11 (November 1991): 2759-66.
       doi:10.1016/0017-9310(91)90234-6.
    .. [2] Fang, Xiande, Zhanru Zhou, and Dingkun Li. "Review of Correlations
       of Flow Boiling Heat Transfer Coefficients for Carbon Dioxide."
       International Journal of Refrigeration 36, no. 8 (December 2013):
       2017-39. doi:10.1016/j.ijrefrig.2013.05.015.
    .. [3] Bertsch, Stefan S., Eckhard A. Groll, and Suresh V. Garimella.
       "Review and Comparative Analysis of Studies on Saturated Flow Boiling in
       Small Channels." Nanoscale and Microscale Thermophysical Engineering 12,
       no. 3 (September 4, 2008): 187-227. doi:10.1080/15567260802317357.
    '''
    G = m/(pi/4*D**2)
    ReL = D*G/mul
    Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
    hl = turbulent_Dittus_Boelter(Re=ReL, Pr=Prl)*kl/D
    F = (1 + x*Prl*(rhol/rhog - 1))**0.35
    S = (1 + 0.055*F**0.1*ReL**0.16)**-1
#    if horizontal:
#        Fr = Froude(V=G/rhol, L=D, squared=True)
#        if Fr < 0.05:
#            ef = Fr**(0.1 - 2*Fr)
#            es = Fr**0.5
#            F *= ef
#            S *= es
    h_nb = Cooper(Te=Te, P=P, Pc=Pc, MW=MW)
    return ((F*hl)**2 + (S*h_nb)**2)**0.5
Пример #21
0
def Cavallini_Smith_Zecchin(m, x, D, rhol, rhog, mul, mug, kl, Cpl):
    r'''Calculates heat transfer coefficient for condensation
    of a fluid inside a tube, as presented in
    [1]_, also given in [2]_ and [3]_.

    .. math::
        Nu = \frac{hD_i}{k_l} = 0.05 Re_e^{0.8} Pr_l^{0.33}

    .. math::
        Re_{eq} = Re_g(\mu_g/\mu_l)(\rho_l/\rho_g)^{0.5} + Re_l

    .. math::
        v_{gs} = \frac{mx}{\rho_g \frac{\pi}{4}D^2}

    .. math::
        v_{ls} = \frac{m(1-x)}{\rho_l \frac{\pi}{4}D^2}

    Parameters
    ----------
    m : float
        Mass flow rate [kg/s]
    x : float
        Quality at the specific interval [-]
    D : float
        Diameter of the channel [m]
    rhol : float
        Density of the liquid [kg/m^3]
    rhog : float
        Density of the gas [kg/m^3]
    mul : float
        Viscosity of liquid [Pa*s]
    mug : float
        Viscosity of gas [Pa*s]
    kl : float
        Thermal conductivity of liquid [W/m/K]
    Cpl : float
        Constant-pressure heat capacity of liquid [J/kg/K]

    Returns
    -------
    h : float
        Heat transfer coefficient [W/m^2/K]

    Notes
    -----

    Examples
    --------
    >>> Cavallini_Smith_Zecchin(m=1, x=0.4, D=.3, rhol=800, rhog=2.5, mul=1E-5, mug=1E-3, kl=0.6, Cpl=2300)
    5578.218369177804

    References
    ----------
    .. [1] A. Cavallini, J. R. Smith and R. Zecchin, A dimensionless correlation
       for heat transfer in forced convection condensation, 6th International
       Heat Transfer Conference., Tokyo, Japan (1974) 309-313.
    .. [2] Kakaç, Sadik, ed. Boilers, Evaporators, and Condensers. 1st.
       Wiley-Interscience, 1991.
    .. [3] Balcılar, Muhammet, Ahmet Selim Dalkılıç, Berna Bolat, and Somchai
       Wongwises. "Investigation of Empirical Correlations on the Determination
       of Condensation Heat Transfer Characteristics during Downward Annular
       Flow of R134a inside a Vertical Smooth Tube Using Artificial
       Intelligence Algorithms." Journal of Mechanical Science and Technology
       25, no. 10 (October 12, 2011): 2683-2701. doi:10.1007/s12206-011-0618-2.
    '''
    Prl = Prandtl(Cp=Cpl, mu=mul, k=kl)
    Vl = m * (1 - x) / (rhol * pi / 4 * D**2)
    Vg = m * x / (rhog * pi / 4 * D**2)
    Rel = Reynolds(V=Vl, D=D, rho=rhol, mu=mul)
    Reg = Reynolds(V=Vg, D=D, rho=rhog, mu=mug)
    '''The following was coded, and may be used instead of the above lines,
    to check that the definitions of parameters here provide the same results
    as those defined in [1]_.
    G = m/(pi/4*D**2)
    Re = G*D/mul
    Rel = Re*(1-x)
    Reg = Re*x/(mug/mul)'''
    Reeq = Reg * (mug / mul) * (rhol / rhog)**0.5 + Rel
    Nul = 0.05 * Reeq**0.8 * Prl**0.33
    return Nul * kl / D  # confirmed to be with respect to the liquid