analytical_model_AFSD_code_and_data/python_functions.py at main · adevaucorbeil/analytical_model_AFSD_code_and_data · GitHub

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def beta_law(T, a, b, c):
    return a*numpy.power(Tm/(Tm-T),1/2)

def beta_law_energy(x, a, b):
    return a*numpy.power(x,b)

def total_heat_output(T_, T0_, vfeed_, ρ_mat_, κ_mat_, κ_tool_, cp_, Rbar_, Rtool_, t_, h_, width_, Ttool_, Tlayer_, C_th_, alpha_th_):
    A_feed_ = 4 * Rbar_**2 # m^2
    A_tool_ = math.pi * Rtool_**2 # m^2

    vtool_ = vfeed_ * A_feed_ / (math.pi*Rtool_*t_)
    Pel_ = width_ * vtool_ * ρ_mat_ * cp_ / κ_mat_
    Q1m_ = -(T_ - T0_)/power_law(Pel_, C_th_, alpha_th_)
    Q2m_ = -κ_tool_*A_tool_*(T_ - Ttool_)/h_
    Q3m_ = -vfeed_*A_feed_*ρ_mat_*cp_*(T_-Tlayer_)

    return Q1m_+Q2m_+Q3m_

def Q3plus(T_, vfeed_, ρ_mat_, cp_, Rbar_, Ttool_):
    A_feed_ = 4 * Rbar_**2 # m^2
    return vfeed_*A_feed_*ρ_mat_*cp_*(T_-Ttool_)


def total_heat_input_motor(T_, Ω_, vfeed_, ρ_mat_, κ_mat_, cp_, α_, A_, n_, Rbar_, Rtool_, t_, h_, width_, Ttool_, Tm_, β0_, β1_, β2_):
    ω_      = 2*math.pi*Ω_/60 # rad/s
    ΔH_     = 145000   # J/mol
    G_      = 8.314    # J/(mol.K)
    A_feed_ = 4 * Rbar_**2 # m^2
    A_tool_ = math.pi * Rtool_**2 # m^2
    ζ_      = 0.9
    G_      = 8.314

    gamma_dot_max_ = Rbar_*ω_/t_
    epsilon_dot_average_1_ = 2/(3*math.sqrt(3))*gamma_dot_max_

    Z_ = epsilon_dot_average_1_*numpy.exp(ΔH_/(G_*T_))
    sigma_e_ = numpy.arcsinh((Z_/A_)**(1/n_))/α_
    Q1p_ = ζ_ * A_feed_*t_*sigma_e_*epsilon_dot_average_1_

    r_ = numpy.linspace(Rbar_,Rtool_,1000)
    Ea = 6e3
    #β_ = beta_law_energy(2*math.pi*ω_*t_/vfeed_*numpy.exp(Ea/(G*(T_+273.15))), β0_, β1_)
    β_ = beta_law(T_, β0_, β1_, β2_)
    δ_ = 1-numpy.exp(-β_*(r_-Rbar_)/Rtool_)

    Δ__ = (Rtool_ / β_**3) * (β_**2*Rbar_**2+2*β_*Rtool_*Rbar_+2*Rtool_**2 - (β_**2+2*β_+2)*Rtool_**2*numpy.exp(-β_*(Rtool_-Rbar_)/Rtool_))
    Q2p_ = ζ_ * 2 * (math.pi/math.sqrt(3)) * ω_ * sigma_e_ * Δ__

    return Q1p_ + Q2p_

def total_heat_input(T_, Ω_, vfeed_, ρ_mat_, κ_mat_, cp_, α_, A_, n_, Rbar_, Rtool_, t_, h_, width_,
                     Ttool_, Tm_, β0_, β1_, β2_):
    return total_heat_input_motor(T_, Ω_, vfeed_, ρ_mat_, κ_mat_, cp_, α_, A_, n_, Rbar_, Rtool_, t_, h_, width_, Ttool_, Tm_, β0_, β1_, β2_) + Q3plus(T_, vfeed_, ρ_mat_, cp_, Rbar_, Ttool_)


def total_heat_abs(T_, T0_, Ω_, vfeed_, ρ_mat_, κ_mat_, κ_tool_, cp_, α_, A_, n_, Rbar_, Rtool_, t_, h_, width_,
                   Ttool_, Tlayer_, C_th_, alpha_th_, Tm_, β0_, β1_, β2_):
    Qout_ = total_heat_output(T_, T0_, vfeed_, ρ_mat_, κ_mat_, κ_tool_, cp_, Rbar_, Rtool_, t_, h_, width_, Ttool_, Tlayer_, C_th_, alpha_th_)
    Qin_  = total_heat_input(T_, Ω_, vfeed_, ρ_mat_, κ_mat_, cp_, α_, A_, n_, Rbar_, Rtool_, t_, h_, width_, Ttool_, Tm_, β0_, β1_, β2_)
    Qtot_ = Qin_ + Qout_
    return abs(Qtot_)

def temperature_offset(Ω, T0, Ttarget, vfeed, ρ_mat, κ_mat, κ_tool, cp, α, A, n, Rbar, Rtool, t, h, width, Ttool, Tlayer, C_th, alpha_th, Tm, β0, β1, β2):
    T = 400 # Guess
    result_process_temp = optimize.minimize(total_heat_abs, T, method='Nelder-Mead', options={'xatol': 1.0}, args=(T0, Ω, vfeed, ρ_mat, κ_mat, κ_tool, cp, α, A, n, Rbar, Rtool, t, h, width, Ttool, Tlayer, C_th, alpha_th, Tm, β0, β1, β2), tol=1.0)
    return abs(result_process_temp.x[0]-Ttarget)