vacuum

Vacuum

Module containing vacuum system routines

This module contains routines for calculating the parameters of the vacuum system for a fusion power plant.

Source code in process/models/vacuum.py

class Vacuum:
    """Module containing vacuum system routines

    This module contains routines for calculating the
    parameters of the vacuum system for a fusion power plant.
    """

    def __init__(self):
        self.outfile: int = constants.NOUT

    def run(self, output: bool):
        """Routine to call the vacuum module
        This routine calls the main vacuum package.

        Parameters
        ----------
        output:
            indicate whether output should be written to the output file, or not

        """
        # (should be) NBI gas load (deuterons/second)

        qtorus = 0.0e0

        #  Total fuel gas load (kg/s)
        #  2 nuclei * nucleus-pairs/sec * mass/nucleus

        # MDK Check this!!
        gasld = (
            2.0e0
            * physics_variables.molflow_plasma_fuelling_required
            * physics_variables.m_fuel_amu
            * constants.UMASS
        )

        self.i_vacuum_pumping = vacuum_variables.i_vacuum_pumping

        # i_vacuum_pumping required to be compared to a b string
        # as this is what f2py returns
        if self.i_vacuum_pumping == "old":
            (
                pumpn,
                vacuum_variables.n_vv_vacuum_ducts,
                vacuum_variables.dlscal,
                vacuum_variables.m_vv_vacuum_duct_shield,
                vacuum_variables.dia_vv_vacuum_ducts,
            ) = self.vacuum(
                physics_variables.p_fusion_total_mw,
                physics_variables.rmajor,
                physics_variables.rminor,
                0.5e0
                * (
                    build_variables.dr_fw_plasma_gap_inboard
                    + build_variables.dr_fw_plasma_gap_outboard
                ),
                physics_variables.a_plasma_surface,
                physics_variables.vol_plasma,
                build_variables.dr_shld_outboard,
                build_variables.dr_shld_inboard,
                build_variables.dr_tf_inboard,
                build_variables.r_shld_inboard_inner
                - build_variables.dr_shld_vv_gap_inboard
                - build_variables.dr_vv_inboard,
                tfcoil_variables.n_tf_coils,
                times_variables.t_plant_pulse_dwell,
                physics_variables.nd_plasma_electrons_vol_avg,
                divertor_variables.n_divertors,
                qtorus,
                gasld,
                output=output,
            )
            # MDK pumpn is real: convert to integer by rounding.
            vacuum_variables.n_vac_pumps_high = math.floor(pumpn + 0.5e0)
        elif self.i_vacuum_pumping == "simple":
            vacuum_variables.n_iter_vacuum_pumps = self.vacuum_simple(output=output)
        else:
            logger.error(
                f"i_vacuum_pumping is invalid: {vacuum_variables.i_vacuum_pumping}"
            )

    def vacuum_simple(self, output) -> float:
        """Simple model of vacuum pumping system


        Parameters
        ----------
        output :

        Returns
        -------
        npump:
            number of pumps for pumpdown and steady-state
            indicate whether output should be written to the output file, or not
        """

        # Steady-state model (super simple)
        # One ITER torus cryopump has a throughput of 50 Pa m3/s = 1.2155e+22 molecules/s
        # Issue #304
        n_iter_vacuum_pumps = (
            physics_variables.molflow_plasma_fuelling_required
            / vacuum_variables.molflow_vac_pumps
        )

        # Pump-down:
        # Pumping speed per pump m3/s
        pumpspeed = (
            vacuum_variables.volflow_vac_pumps_max
            * vacuum_variables.f_a_vac_pump_port_plasma_surface
            * vacuum_variables.f_volflow_vac_pumps_impedance
            * physics_variables.a_plasma_surface
            / tfcoil_variables.n_tf_coils
        )

        wallarea = (physics_variables.a_plasma_surface / 1084.0e0) * 2000.0e0
        # Required pumping speed for pump-down
        pumpdownspeed = (
            vacuum_variables.outgasfactor
            * wallarea
            / vacuum_variables.pres_vv_chamber_base
        ) * times_variables.t_plant_pulse_dwell ** (-vacuum_variables.outgasindex)
        # Number of pumps required for pump-down
        npumpdown = pumpdownspeed / pumpspeed

        # Combine the two (somewhat inconsistent) models
        # Note that 'npump' can be constrained by constraint equation 63
        npump = max(n_iter_vacuum_pumps, npumpdown)

        #  Output section
        if output:
            process_output.oheadr(self.outfile, "Vacuum System")
            process_output.ovarst(
                self.outfile,
                "Switch for vacuum pumping model",
                "(i_vacuum_pumping)",
                '"' + self.i_vacuum_pumping + '"',
            )
            process_output.ocmmnt(
                self.outfile,
                "Simple steady-state model with comparison to ITER cryopumps",
            )
            process_output.ovarre(
                self.outfile,
                "Plasma fuelling rate (nucleus-pairs/s)",
                "(molflow_plasma_fuelling_required)",
                physics_variables.molflow_plasma_fuelling_required,
                "OP ",
            )
            process_output.ocmmnt(
                self.outfile, "Number of high vacuum pumps, each with the throughput"
            )
            process_output.ocmmnt(
                self.outfile,
                " of one ITER cryopump (50 Pa m3 s-1 = 1.2e+22 molecules/s),",
            )
            process_output.ovarre(
                self.outfile,
                " all operating at the same time",
                "(n_iter_vacuum_pumps)",
                n_iter_vacuum_pumps,
                "OP ",
            )

            process_output.ovarre(
                self.outfile,
                "Dwell time",
                "(t_plant_pulse_dwell)",
                times_variables.t_plant_pulse_dwell,
            )
            process_output.ovarre(
                self.outfile,
                "Number of pumps required for pump-down",
                "(npumpdown)",
                npumpdown,
                "OP ",
            )
            process_output.ovarre(
                self.outfile,
                "Number of pumps required overall",
                "(npump)",
                npump,
                "OP ",
            )

        return npump

    def vacuum(
        self,
        pfusmw,
        r0,
        aw,
        dsol,
        plasma_sarea,
        plasma_vol,
        thshldo,
        thshldi,
        thtf,
        ritf,
        n_tf_coils,
        t_plant_pulse_dwell,
        nplasma,
        ndiv,
        qtorus,
        gasld,
        output,
    ):
        """Routine to calculate the parameters of the vacuum system

        Parameters
        ----------
        pfusmw : float
            Fusion power (MW)
        r0 : float
            Major radius (m)
        aw : float
            Minor radius (m)
        dsol :
            Scrape-off layer average width (m)
        plasma_sarea :
            Plasma surface area (m2)
        plasma_vol :
            Plasma volume (m3)
        thshldo :
            Outboard shield thickness (m)
        thshldi :
            Inboard shield thickness (m)
        thtf :
            TF coil thickness (m)
        ritf :
            Radius of inboard TF leg point nearest plasma (m)
        n_tf_coils :
            Number of TF coils
        t_plant_pulse_dwell :
            Dwell time between pulses (s)
        nplasma :
            Plasma density (m**-3)
        ndiv :
            Number of divertors with pumping (single null = 1, double null = 2 if pumping provided at both locations)
        qtorus :
            Gas load  from NBI (deuterons/second)
        gasld :
            Total D-T gas load (kg/s)
        output :
            indicate whether output should be written to the output file, or not


        Returns
        -------
        :
            pumpn (`float`) - Number of high vacuum pumps
            - nduct (`int`) - Number of ducts
            - dlscalc (`float`) - Duct-length equivalent for costing purposes (m)
            - mvdsh (`float`) - Mass of a single vacuum duct shield (kg)
            - dimax (`float`) -  Diameter of passage from divertor to pumping ducts (m)
        """
        k = 1.38e-23  # Boltzmann's constant (J/K)
        densh = 7900.0e0  # Density of shielding material (kg/m2)
        fsolid = 0.9e0  # Fraction of duct shielding that is solid material

        #  Pump type;
        #    i_vacuum_pump_type = 0 for turbomolecular pump (mag. bearing) with a nominal
        #              speed of 2.0 m^3/s (1.95 for N2, 1.8 for He, 1.8 for DT)
        #    i_vacuum_pump_type = 1 for compound cryopump with nominal speed of 10 m^3/s
        #              (9.0 for N2, 5.0 for He and 25. for DT)

        pfus = pfusmw * 1.0e6  # Fusion power (W)
        ntf = int(n_tf_coils)

        #  Feed rate (gas load) of D-T into chamber (pellets + gas puffing +
        #     NBI + ...) = load from fueller + load from NBI
        #  frate (kg/s) = gasld (kg/s) + qtorus (D2/s) * 6.64e-27 (kg/D2)

        frate = gasld + qtorus * 6.64e-27

        #  Set duct shield thickness to zero for no biological shielding
        #  instead of thshldo/3.0e0

        thdsh = 0.0e0

        #  Shielding (m) between duct and TF coils is scaled from inboard shield
        #  thickness

        thcsh = thshldi / 3.0e0

        #  Multiplier to convert conductance from gas species i to nitrogen
        xmult = [1.0e0, 0.423e0, 0.378e0, 0.423e0]
        # nitrogen, D-T, helium, D-T again

        nduct = ntf * ndiv

        #  Speed of high-vacuum pumps (m^3/s)

        # nitrogen, DT, helium, DT again
        sp = (
            [1.95, 1.8, 1.8, 1.8]
            if vacuum_variables.i_vacuum_pump_type == 0
            else [9.0, 25.0, 5.0, 25.0]
        )

        #  Calculate required pumping speeds

        s = []

        #  Initial pumpdown based on outgassing
        #  s(1) = net pump speed (N2) required for pumpdown to base pressure (m^3/s)
        #  area = vacuum chamber/fw area (m^2)  ;  outgassing area = 10 x area
        #  outgrat_fw = outgassing rate (effective for N2) of plasma chamber surface (Pa-m/s)
        #  pres_vv_chamber_base = base pressure (Pa)

        #  Old method: area = 4.0e0 * pi*pi * r0 * aw * sqrt(0.5e0*(1.0e0 + kappa*kappa))

        area = plasma_sarea * (aw + dsol) / aw

        ogas = vacuum_variables.outgrat_fw * area * 10.0e0  # Outgassing rate (Pa-m^3/s)
        s.append(ogas / vacuum_variables.pres_vv_chamber_base)

        #  Pumpdown between burns
        #  s(2) = net pump speed (DT) required for pumpdown between burns (m^3/s)
        #  temp_vv_chamber_gas_burn_end = temperature of neutral gas in chamber (K)
        #  t_plant_pulse_dwell = dwell time between burns (s)

        pend = (
            0.5e0 * nplasma * k * vacuum_variables.temp_vv_chamber_gas_burn_end
        )  # pressure in plasma chamber after burn (Pa)
        pstart = 0.01e0 * pend  # pressure in chamber before start of burn (Pa)

        #  Chamber volume (m^3)

        #  Old method: volume = 2.0e0 * pi*pi * r0 * aw*aw * kappa

        volume = plasma_vol * (aw + dsol) * (aw + dsol) / (aw * aw)

        #  dwell pumping options
        if (vacuum_variables.i_vac_pump_dwell == 1) or (t_plant_pulse_dwell == 0):
            tpump = times_variables.t_plant_pulse_coil_precharge
        elif vacuum_variables.i_vac_pump_dwell == 2:
            tpump = t_plant_pulse_dwell + times_variables.t_plant_pulse_coil_precharge
        else:
            tpump = t_plant_pulse_dwell

        s.append(volume / tpump * math.log(pend / pstart))

        #  Helium ash removal
        #  s(3) = net pump speed (He) required for helium ash removal (m^3/s)
        #  source = alpha production rate (pa - m^3/s)
        #  fhe = fraction of neutral gas in divertor chamber that is helium
        #  pres_div_chamber_burn = pressure in divertor chamber during burn (Pa)

        source = pfus * 1.47e-09
        fhe = source / (frate * 4.985e5)
        s.extend(
            (
                (source / vacuum_variables.pres_div_chamber_burn / fhe),
                #  Removal of dt on steady state basis
                #  s(4) = net speed (D-T) required to remove dt at fuelling rate (m^3/s)
                (
                    (frate * 4.985e5 - source)
                    / (vacuum_variables.pres_div_chamber_burn * (1.0e0 - fhe))
                ),
            ),
        )

        #  Calculate conductance of a single duct

        imax = 1
        cmax = 0.01e0
        pumpn = 1.0e0
        nflag = 0  # Control option if ducts are too small in x-sectional area
        #  = 1 if problem is identified in output, but run continues
        #  = 0 otherwise

        l1 = thshldo + thtf  # Length of passage from divertor to ducts (m)
        l2 = thshldo + 4.0e0  # Length of ducts from divertor passage to elbow (m)
        l3 = 2.0e0  # Length of ducts from elbow to hi-vac pumps (m)
        ltot = l1 + l2 + l3

        # ceff and d require initialising too small positive values; they're not
        # always overwritten in the following loop and can cause div by 0 errors
        # otherwise
        ceff = np.full(4, 1e-6)
        d = np.full(4, 1e-6)

        for i in range(4):
            sss = nduct / (1.0e0 / sp[i] / pumpn + 1.0e0 / cmax * xmult[i] / xmult[imax])
            if sss > s[i]:
                continue
            imax = i

            ccc = 2.0e0 * s[i] / nduct
            pumpn1 = 1.0e0 / (sp[i] * (nduct / s[i] - 1.0e0 / ccc))
            pumpn2 = 1.01e0 * s[i] / (sp[i] * nduct)
            pumpn = max(pumpn, pumpn1, pumpn2)
            ceff[i] = 1.0e0 / (nduct / s[i] - 1.0e0 / (sp[i] * pumpn))

            #  Newton's method solution for duct diameter
            while True:
                d[i] = 1.0e0

                for _ in range(100):
                    a1 = (
                        0.25e0 * math.pi * d[i] * d[i]
                    )  # Area of aperture and duct (m^2)
                    a2 = 1.44e0 * a1
                    a3 = a2
                    k1 = 4.0e0 / 3.0e0 * d[i] / (l1 + 4.0e0 / 3.0e0 * d[i])
                    k2 = (
                        4.0e0
                        / 3.0e0
                        * d[i]
                        * 1.2e0
                        / (l2 + 4.0e0 / 3.0e0 * d[i] * 1.2e0)
                    )
                    k3 = (
                        4.0e0
                        / 3.0e0
                        * d[i]
                        * 1.2e0
                        / (l3 + 4.0e0 / 3.0e0 * d[i] * 1.2e0)
                    )
                    cap = 119.0e0 * a1 / xmult[i]
                    dcap = 2.0e0 * cap / d[i]
                    c1 = 119.0e0 * a1 * k1 / xmult[i]
                    dc1 = c1 / d[i] * (3.0e0 - k1)
                    c2 = 119.0e0 * a2 * k2 / xmult[i]
                    dc2 = c2 / d[i] / 1.2e0 * (3.0e0 - k2)
                    c3 = 119.0e0 * a3 * k3 / xmult[i]
                    dc3 = c3 / d[i] / 1.2e0 * (3.0e0 - k3)
                    cnew = 1.0e0 / (1.0e0 / cap + 1.0e0 / c1 + 1.0e0 / c2 + 1.0e0 / c3)
                    y = -ceff[i] + cnew
                    dy = (
                        cnew
                        * cnew
                        * (
                            dcap / cap / cap
                            + dc1 / c1 / c1
                            + dc2 / c2 / c2
                            + dc3 / c3 / c3
                        )
                    )
                    dnew = d[i] - y / dy
                    dd = abs((d[i] - dnew) / d[i])
                    d[i] = dnew
                    if dd <= 0.01e0:
                        break

                else:
                    logger.error(
                        f"Newton's method not converging; check fusion power, te {physics_variables.p_fusion_total_mw=} {physics_variables.temp_plasma_electron_vol_avg_kev=}"
                    )

                theta = math.pi / ntf

                #  Area between adjacent TF coils available for pump ducts
                #  ritf = outer radius of inboard leg of TF coil (m)

                a1max = (r0 + aw - ritf - thcsh / math.tan(theta)) ** 2 * math.tan(theta)
                d1max = math.sqrt(4.0e0 * a1max / math.pi)  # Equivalent diameter
                if a1 < a1max:
                    break

                ceff[i] = 0.9e0 * ceff[i]
                if ceff[i] <= (1.1e0 * s[i]):
                    #  Ducts are not big enough. Flag and continue.
                    nflag = 1
                    break

            cmax = ceff[i]

        pumpn = pumpn * nduct

        #  d[imax]= diameter of passage from divertor to pumping ducts (m)
        #  dout    = diameter of ducts from passage to hi-vac pumps (m)

        dout = d[imax] * 1.2e0

        #  Net pumping speeds provided by vacuum pumping system
        #  snet(1) - net pump speed (N2) provided (m^3/s)
        #  snet(2) - net pump speed (D-T) provided (m^3/s)
        #  snet(3) - net pump speed (He) provided (m^3/s)
        #  snet(4) - snet(2)
        snet = []
        for i in range(4):
            ceff1 = ceff[imax] * nduct
            snet.append(
                1.0e0
                / (1.0e0 / (ceff1 * xmult[imax] / xmult[i]) + 1.0e0 / sp[i] / pumpn)
            )

        #  If cryopumps are used then an additional pump is required
        #  for continuous operation with regeneration.

        if vacuum_variables.i_vacuum_pump_type == 1:
            pumpn = pumpn * 2.0e0

        #  Information for costing routine

        dlscalc = l1 * d[imax] ** 1.4e0 + (ltot - l1) * (d[imax] * 1.2e0) ** 1.4e0

        #  Mass of duct shielding

        arsh = (
            0.25e0 * math.pi * ((d[imax] * 1.2e0 + thdsh) ** 2 - (d[imax] * 1.2e0) ** 2)
        )
        mvdsh = arsh * (ltot - l1) * densh * fsolid

        dimax = d[imax]

        if output:
            #  Output section

            process_output.oheadr(self.outfile, "Vacuum System")

            process_output.ocmmnt(self.outfile, "Pumpdown to Base Pressure :")
            process_output.oblnkl(self.outfile)
            process_output.ovarre(
                self.outfile,
                "First wall outgassing rate (Pa m/s)",
                "(outgrat_fw)",
                vacuum_variables.outgrat_fw,
            )
            process_output.ovarre(
                self.outfile, "Total outgassing load (Pa m3/s)", "(ogas)", ogas, "OP "
            )
            process_output.ovarre(
                self.outfile,
                "Base pressure required (Pa)",
                "(pres_vv_chamber_base)",
                vacuum_variables.pres_vv_chamber_base,
            )
            process_output.ovarre(
                self.outfile, "Required N2 pump speed (m3/s)", "(s(1))", s[0], "OP "
            )
            process_output.ovarre(
                self.outfile,
                "N2 pump speed provided (m3/s)",
                "(snet(1))",
                snet[0],
                "OP ",
            )

            process_output.osubhd(self.outfile, "Pumpdown between Burns :")
            process_output.ovarre(
                self.outfile, "Plasma chamber volume (m3)", "(volume)", volume, "OP "
            )
            process_output.ovarre(
                self.outfile, "Chamber pressure after burn (Pa)", "(pend)", pend, "OP "
            )
            process_output.ovarre(
                self.outfile, "Chamber pressure before burn (Pa)", "(pstart)", pstart
            )
            process_output.ovarin(
                self.outfile,
                "Allowable pumping time switch",
                "(i_vac_pump_dwell)",
                vacuum_variables.i_vac_pump_dwell,
            )
            process_output.ovarre(
                self.outfile,
                "Dwell time between burns (s)",
                "(t_plant_pulse_dwell.)",
                t_plant_pulse_dwell,
            )
            process_output.ovarre(
                self.outfile,
                "CS ramp-up time burns (s)",
                "(t_plant_pulse_coil_precharge.)",
                times_variables.t_plant_pulse_coil_precharge,
            )
            process_output.ovarre(
                self.outfile,
                "Allowable pumping time between burns (s)",
                "(tpump)",
                tpump,
            )
            process_output.ovarre(
                self.outfile, "Required D-T pump speed (m3/s)", "(s(2))", s[1], "OP "
            )
            process_output.ovarre(
                self.outfile,
                "D-T pump speed provided (m3/s)",
                "(snet(2))",
                snet[1],
                "OP ",
            )

            process_output.osubhd(self.outfile, "Helium Ash Removal :")
            process_output.ovarre(
                self.outfile,
                "Divertor chamber gas pressure (Pa)",
                "(pres_div_chamber_burn)",
                vacuum_variables.pres_div_chamber_burn,
            )
            process_output.ovarre(
                self.outfile,
                "Helium gas fraction in divertor chamber",
                "(fhe)",
                fhe,
                "OP ",
            )
            process_output.ovarre(
                self.outfile, "Required helium pump speed (m3/s)", "(s(3))", s[2], "OP "
            )
            process_output.ovarre(
                self.outfile,
                "Helium pump speed provided (m3/s)",
                "(snet(3))",
                snet[2],
                "OP ",
            )

            process_output.osubhd(self.outfile, "D-T Removal at Fuelling Rate :")
            process_output.ovarre(
                self.outfile, "D-T fuelling rate (kg/s)", "(frate)", frate, "OP "
            )
            process_output.ovarre(
                self.outfile, "Required D-T pump speed (m3/s)", "(s(4))", s[3], "OP "
            )
            process_output.ovarre(
                self.outfile,
                "D-T pump speed provided (m3/s)",
                "(snet(4))",
                snet[3],
                "OP ",
            )

            if nflag == 1:
                process_output.oblnkl(self.outfile)
                process_output.ocmmnt(
                    self.outfile, "Vacuum pumping ducts are space limited."
                )
                process_output.ocmmnt(
                    self.outfile, f"Maximum duct diameter is only {d1max} m"
                )
                process_output.ocmmnt(self.outfile, "Conductance is inadequate.")
                process_output.oblnkl(self.outfile)

            i_fw_blkt_shared_coolant = (
                "cryo " if vacuum_variables.i_vacuum_pump_type == 1 else "turbo"
            )

            process_output.oblnkl(self.outfile)
            process_output.ocmmnt(
                self.outfile, "The vacuum pumping system size is governed by the"
            )

            if imax == 1:
                process_output.ocmmnt(
                    self.outfile, "requirements for pumpdown to base pressure."
                )
            elif imax == 2:
                process_output.ocmmnt(
                    self.outfile, "requirements for pumpdown between burns."
                )
            elif imax == 3:
                process_output.ocmmnt(
                    self.outfile, "requirements for helium ash removal."
                )
            else:
                process_output.ocmmnt(
                    self.outfile, "requirements for D-T removal at fuelling rate."
                )

            process_output.oblnkl(self.outfile)
            process_output.ovarin(
                self.outfile, "Number of large pump ducts", "(nduct)", nduct
            )
            process_output.ovarre(
                self.outfile,
                "Passage diameter, divertor to ducts (m)",
                "(d(imax))",
                d[imax],
                "OP ",
            )
            process_output.ovarre(self.outfile, "Passage length (m)", "(l1)", l1, "OP ")
            process_output.ovarre(
                self.outfile, "Diameter of ducts (m)", "(dout)", dout, "OP "
            )

            process_output.ovarre(
                self.outfile, "Duct length, divertor to elbow (m)", "(l2)", l2, "OP "
            )
            process_output.ovarre(
                self.outfile, "Duct length, elbow to pumps (m)", "(l3)", l3
            )
            process_output.ovarre(
                self.outfile, "Number of pumps", "(pumpn)", pumpn, "OP "
            )
            process_output.oblnkl(self.outfile)
            process_output.ocmmnt(
                self.outfile,
                f"The vacuum system uses {i_fw_blkt_shared_coolant} pumps.",
            )

        return pumpn, nduct, dlscalc, mvdsh, dimax

outfile = constants.NOUT instance-attribute

run(output)

Routine to call the vacuum module This routine calls the main vacuum package.

Parameters:

Name	Type	Description	Default
output	bool	indicate whether output should be written to the output file, or not	required

Source code in process/models/vacuum.py

def run(self, output: bool):
    """Routine to call the vacuum module
    This routine calls the main vacuum package.

    Parameters
    ----------
    output:
        indicate whether output should be written to the output file, or not

    """
    # (should be) NBI gas load (deuterons/second)

    qtorus = 0.0e0

    #  Total fuel gas load (kg/s)
    #  2 nuclei * nucleus-pairs/sec * mass/nucleus

    # MDK Check this!!
    gasld = (
        2.0e0
        * physics_variables.molflow_plasma_fuelling_required
        * physics_variables.m_fuel_amu
        * constants.UMASS
    )

    self.i_vacuum_pumping = vacuum_variables.i_vacuum_pumping

    # i_vacuum_pumping required to be compared to a b string
    # as this is what f2py returns
    if self.i_vacuum_pumping == "old":
        (
            pumpn,
            vacuum_variables.n_vv_vacuum_ducts,
            vacuum_variables.dlscal,
            vacuum_variables.m_vv_vacuum_duct_shield,
            vacuum_variables.dia_vv_vacuum_ducts,
        ) = self.vacuum(
            physics_variables.p_fusion_total_mw,
            physics_variables.rmajor,
            physics_variables.rminor,
            0.5e0
            * (
                build_variables.dr_fw_plasma_gap_inboard
                + build_variables.dr_fw_plasma_gap_outboard
            ),
            physics_variables.a_plasma_surface,
            physics_variables.vol_plasma,
            build_variables.dr_shld_outboard,
            build_variables.dr_shld_inboard,
            build_variables.dr_tf_inboard,
            build_variables.r_shld_inboard_inner
            - build_variables.dr_shld_vv_gap_inboard
            - build_variables.dr_vv_inboard,
            tfcoil_variables.n_tf_coils,
            times_variables.t_plant_pulse_dwell,
            physics_variables.nd_plasma_electrons_vol_avg,
            divertor_variables.n_divertors,
            qtorus,
            gasld,
            output=output,
        )
        # MDK pumpn is real: convert to integer by rounding.
        vacuum_variables.n_vac_pumps_high = math.floor(pumpn + 0.5e0)
    elif self.i_vacuum_pumping == "simple":
        vacuum_variables.n_iter_vacuum_pumps = self.vacuum_simple(output=output)
    else:
        logger.error(
            f"i_vacuum_pumping is invalid: {vacuum_variables.i_vacuum_pumping}"
        )

vacuum_simple(output)

Simple model of vacuum pumping system

Parameters:

Name	Type	Description	Default
output			required

Returns:

Name	Type	Description
npump	float	number of pumps for pumpdown and steady-state indicate whether output should be written to the output file, or not

Source code in process/models/vacuum.py

def vacuum_simple(self, output) -> float:
    """Simple model of vacuum pumping system


    Parameters
    ----------
    output :

    Returns
    -------
    npump:
        number of pumps for pumpdown and steady-state
        indicate whether output should be written to the output file, or not
    """

    # Steady-state model (super simple)
    # One ITER torus cryopump has a throughput of 50 Pa m3/s = 1.2155e+22 molecules/s
    # Issue #304
    n_iter_vacuum_pumps = (
        physics_variables.molflow_plasma_fuelling_required
        / vacuum_variables.molflow_vac_pumps
    )

    # Pump-down:
    # Pumping speed per pump m3/s
    pumpspeed = (
        vacuum_variables.volflow_vac_pumps_max
        * vacuum_variables.f_a_vac_pump_port_plasma_surface
        * vacuum_variables.f_volflow_vac_pumps_impedance
        * physics_variables.a_plasma_surface
        / tfcoil_variables.n_tf_coils
    )

    wallarea = (physics_variables.a_plasma_surface / 1084.0e0) * 2000.0e0
    # Required pumping speed for pump-down
    pumpdownspeed = (
        vacuum_variables.outgasfactor
        * wallarea
        / vacuum_variables.pres_vv_chamber_base
    ) * times_variables.t_plant_pulse_dwell ** (-vacuum_variables.outgasindex)
    # Number of pumps required for pump-down
    npumpdown = pumpdownspeed / pumpspeed

    # Combine the two (somewhat inconsistent) models
    # Note that 'npump' can be constrained by constraint equation 63
    npump = max(n_iter_vacuum_pumps, npumpdown)

    #  Output section
    if output:
        process_output.oheadr(self.outfile, "Vacuum System")
        process_output.ovarst(
            self.outfile,
            "Switch for vacuum pumping model",
            "(i_vacuum_pumping)",
            '"' + self.i_vacuum_pumping + '"',
        )
        process_output.ocmmnt(
            self.outfile,
            "Simple steady-state model with comparison to ITER cryopumps",
        )
        process_output.ovarre(
            self.outfile,
            "Plasma fuelling rate (nucleus-pairs/s)",
            "(molflow_plasma_fuelling_required)",
            physics_variables.molflow_plasma_fuelling_required,
            "OP ",
        )
        process_output.ocmmnt(
            self.outfile, "Number of high vacuum pumps, each with the throughput"
        )
        process_output.ocmmnt(
            self.outfile,
            " of one ITER cryopump (50 Pa m3 s-1 = 1.2e+22 molecules/s),",
        )
        process_output.ovarre(
            self.outfile,
            " all operating at the same time",
            "(n_iter_vacuum_pumps)",
            n_iter_vacuum_pumps,
            "OP ",
        )

        process_output.ovarre(
            self.outfile,
            "Dwell time",
            "(t_plant_pulse_dwell)",
            times_variables.t_plant_pulse_dwell,
        )
        process_output.ovarre(
            self.outfile,
            "Number of pumps required for pump-down",
            "(npumpdown)",
            npumpdown,
            "OP ",
        )
        process_output.ovarre(
            self.outfile,
            "Number of pumps required overall",
            "(npump)",
            npump,
            "OP ",
        )

    return npump

vacuum(pfusmw, r0, aw, dsol, plasma_sarea, plasma_vol, thshldo, thshldi, thtf, ritf, n_tf_coils, t_plant_pulse_dwell, nplasma, ndiv, qtorus, gasld, output)

Routine to calculate the parameters of the vacuum system

Parameters:

Name	Type	Description	Default
pfusmw	float	Fusion power (MW)	required
r0	float	Major radius (m)	required
aw	float	Minor radius (m)	required
dsol		Scrape-off layer average width (m)	required
plasma_sarea		Plasma surface area (m2)	required
plasma_vol		Plasma volume (m3)	required
thshldo		Outboard shield thickness (m)	required
thshldi		Inboard shield thickness (m)	required
thtf		TF coil thickness (m)	required
ritf		Radius of inboard TF leg point nearest plasma (m)	required
n_tf_coils		Number of TF coils	required
t_plant_pulse_dwell		Dwell time between pulses (s)	required
nplasma		Plasma density (m**-3)	required
ndiv		Number of divertors with pumping (single null = 1, double null = 2 if pumping provided at both locations)	required
qtorus		Gas load from NBI (deuterons/second)	required
gasld		Total D-T gas load (kg/s)	required
output		indicate whether output should be written to the output file, or not	required

Returns:

Type	Description
	pumpn (float) - Number of high vacuum pumps - nduct (int) - Number of ducts - dlscalc (float) - Duct-length equivalent for costing purposes (m) - mvdsh (float) - Mass of a single vacuum duct shield (kg) - dimax (float) - Diameter of passage from divertor to pumping ducts (m)

Source code in process/models/vacuum.py

def vacuum(
    self,
    pfusmw,
    r0,
    aw,
    dsol,
    plasma_sarea,
    plasma_vol,
    thshldo,
    thshldi,
    thtf,
    ritf,
    n_tf_coils,
    t_plant_pulse_dwell,
    nplasma,
    ndiv,
    qtorus,
    gasld,
    output,
):
    """Routine to calculate the parameters of the vacuum system

    Parameters
    ----------
    pfusmw : float
        Fusion power (MW)
    r0 : float
        Major radius (m)
    aw : float
        Minor radius (m)
    dsol :
        Scrape-off layer average width (m)
    plasma_sarea :
        Plasma surface area (m2)
    plasma_vol :
        Plasma volume (m3)
    thshldo :
        Outboard shield thickness (m)
    thshldi :
        Inboard shield thickness (m)
    thtf :
        TF coil thickness (m)
    ritf :
        Radius of inboard TF leg point nearest plasma (m)
    n_tf_coils :
        Number of TF coils
    t_plant_pulse_dwell :
        Dwell time between pulses (s)
    nplasma :
        Plasma density (m**-3)
    ndiv :
        Number of divertors with pumping (single null = 1, double null = 2 if pumping provided at both locations)
    qtorus :
        Gas load  from NBI (deuterons/second)
    gasld :
        Total D-T gas load (kg/s)
    output :
        indicate whether output should be written to the output file, or not


    Returns
    -------
    :
        pumpn (`float`) - Number of high vacuum pumps
        - nduct (`int`) - Number of ducts
        - dlscalc (`float`) - Duct-length equivalent for costing purposes (m)
        - mvdsh (`float`) - Mass of a single vacuum duct shield (kg)
        - dimax (`float`) -  Diameter of passage from divertor to pumping ducts (m)
    """
    k = 1.38e-23  # Boltzmann's constant (J/K)
    densh = 7900.0e0  # Density of shielding material (kg/m2)
    fsolid = 0.9e0  # Fraction of duct shielding that is solid material

    #  Pump type;
    #    i_vacuum_pump_type = 0 for turbomolecular pump (mag. bearing) with a nominal
    #              speed of 2.0 m^3/s (1.95 for N2, 1.8 for He, 1.8 for DT)
    #    i_vacuum_pump_type = 1 for compound cryopump with nominal speed of 10 m^3/s
    #              (9.0 for N2, 5.0 for He and 25. for DT)

    pfus = pfusmw * 1.0e6  # Fusion power (W)
    ntf = int(n_tf_coils)

    #  Feed rate (gas load) of D-T into chamber (pellets + gas puffing +
    #     NBI + ...) = load from fueller + load from NBI
    #  frate (kg/s) = gasld (kg/s) + qtorus (D2/s) * 6.64e-27 (kg/D2)

    frate = gasld + qtorus * 6.64e-27

    #  Set duct shield thickness to zero for no biological shielding
    #  instead of thshldo/3.0e0

    thdsh = 0.0e0

    #  Shielding (m) between duct and TF coils is scaled from inboard shield
    #  thickness

    thcsh = thshldi / 3.0e0

    #  Multiplier to convert conductance from gas species i to nitrogen
    xmult = [1.0e0, 0.423e0, 0.378e0, 0.423e0]
    # nitrogen, D-T, helium, D-T again

    nduct = ntf * ndiv

    #  Speed of high-vacuum pumps (m^3/s)

    # nitrogen, DT, helium, DT again
    sp = (
        [1.95, 1.8, 1.8, 1.8]
        if vacuum_variables.i_vacuum_pump_type == 0
        else [9.0, 25.0, 5.0, 25.0]
    )

    #  Calculate required pumping speeds

    s = []

    #  Initial pumpdown based on outgassing
    #  s(1) = net pump speed (N2) required for pumpdown to base pressure (m^3/s)
    #  area = vacuum chamber/fw area (m^2)  ;  outgassing area = 10 x area
    #  outgrat_fw = outgassing rate (effective for N2) of plasma chamber surface (Pa-m/s)
    #  pres_vv_chamber_base = base pressure (Pa)

    #  Old method: area = 4.0e0 * pi*pi * r0 * aw * sqrt(0.5e0*(1.0e0 + kappa*kappa))

    area = plasma_sarea * (aw + dsol) / aw

    ogas = vacuum_variables.outgrat_fw * area * 10.0e0  # Outgassing rate (Pa-m^3/s)
    s.append(ogas / vacuum_variables.pres_vv_chamber_base)

    #  Pumpdown between burns
    #  s(2) = net pump speed (DT) required for pumpdown between burns (m^3/s)
    #  temp_vv_chamber_gas_burn_end = temperature of neutral gas in chamber (K)
    #  t_plant_pulse_dwell = dwell time between burns (s)

    pend = (
        0.5e0 * nplasma * k * vacuum_variables.temp_vv_chamber_gas_burn_end
    )  # pressure in plasma chamber after burn (Pa)
    pstart = 0.01e0 * pend  # pressure in chamber before start of burn (Pa)

    #  Chamber volume (m^3)

    #  Old method: volume = 2.0e0 * pi*pi * r0 * aw*aw * kappa

    volume = plasma_vol * (aw + dsol) * (aw + dsol) / (aw * aw)

    #  dwell pumping options
    if (vacuum_variables.i_vac_pump_dwell == 1) or (t_plant_pulse_dwell == 0):
        tpump = times_variables.t_plant_pulse_coil_precharge
    elif vacuum_variables.i_vac_pump_dwell == 2:
        tpump = t_plant_pulse_dwell + times_variables.t_plant_pulse_coil_precharge
    else:
        tpump = t_plant_pulse_dwell

    s.append(volume / tpump * math.log(pend / pstart))

    #  Helium ash removal
    #  s(3) = net pump speed (He) required for helium ash removal (m^3/s)
    #  source = alpha production rate (pa - m^3/s)
    #  fhe = fraction of neutral gas in divertor chamber that is helium
    #  pres_div_chamber_burn = pressure in divertor chamber during burn (Pa)

    source = pfus * 1.47e-09
    fhe = source / (frate * 4.985e5)
    s.extend(
        (
            (source / vacuum_variables.pres_div_chamber_burn / fhe),
            #  Removal of dt on steady state basis
            #  s(4) = net speed (D-T) required to remove dt at fuelling rate (m^3/s)
            (
                (frate * 4.985e5 - source)
                / (vacuum_variables.pres_div_chamber_burn * (1.0e0 - fhe))
            ),
        ),
    )

    #  Calculate conductance of a single duct

    imax = 1
    cmax = 0.01e0
    pumpn = 1.0e0
    nflag = 0  # Control option if ducts are too small in x-sectional area
    #  = 1 if problem is identified in output, but run continues
    #  = 0 otherwise

    l1 = thshldo + thtf  # Length of passage from divertor to ducts (m)
    l2 = thshldo + 4.0e0  # Length of ducts from divertor passage to elbow (m)
    l3 = 2.0e0  # Length of ducts from elbow to hi-vac pumps (m)
    ltot = l1 + l2 + l3

    # ceff and d require initialising too small positive values; they're not
    # always overwritten in the following loop and can cause div by 0 errors
    # otherwise
    ceff = np.full(4, 1e-6)
    d = np.full(4, 1e-6)

    for i in range(4):
        sss = nduct / (1.0e0 / sp[i] / pumpn + 1.0e0 / cmax * xmult[i] / xmult[imax])
        if sss > s[i]:
            continue
        imax = i

        ccc = 2.0e0 * s[i] / nduct
        pumpn1 = 1.0e0 / (sp[i] * (nduct / s[i] - 1.0e0 / ccc))
        pumpn2 = 1.01e0 * s[i] / (sp[i] * nduct)
        pumpn = max(pumpn, pumpn1, pumpn2)
        ceff[i] = 1.0e0 / (nduct / s[i] - 1.0e0 / (sp[i] * pumpn))

        #  Newton's method solution for duct diameter
        while True:
            d[i] = 1.0e0

            for _ in range(100):
                a1 = (
                    0.25e0 * math.pi * d[i] * d[i]
                )  # Area of aperture and duct (m^2)
                a2 = 1.44e0 * a1
                a3 = a2
                k1 = 4.0e0 / 3.0e0 * d[i] / (l1 + 4.0e0 / 3.0e0 * d[i])
                k2 = (
                    4.0e0
                    / 3.0e0
                    * d[i]
                    * 1.2e0
                    / (l2 + 4.0e0 / 3.0e0 * d[i] * 1.2e0)
                )
                k3 = (
                    4.0e0
                    / 3.0e0
                    * d[i]
                    * 1.2e0
                    / (l3 + 4.0e0 / 3.0e0 * d[i] * 1.2e0)
                )
                cap = 119.0e0 * a1 / xmult[i]
                dcap = 2.0e0 * cap / d[i]
                c1 = 119.0e0 * a1 * k1 / xmult[i]
                dc1 = c1 / d[i] * (3.0e0 - k1)
                c2 = 119.0e0 * a2 * k2 / xmult[i]
                dc2 = c2 / d[i] / 1.2e0 * (3.0e0 - k2)
                c3 = 119.0e0 * a3 * k3 / xmult[i]
                dc3 = c3 / d[i] / 1.2e0 * (3.0e0 - k3)
                cnew = 1.0e0 / (1.0e0 / cap + 1.0e0 / c1 + 1.0e0 / c2 + 1.0e0 / c3)
                y = -ceff[i] + cnew
                dy = (
                    cnew
                    * cnew
                    * (
                        dcap / cap / cap
                        + dc1 / c1 / c1
                        + dc2 / c2 / c2
                        + dc3 / c3 / c3
                    )
                )
                dnew = d[i] - y / dy
                dd = abs((d[i] - dnew) / d[i])
                d[i] = dnew
                if dd <= 0.01e0:
                    break

            else:
                logger.error(
                    f"Newton's method not converging; check fusion power, te {physics_variables.p_fusion_total_mw=} {physics_variables.temp_plasma_electron_vol_avg_kev=}"
                )

            theta = math.pi / ntf

            #  Area between adjacent TF coils available for pump ducts
            #  ritf = outer radius of inboard leg of TF coil (m)

            a1max = (r0 + aw - ritf - thcsh / math.tan(theta)) ** 2 * math.tan(theta)
            d1max = math.sqrt(4.0e0 * a1max / math.pi)  # Equivalent diameter
            if a1 < a1max:
                break

            ceff[i] = 0.9e0 * ceff[i]
            if ceff[i] <= (1.1e0 * s[i]):
                #  Ducts are not big enough. Flag and continue.
                nflag = 1
                break

        cmax = ceff[i]

    pumpn = pumpn * nduct

    #  d[imax]= diameter of passage from divertor to pumping ducts (m)
    #  dout    = diameter of ducts from passage to hi-vac pumps (m)

    dout = d[imax] * 1.2e0

    #  Net pumping speeds provided by vacuum pumping system
    #  snet(1) - net pump speed (N2) provided (m^3/s)
    #  snet(2) - net pump speed (D-T) provided (m^3/s)
    #  snet(3) - net pump speed (He) provided (m^3/s)
    #  snet(4) - snet(2)
    snet = []
    for i in range(4):
        ceff1 = ceff[imax] * nduct
        snet.append(
            1.0e0
            / (1.0e0 / (ceff1 * xmult[imax] / xmult[i]) + 1.0e0 / sp[i] / pumpn)
        )

    #  If cryopumps are used then an additional pump is required
    #  for continuous operation with regeneration.

    if vacuum_variables.i_vacuum_pump_type == 1:
        pumpn = pumpn * 2.0e0

    #  Information for costing routine

    dlscalc = l1 * d[imax] ** 1.4e0 + (ltot - l1) * (d[imax] * 1.2e0) ** 1.4e0

    #  Mass of duct shielding

    arsh = (
        0.25e0 * math.pi * ((d[imax] * 1.2e0 + thdsh) ** 2 - (d[imax] * 1.2e0) ** 2)
    )
    mvdsh = arsh * (ltot - l1) * densh * fsolid

    dimax = d[imax]

    if output:
        #  Output section

        process_output.oheadr(self.outfile, "Vacuum System")

        process_output.ocmmnt(self.outfile, "Pumpdown to Base Pressure :")
        process_output.oblnkl(self.outfile)
        process_output.ovarre(
            self.outfile,
            "First wall outgassing rate (Pa m/s)",
            "(outgrat_fw)",
            vacuum_variables.outgrat_fw,
        )
        process_output.ovarre(
            self.outfile, "Total outgassing load (Pa m3/s)", "(ogas)", ogas, "OP "
        )
        process_output.ovarre(
            self.outfile,
            "Base pressure required (Pa)",
            "(pres_vv_chamber_base)",
            vacuum_variables.pres_vv_chamber_base,
        )
        process_output.ovarre(
            self.outfile, "Required N2 pump speed (m3/s)", "(s(1))", s[0], "OP "
        )
        process_output.ovarre(
            self.outfile,
            "N2 pump speed provided (m3/s)",
            "(snet(1))",
            snet[0],
            "OP ",
        )

        process_output.osubhd(self.outfile, "Pumpdown between Burns :")
        process_output.ovarre(
            self.outfile, "Plasma chamber volume (m3)", "(volume)", volume, "OP "
        )
        process_output.ovarre(
            self.outfile, "Chamber pressure after burn (Pa)", "(pend)", pend, "OP "
        )
        process_output.ovarre(
            self.outfile, "Chamber pressure before burn (Pa)", "(pstart)", pstart
        )
        process_output.ovarin(
            self.outfile,
            "Allowable pumping time switch",
            "(i_vac_pump_dwell)",
            vacuum_variables.i_vac_pump_dwell,
        )
        process_output.ovarre(
            self.outfile,
            "Dwell time between burns (s)",
            "(t_plant_pulse_dwell.)",
            t_plant_pulse_dwell,
        )
        process_output.ovarre(
            self.outfile,
            "CS ramp-up time burns (s)",
            "(t_plant_pulse_coil_precharge.)",
            times_variables.t_plant_pulse_coil_precharge,
        )
        process_output.ovarre(
            self.outfile,
            "Allowable pumping time between burns (s)",
            "(tpump)",
            tpump,
        )
        process_output.ovarre(
            self.outfile, "Required D-T pump speed (m3/s)", "(s(2))", s[1], "OP "
        )
        process_output.ovarre(
            self.outfile,
            "D-T pump speed provided (m3/s)",
            "(snet(2))",
            snet[1],
            "OP ",
        )

        process_output.osubhd(self.outfile, "Helium Ash Removal :")
        process_output.ovarre(
            self.outfile,
            "Divertor chamber gas pressure (Pa)",
            "(pres_div_chamber_burn)",
            vacuum_variables.pres_div_chamber_burn,
        )
        process_output.ovarre(
            self.outfile,
            "Helium gas fraction in divertor chamber",
            "(fhe)",
            fhe,
            "OP ",
        )
        process_output.ovarre(
            self.outfile, "Required helium pump speed (m3/s)", "(s(3))", s[2], "OP "
        )
        process_output.ovarre(
            self.outfile,
            "Helium pump speed provided (m3/s)",
            "(snet(3))",
            snet[2],
            "OP ",
        )

        process_output.osubhd(self.outfile, "D-T Removal at Fuelling Rate :")
        process_output.ovarre(
            self.outfile, "D-T fuelling rate (kg/s)", "(frate)", frate, "OP "
        )
        process_output.ovarre(
            self.outfile, "Required D-T pump speed (m3/s)", "(s(4))", s[3], "OP "
        )
        process_output.ovarre(
            self.outfile,
            "D-T pump speed provided (m3/s)",
            "(snet(4))",
            snet[3],
            "OP ",
        )

        if nflag == 1:
            process_output.oblnkl(self.outfile)
            process_output.ocmmnt(
                self.outfile, "Vacuum pumping ducts are space limited."
            )
            process_output.ocmmnt(
                self.outfile, f"Maximum duct diameter is only {d1max} m"
            )
            process_output.ocmmnt(self.outfile, "Conductance is inadequate.")
            process_output.oblnkl(self.outfile)

        i_fw_blkt_shared_coolant = (
            "cryo " if vacuum_variables.i_vacuum_pump_type == 1 else "turbo"
        )

        process_output.oblnkl(self.outfile)
        process_output.ocmmnt(
            self.outfile, "The vacuum pumping system size is governed by the"
        )

        if imax == 1:
            process_output.ocmmnt(
                self.outfile, "requirements for pumpdown to base pressure."
            )
        elif imax == 2:
            process_output.ocmmnt(
                self.outfile, "requirements for pumpdown between burns."
            )
        elif imax == 3:
            process_output.ocmmnt(
                self.outfile, "requirements for helium ash removal."
            )
        else:
            process_output.ocmmnt(
                self.outfile, "requirements for D-T removal at fuelling rate."
            )

        process_output.oblnkl(self.outfile)
        process_output.ovarin(
            self.outfile, "Number of large pump ducts", "(nduct)", nduct
        )
        process_output.ovarre(
            self.outfile,
            "Passage diameter, divertor to ducts (m)",
            "(d(imax))",
            d[imax],
            "OP ",
        )
        process_output.ovarre(self.outfile, "Passage length (m)", "(l1)", l1, "OP ")
        process_output.ovarre(
            self.outfile, "Diameter of ducts (m)", "(dout)", dout, "OP "
        )

        process_output.ovarre(
            self.outfile, "Duct length, divertor to elbow (m)", "(l2)", l2, "OP "
        )
        process_output.ovarre(
            self.outfile, "Duct length, elbow to pumps (m)", "(l3)", l3
        )
        process_output.ovarre(
            self.outfile, "Number of pumps", "(pumpn)", pumpn, "OP "
        )
        process_output.oblnkl(self.outfile)
        process_output.ocmmnt(
            self.outfile,
            f"The vacuum system uses {i_fw_blkt_shared_coolant} pumps.",
        )

    return pumpn, nduct, dlscalc, mvdsh, dimax

VacuumVessel

Class containing vacuum vessel routines

Source code in process/models/vacuum.py

class VacuumVessel:
    """Class containing vacuum vessel routines"""

    def __init__(self):
        self.outfile = constants.NOUT

    def run(self):
        blanket_library.dz_vv_half = self.calculate_vessel_half_height(
            z_tf_inside_half=build_variables.z_tf_inside_half,
            dz_shld_vv_gap=build_variables.dz_shld_vv_gap,
            dz_vv_lower=build_variables.dz_vv_lower,
            n_divertors=divertor_variables.n_divertors,
            dz_blkt_upper=build_variables.dz_blkt_upper,
            dz_shld_upper=build_variables.dz_shld_upper,
            z_plasma_xpoint_upper=build_variables.z_plasma_xpoint_upper,
            dr_fw_plasma_gap_inboard=build_variables.dr_fw_plasma_gap_inboard,
            dr_fw_plasma_gap_outboard=build_variables.dr_fw_plasma_gap_outboard,
            dr_fw_inboard=build_variables.dr_fw_inboard,
            dr_fw_outboard=build_variables.dr_fw_outboard,
        )
        # D-shaped blanket and shield
        if physics_variables.itart == 1 or fwbs_variables.i_fw_blkt_vv_shape == 1:
            (
                blanket_library.vol_vv_inboard,
                blanket_library.vol_vv_outboard,
                fwbs_variables.vol_vv,
            ) = self.calculate_dshaped_vessel_volumes(
                r_shld_inboard_inner=build_variables.r_shld_inboard_inner,
                r_shld_outboard_outer=build_variables.r_shld_outboard_outer,
                dz_vv_half=blanket_library.dz_vv_half,
                dr_vv_inboard=build_variables.dr_vv_inboard,
                dr_vv_outboard=build_variables.dr_vv_outboard,
                dz_vv_upper=build_variables.dz_vv_upper,
                dz_vv_lower=build_variables.dz_vv_lower,
            )
        else:
            (
                blanket_library.vol_vv_inboard,
                blanket_library.vol_vv_outboard,
                fwbs_variables.vol_vv,
            ) = self.calculate_elliptical_vessel_volumes(
                rmajor=physics_variables.rmajor,
                rminor=physics_variables.rminor,
                triang=physics_variables.triang,
                r_shld_inboard_inner=build_variables.r_shld_inboard_inner,
                r_shld_outboard_outer=build_variables.r_shld_outboard_outer,
                dz_vv_half=blanket_library.dz_vv_half,
                dr_vv_inboard=build_variables.dr_vv_inboard,
                dr_vv_outboard=build_variables.dr_vv_outboard,
                dz_vv_upper=build_variables.dz_vv_upper,
                dz_vv_lower=build_variables.dz_vv_lower,
            )

        # Apply vacuum vessel coverage factor
        # moved from dshaped_* and elliptical_* to keep coverage factor
        # changes in the same location.
        fwbs_variables.vol_vv = fwbs_variables.fvoldw * fwbs_variables.vol_vv

        # Vacuum vessel mass (kg)
        fwbs_variables.m_vv = fwbs_variables.vol_vv * fwbs_variables.den_steel

    @staticmethod
    def calculate_vessel_half_height(
        z_tf_inside_half: float,
        dz_shld_vv_gap: float,
        dz_vv_lower: float,
        n_divertors: int,
        dz_blkt_upper: float,
        dz_shld_upper: float,
        z_plasma_xpoint_upper: float,
        dr_fw_plasma_gap_inboard: float,
        dr_fw_plasma_gap_outboard: float,
        dr_fw_inboard: float,
        dr_fw_outboard: float,
    ) -> float:
        """Calculate vacuum vessel internal half-height (m)

        Parameters
        ----------
        z_tf_inside_half:

        dz_shld_vv_gap:

        dz_vv_lower:

        n_divertors: int :

        dz_blkt_upper:

        dz_shld_upper:

        z_plasma_xpoint_upper:

        dr_fw_plasma_gap_inboard:

        dr_fw_plasma_gap_outboard:

        dr_fw_inboard:

        dr_fw_outboard:

        """

        z_bottom = z_tf_inside_half - dz_shld_vv_gap - dz_vv_lower

        # Calculate component internal upper half-height (m)
        # If a double null machine then symmetric
        if n_divertors == 2:
            z_top = z_bottom
        else:
            z_top = z_plasma_xpoint_upper + 0.5 * (
                dr_fw_plasma_gap_inboard
                + dr_fw_plasma_gap_outboard
                + dr_fw_inboard
                + dr_fw_outboard
            )

            z_top = z_top + dz_blkt_upper + dz_shld_upper

        # Average of top and bottom (m)
        return 0.5 * (z_top + z_bottom)

    @staticmethod
    def calculate_dshaped_vessel_volumes(
        r_shld_inboard_inner: float,
        r_shld_outboard_outer: float,
        dz_vv_half: float,
        dr_vv_inboard: float,
        dr_vv_outboard: float,
        dz_vv_upper: float,
        dz_vv_lower: float,
    ) -> tuple[float, float, float]:
        """Calculate volumes of D-shaped vacuum vessel segments

        Parameters
        ----------
        r_shld_inboard_inner:

        r_shld_outboard_outer:

        dz_vv_half:

        dr_vv_inboard:

        dr_vv_outboard:

        dz_vv_upper:

        dz_vv_lower:

        """

        r_1 = r_shld_inboard_inner
        r_2 = r_shld_outboard_outer - r_1

        (
            vol_vv_inboard,
            vol_vv_outboard,
            vol_vv,
        ) = dshellvol(
            rmajor=r_1,
            rminor=r_2,
            zminor=dz_vv_half,
            drin=dr_vv_inboard,
            drout=dr_vv_outboard,
            dz=(dz_vv_upper + dz_vv_lower) / 2,
        )

        return vol_vv_inboard, vol_vv_outboard, vol_vv

    @staticmethod
    def calculate_elliptical_vessel_volumes(
        rmajor: float,
        rminor: float,
        triang: float,
        r_shld_inboard_inner: float,
        r_shld_outboard_outer: float,
        dz_vv_half: float,
        dr_vv_inboard: float,
        dr_vv_outboard: float,
        dz_vv_upper: float,
        dz_vv_lower: float,
    ) -> tuple[float, float, float]:
        """Calculate volumes of elliptical vacuum vessel segments

        Parameters
        ----------
        rmajor:

        rminor:

        triang:

        r_shld_inboard_inner:

        r_shld_outboard_outer:

        dz_vv_half:

        dr_vv_inboard:

        dr_vv_outboard:

        dz_vv_upper:

        dz_vv_lower:

        """
        # Major radius to centre of inboard and outboard ellipses (m)
        # (coincident in radius with top of plasma)
        r_1 = rmajor - rminor * triang

        # Calculate distance between r1 and outer edge of inboard ...
        # ... section (m)
        r_2 = r_1 - r_shld_inboard_inner
        r_3 = r_shld_outboard_outer - r_1

        (
            vol_vv_inboard,
            vol_vv_outboard,
            vol_vv,
        ) = eshellvol(
            r_1,
            r_2,
            r_3,
            dz_vv_half,
            dr_vv_inboard,
            dr_vv_outboard,
            (dz_vv_upper + dz_vv_lower) / 2,
        )
        return vol_vv_inboard, vol_vv_outboard, vol_vv

    def output_vv_areas_and_volumes(self):
        """Output shield areas and volumes to log."""

        po.oheadr(self.outfile, "Vacuum Vessel Areas and Volumes")

        po.ovarrf(
            self.outfile,
            "Volume of inboard vacuum vessel (m^3)",
            "(vol_vv_inboard)",
            blanket_library.vol_vv_inboard,
            "OP ",
        )
        po.ovarrf(
            self.outfile,
            "Volume of outboard vacuum vessel (m^3)",
            "(vol_vv_outboard)",
            blanket_library.vol_vv_outboard,
            "OP ",
        )
        po.ovarrf(
            self.outfile,
            "Total volume of vacuum vessel (m^3)",
            "(vol_vv)",
            fwbs_variables.vol_vv,
            "OP ",
        )

outfile = constants.NOUT instance-attribute

run()

Source code in process/models/vacuum.py

def run(self):
    blanket_library.dz_vv_half = self.calculate_vessel_half_height(
        z_tf_inside_half=build_variables.z_tf_inside_half,
        dz_shld_vv_gap=build_variables.dz_shld_vv_gap,
        dz_vv_lower=build_variables.dz_vv_lower,
        n_divertors=divertor_variables.n_divertors,
        dz_blkt_upper=build_variables.dz_blkt_upper,
        dz_shld_upper=build_variables.dz_shld_upper,
        z_plasma_xpoint_upper=build_variables.z_plasma_xpoint_upper,
        dr_fw_plasma_gap_inboard=build_variables.dr_fw_plasma_gap_inboard,
        dr_fw_plasma_gap_outboard=build_variables.dr_fw_plasma_gap_outboard,
        dr_fw_inboard=build_variables.dr_fw_inboard,
        dr_fw_outboard=build_variables.dr_fw_outboard,
    )
    # D-shaped blanket and shield
    if physics_variables.itart == 1 or fwbs_variables.i_fw_blkt_vv_shape == 1:
        (
            blanket_library.vol_vv_inboard,
            blanket_library.vol_vv_outboard,
            fwbs_variables.vol_vv,
        ) = self.calculate_dshaped_vessel_volumes(
            r_shld_inboard_inner=build_variables.r_shld_inboard_inner,
            r_shld_outboard_outer=build_variables.r_shld_outboard_outer,
            dz_vv_half=blanket_library.dz_vv_half,
            dr_vv_inboard=build_variables.dr_vv_inboard,
            dr_vv_outboard=build_variables.dr_vv_outboard,
            dz_vv_upper=build_variables.dz_vv_upper,
            dz_vv_lower=build_variables.dz_vv_lower,
        )
    else:
        (
            blanket_library.vol_vv_inboard,
            blanket_library.vol_vv_outboard,
            fwbs_variables.vol_vv,
        ) = self.calculate_elliptical_vessel_volumes(
            rmajor=physics_variables.rmajor,
            rminor=physics_variables.rminor,
            triang=physics_variables.triang,
            r_shld_inboard_inner=build_variables.r_shld_inboard_inner,
            r_shld_outboard_outer=build_variables.r_shld_outboard_outer,
            dz_vv_half=blanket_library.dz_vv_half,
            dr_vv_inboard=build_variables.dr_vv_inboard,
            dr_vv_outboard=build_variables.dr_vv_outboard,
            dz_vv_upper=build_variables.dz_vv_upper,
            dz_vv_lower=build_variables.dz_vv_lower,
        )

    # Apply vacuum vessel coverage factor
    # moved from dshaped_* and elliptical_* to keep coverage factor
    # changes in the same location.
    fwbs_variables.vol_vv = fwbs_variables.fvoldw * fwbs_variables.vol_vv

    # Vacuum vessel mass (kg)
    fwbs_variables.m_vv = fwbs_variables.vol_vv * fwbs_variables.den_steel

calculate_vessel_half_height(z_tf_inside_half, dz_shld_vv_gap, dz_vv_lower, n_divertors, dz_blkt_upper, dz_shld_upper, z_plasma_xpoint_upper, dr_fw_plasma_gap_inboard, dr_fw_plasma_gap_outboard, dr_fw_inboard, dr_fw_outboard) staticmethod

Calculate vacuum vessel internal half-height (m)

Parameters:

Name	Type	Description	Default
z_tf_inside_half	float		required
dz_shld_vv_gap	float		required
dz_vv_lower	float		required
n_divertors	int		required
dz_blkt_upper	float		required
dz_shld_upper	float		required
z_plasma_xpoint_upper	float		required
dr_fw_plasma_gap_inboard	float		required
dr_fw_plasma_gap_outboard	float		required
dr_fw_inboard	float		required
dr_fw_outboard	float		required

Source code in process/models/vacuum.py

@staticmethod
def calculate_vessel_half_height(
    z_tf_inside_half: float,
    dz_shld_vv_gap: float,
    dz_vv_lower: float,
    n_divertors: int,
    dz_blkt_upper: float,
    dz_shld_upper: float,
    z_plasma_xpoint_upper: float,
    dr_fw_plasma_gap_inboard: float,
    dr_fw_plasma_gap_outboard: float,
    dr_fw_inboard: float,
    dr_fw_outboard: float,
) -> float:
    """Calculate vacuum vessel internal half-height (m)

    Parameters
    ----------
    z_tf_inside_half:

    dz_shld_vv_gap:

    dz_vv_lower:

    n_divertors: int :

    dz_blkt_upper:

    dz_shld_upper:

    z_plasma_xpoint_upper:

    dr_fw_plasma_gap_inboard:

    dr_fw_plasma_gap_outboard:

    dr_fw_inboard:

    dr_fw_outboard:

    """

    z_bottom = z_tf_inside_half - dz_shld_vv_gap - dz_vv_lower

    # Calculate component internal upper half-height (m)
    # If a double null machine then symmetric
    if n_divertors == 2:
        z_top = z_bottom
    else:
        z_top = z_plasma_xpoint_upper + 0.5 * (
            dr_fw_plasma_gap_inboard
            + dr_fw_plasma_gap_outboard
            + dr_fw_inboard
            + dr_fw_outboard
        )

        z_top = z_top + dz_blkt_upper + dz_shld_upper

    # Average of top and bottom (m)
    return 0.5 * (z_top + z_bottom)

calculate_dshaped_vessel_volumes(r_shld_inboard_inner, r_shld_outboard_outer, dz_vv_half, dr_vv_inboard, dr_vv_outboard, dz_vv_upper, dz_vv_lower) staticmethod

Calculate volumes of D-shaped vacuum vessel segments

Parameters:

Name	Type	Description	Default
r_shld_inboard_inner	float		required
r_shld_outboard_outer	float		required
dz_vv_half	float		required
dr_vv_inboard	float		required
dr_vv_outboard	float		required
dz_vv_upper	float		required
dz_vv_lower	float		required

Source code in process/models/vacuum.py

@staticmethod
def calculate_dshaped_vessel_volumes(
    r_shld_inboard_inner: float,
    r_shld_outboard_outer: float,
    dz_vv_half: float,
    dr_vv_inboard: float,
    dr_vv_outboard: float,
    dz_vv_upper: float,
    dz_vv_lower: float,
) -> tuple[float, float, float]:
    """Calculate volumes of D-shaped vacuum vessel segments

    Parameters
    ----------
    r_shld_inboard_inner:

    r_shld_outboard_outer:

    dz_vv_half:

    dr_vv_inboard:

    dr_vv_outboard:

    dz_vv_upper:

    dz_vv_lower:

    """

    r_1 = r_shld_inboard_inner
    r_2 = r_shld_outboard_outer - r_1

    (
        vol_vv_inboard,
        vol_vv_outboard,
        vol_vv,
    ) = dshellvol(
        rmajor=r_1,
        rminor=r_2,
        zminor=dz_vv_half,
        drin=dr_vv_inboard,
        drout=dr_vv_outboard,
        dz=(dz_vv_upper + dz_vv_lower) / 2,
    )

    return vol_vv_inboard, vol_vv_outboard, vol_vv

calculate_elliptical_vessel_volumes(rmajor, rminor, triang, r_shld_inboard_inner, r_shld_outboard_outer, dz_vv_half, dr_vv_inboard, dr_vv_outboard, dz_vv_upper, dz_vv_lower) staticmethod

Calculate volumes of elliptical vacuum vessel segments

Parameters:

Name	Type	Description	Default
rmajor	float		required
rminor	float		required
triang	float		required
r_shld_inboard_inner	float		required
r_shld_outboard_outer	float		required
dz_vv_half	float		required
dr_vv_inboard	float		required
dr_vv_outboard	float		required
dz_vv_upper	float		required
dz_vv_lower	float		required

Source code in process/models/vacuum.py

@staticmethod
def calculate_elliptical_vessel_volumes(
    rmajor: float,
    rminor: float,
    triang: float,
    r_shld_inboard_inner: float,
    r_shld_outboard_outer: float,
    dz_vv_half: float,
    dr_vv_inboard: float,
    dr_vv_outboard: float,
    dz_vv_upper: float,
    dz_vv_lower: float,
) -> tuple[float, float, float]:
    """Calculate volumes of elliptical vacuum vessel segments

    Parameters
    ----------
    rmajor:

    rminor:

    triang:

    r_shld_inboard_inner:

    r_shld_outboard_outer:

    dz_vv_half:

    dr_vv_inboard:

    dr_vv_outboard:

    dz_vv_upper:

    dz_vv_lower:

    """
    # Major radius to centre of inboard and outboard ellipses (m)
    # (coincident in radius with top of plasma)
    r_1 = rmajor - rminor * triang

    # Calculate distance between r1 and outer edge of inboard ...
    # ... section (m)
    r_2 = r_1 - r_shld_inboard_inner
    r_3 = r_shld_outboard_outer - r_1

    (
        vol_vv_inboard,
        vol_vv_outboard,
        vol_vv,
    ) = eshellvol(
        r_1,
        r_2,
        r_3,
        dz_vv_half,
        dr_vv_inboard,
        dr_vv_outboard,
        (dz_vv_upper + dz_vv_lower) / 2,
    )
    return vol_vv_inboard, vol_vv_outboard, vol_vv

output_vv_areas_and_volumes()

Output shield areas and volumes to log.

Source code in process/models/vacuum.py

def output_vv_areas_and_volumes(self):
    """Output shield areas and volumes to log."""

    po.oheadr(self.outfile, "Vacuum Vessel Areas and Volumes")

    po.ovarrf(
        self.outfile,
        "Volume of inboard vacuum vessel (m^3)",
        "(vol_vv_inboard)",
        blanket_library.vol_vv_inboard,
        "OP ",
    )
    po.ovarrf(
        self.outfile,
        "Volume of outboard vacuum vessel (m^3)",
        "(vol_vv_outboard)",
        blanket_library.vol_vv_outboard,
        "OP ",
    )
    po.ovarrf(
        self.outfile,
        "Total volume of vacuum vessel (m^3)",
        "(vol_vv)",
        fwbs_variables.vol_vv,
        "OP ",
    )