- Email: [email protected]
Optimization of high heat flux components for DIII-D neutral beam upgrades
Fusion Engineering and Design 146 (2019) 1233–1236
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Optimization of high heat flux components for DIII-D neutral beam upgrades a,⁎
a
a
a
a
T
a
Andrei Khodak , Irving Zatz , Wenping Wang , Alex Finehart , Yury Malament , Alex Nagy , Peter Titusa, Raffi Nazikiana, Tim Scovilleb a b
Princeton Plasma Physics Laboratory, Princeton, United States General Atomics, San Diego, United States
A R T I C LE I N FO
A B S T R A C T
Keywords: Neutral beam Fusion device Numerical analysis Heat load mitigation
Upgrade of the DIII-D neutral beams leads to enhanced heat loads on many components, such as calorimeter, collimator, and pole shields which protect neutral beam magnets. Power increase from 2.6 MW to 3.2 MW per source leads to a normal heat flux loads of up to 55 MW/m2 for the calorimeter. The Princeton Plasma Physics Laboratory is responsible for the design and manufacturing of the upgrades of these components. Heat flux distribution on neutral beam components is very uneven and leads to significant thermal stresses. High heat flux density impact requires surface optimization to reduce surface heat flux projection, and avoid localized melting. Several new design features were introduced to accommodate increased heat loads, such as molybdenum inserts for the pole shields, two-dimensional shaping for the calorimeter, and three-dimensional shape optimization and replaceable copper inserts for the collimator. Additionally, all three components include an optimized cooling system design featuring peripheral cooling of copper components. The optimization process included applying analytical relations for the transient temperature distributions on the high heat flux components. These relations were confirmed by previous DIII-D experimental results. To validate the designs, numerical simulations were performed. Results of the design optimization and numerical simulations will be presented.
1. Introduction
power. New requirements call for neutral beam power to 3.2 MW increasing thermal load on the neutral beam. Thus redesign of the pole shields was needed to withstand elevated load and remove excessive heat without melting. Design of the pole shield upgrade is described in detail in [1]. It includes molybdenum insert in the original copper plate. Removable insert is positioned in the area of the highest heat flux.
Upgrades for DIII-D neutral beams designed by PPPL are presented on Fig. 1. The upgrades include: new pole shields [1], calorimeter, and absolute collimator [2]. These upgrades allowed neutral beam power increase from 2.6 MW to 3.2 MW per source. Common features defining the design of these devices are: pulsed high heat flux impact, uneven spatial distribution of the heat load, reliance on water cooling system. These aspects defined the design features common for each of the upgrade: geometrical shaping, uneven heat load accommodation, and peripheral cooling system design, which will be described in detail for each upgraded component in the following sections. 2. Geometrical shaping 2.1. Pole shields Water cooled 12.7 mm thick copper pole shields were used in DIII-D neutral beams original design. Theses pole shields showed localized melting and fatigue cracks during the operation with 2.6 MW maximum
⁎
2.2. Calorimeter Copper is chosen for the upgraded calorimeter plates, which is the same material used in the original plates. The upgraded calorimeter should be capable to withstand a spectrum of pulses up to 6.3 MW per beam source. The requirement is to determine the maximum pulse lengths the calorimeter can withstand for each level of loading to qualify the calorimeter for a 100,000 cycle minimum design fatigue life. Additionally, a maximum pulse length will also be determined for a 7.5 MW pulse. Accordingly, a maximum front surface plate temperature that can achieve the desired life will be calculated. Cooling needs to be sufficient to permit a 3 min repetition rate for the spectrum of defined
Corresponding author. E-mail address: [email protected] (A. Khodak).
https://doi.org/10.1016/j.fusengdes.2019.02.047 Received 8 October 2018; Received in revised form 9 February 2019; Accepted 11 February 2019 Available online 05 March 2019 0920-3796/ Published by Elsevier B.V.
Fusion Engineering and Design 146 (2019) 1233–1236
A. Khodak, et al.
Fig. 1. DIII-D Neutral beam upgrades designed by PPPL.
3. Heat load accommodation
pulses. The repetition rate will also be determined for the aforementioned 7.5 MW pulse (which can exceed 3 min). Original calorimeter model had two opening angles of the heated surface leading to excessive heat flux on the front areas of the calorimeter. Changing the model to one opening angle allowed 20% reduction of the peak temperature as shown on Fig. 2. New plates were designed to fit into the same mounting halls, so original bracket design can be used.
3.1. Pole shields Ten segment molybdenum insert is fitted into the pole shield copper plate using loose tongue and groove pattern. 0.254 mm gaps between the segments, and between the segments and the plate, accommodate deformation of the segments due to non-uniform thermal expansion. Analysis of this design presented in [1] shows significant reduction of thermal stresses due to loose segmented design. At this point four pole shields are installed and operated for a year. Inspection of the pole shields, revealed no visible change. Fig. 3 shows one of the pole shields in the neutral beam opened for the planned maintenance, after a year of successful operation
2.3. Collimator DIII-D Neutral beam collimator was designed to shape two neutral beams at 4.33° each. Initial shape is modified to accommodate peak heat loads at an angle. So heat flux is spread over the surface. Threedimensional shape optimization allowed using copper for high heat flux areas. Interchangeable inserts are designed to reduce stresses. Details of the design are presented in [2].
3.2. Heat load accommodation In the pulsed operation heating of the calorimeter plate can be estimated using relations for the semi-infinite domain presented on Fig. 4: ∂T
ρcp ∂t =
∂q ; ∂x
∂T
q = − λ ∂x
(1)
where: T [℃] – temperature; q [W /m2] – heat flux; λ[W /(mK )] – thermal conductivity; cp [J /(kgK )] – heat capacity; ρ [kg /m3] – density; t [s] – time; x [m] – distance from the wall. Solution of (1) for constant heat flux can be found in [3]:
Fig. 2. Calorimeter plate shape modification.
Fig. 3. Installed pole shield after a year of operation. 1234
Fusion Engineering and Design 146 (2019) 1233–1236
A. Khodak, et al.
Fig. 4. Semi-infinite domain heating.
2 q π w
T − T0 =
x −⎛ 2 ⎝ ⎜
t ⎛ x exp ⎜⎛−⎛ λρcp ⎜ 2 ⎝ ⎝ ⎝ ⎜
ρcp ⎞ ⎟
λt ⎠
x erfc ⎜⎛ ⎛ 2 ⎝⎝ ⎜
ρcp ⎞2⎞ ⎟
⎟
λt ⎠ ⎠
ρcp ⎞ ⎞ ⎞ ⎟ λt ⎠ ⎠ ⎟ ⎠ ⎟
(2)
Fig. 6. Damage observed on GA calorimeter plates.
For wall temperature at x = 0 :
Tw − T0 =
2 q π w
Tc =
t λρcp
(3)
⎛x −⎜ 2 ⎝
Formula (3) was used in [4] to get limiting temperature of copper as shown on Fig. 5. Fig. 5 also shows GA shots data superimposed on the melting curves. Several shots exceeded melting conditions leading to some damage of the calorimeter plates as shown on Fig. 6. Formula (3) with copper properties was used as a guidance to determine calorimeter pulse power and duration. Assuming almost semi-infinite domain heating during the pulse, strain range is close to thermal strain range. At each pulse strain range is proportional to the peak surface temperature:
Δε ∼ α (Tw − T0) =
2α q π w
t λρcp
t − tp ⎛ ⎛ ⎛x exp ⎜−⎜ λρcp ⎜ 2 ⎝ ⎝ ⎝ ρcp ⎛⎛ x ⎞ erfc ⎜ ⎜ λ (t − tp ) ⎟ 2 ⎠ ⎝⎝
ρcp
2
⎞⎞ λ (t − tp ) ⎟ ⎟ ⎠⎠ ρcp ⎞⎞⎞ ; t > tp λ (t − tp ) ⎟ ⎟ ⎟ ⎠⎠⎠
(6)
Total thermal solution can found by adding (2) and (6) which for the wall x = 0 gives:
Tt − T0 =
2qw πλρcp
( t −
max (t − tp, 0) ) (7)
Temperature distributions presented on Fig. 7 shows that formula (7) allows accurate estimation of maximum wall temperature of the calorimeter during cooling period as well as the pulse itself
(4)
3.3. Collimator
Strain range obtained using relation (5) was used to define fatigue cycle limits of the design for various levels of pulse power and duration. Semi-infinite domain heating assumption can be expanded to the cooling period after the pulse. For the pulse of duration tp assume additional problem with
qwc = −qw ; t > tp
2 q π wc
As in the pole shields design collimator inserts we attached using loose tongue and groove pattern. 0.254 mm gaps between the inserts and the main body, accommodate deformation of the segments due to non-uniform thermal expansion. Analysis of this design presented in [2] shows significant reduction of thermal stresses due to loose segmented design.
(5)
4. Cooling system
Solution for the setup (5) can be found using the same procedure described in [3]:
4.1. Pole shields Cooling system of the pole shields includes a stainless steel tube
Fig. 5. Strongly focused GA ion source shots since 2009 Superimposed on melting of different materials depending on heat flux and pulse duration [4].
Fig. 7. Calorimeter cooling system with four straight gun drilled holes and four plugs. 1235
Fusion Engineering and Design 146 (2019) 1233–1236
A. Khodak, et al.
the new collimator design, with only minor changes. It includes stainless still conduit routed at the periphery of the main collimator frame. Analysis presented in [2] confirmed efficiency of such system. 5. Conclusions Geometrical shaping of the modified neutral beam components, allowed qualification at elevated requirements, by redistributing heat load on the wider surface area for calorimeter and collimator, or by positioning molybdenum insert in the high heat flux zone. For the pulsed device semi-infinite domain solution provide accurate estimation for the peak temperature and strain in the heated component, allowing fatigue assessment for different pulse power. Gaps between the components, allowed relieve of the stresses due to different thermal expansion. Peripheral channel routing creates robust and efficient cooling system. In all upgraded component this system relies on high thermal conductivity copper, and leads to thermal stress reduction.
Fig. 8. Calorimeter cooling system with four straight gun drilled holes and four plugs.
embedded into a pole shield copper plate groove using plasma spraying. Major design feature of the upgraded pole shields was peripheral routing of the cooling tube, which allows reduction of the effect of different thermal expansion of copper and stainless steel. Analysis presented in [1] show that cooling efficiency of is not affected by the peripheral location of the cooling pipe due to the high thermal conductivity of copper.
Acknowledgments This manuscript is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, and has been authored by Princeton University under Contract Number DE-AC02-09CH11466 with the U.S. Department of Energy. The publisher, by accepting the article for publication acknowledges, that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.
4.2. Calorimeter The existing NB210 Calorimeter is not using water cooling because of systemic water leaks in the stainless steel cooling tube brazed into the calorimeter two-inch thick copper plate. This leak occurred after 30–40 years of operating time. An upgraded calorimeter cooling plate set is required to replace the failed units with a more robust design, additional thermocouple instrumentation, and upgrading the cooling tube design with gun drilling of the water passages, if feasible. Peripheral routing was again used in the cooling system design as shown on Fig. 8. Geometrical modification of the calorimeter plate allows using four straight gun drilled holes to form a cooling system. Results of numerical analysis confirmed the efficiency of this cooling system.
References [1] A. Khodak, et al., dIII-D neutral beam pole shields design including copper plate with removable molybdenum insert, Fusion Sci. Technol. 68 (2) (2015) 373–377. [2] W. Wang, et al., Shaping the aperture of the absolute collimator in DIII-D neutral beam line upgrade, Presentation at TOFE 2018 to be published in Fusion Science and Technology, (2018). [3] H. Carslaw, J. Jaeger, Conduction of Heat in Solids, Oxford University Press, 1947. [4] M.A. Abdou, et al., Technical Assessment of the Critical Issues and Problem Areas in High Heat Flux Materials and Component Development Vol. 2 (1984) UCLA/ PPG—815 DE85 001155.
4.3. Collimator Existing DIII-D collimator cooling system consists was transferred to
1236
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Optimization of high heat flux components for DIII-D neutral beam upgrades a,⁎
a
a
a
a
T
a
Andrei Khodak , Irving Zatz , Wenping Wang , Alex Finehart , Yury Malament , Alex Nagy , Peter Titusa, Raffi Nazikiana, Tim Scovilleb a b
Princeton Plasma Physics Laboratory, Princeton, United States General Atomics, San Diego, United States
A R T I C LE I N FO
A B S T R A C T
Keywords: Neutral beam Fusion device Numerical analysis Heat load mitigation
Upgrade of the DIII-D neutral beams leads to enhanced heat loads on many components, such as calorimeter, collimator, and pole shields which protect neutral beam magnets. Power increase from 2.6 MW to 3.2 MW per source leads to a normal heat flux loads of up to 55 MW/m2 for the calorimeter. The Princeton Plasma Physics Laboratory is responsible for the design and manufacturing of the upgrades of these components. Heat flux distribution on neutral beam components is very uneven and leads to significant thermal stresses. High heat flux density impact requires surface optimization to reduce surface heat flux projection, and avoid localized melting. Several new design features were introduced to accommodate increased heat loads, such as molybdenum inserts for the pole shields, two-dimensional shaping for the calorimeter, and three-dimensional shape optimization and replaceable copper inserts for the collimator. Additionally, all three components include an optimized cooling system design featuring peripheral cooling of copper components. The optimization process included applying analytical relations for the transient temperature distributions on the high heat flux components. These relations were confirmed by previous DIII-D experimental results. To validate the designs, numerical simulations were performed. Results of the design optimization and numerical simulations will be presented.
1. Introduction
power. New requirements call for neutral beam power to 3.2 MW increasing thermal load on the neutral beam. Thus redesign of the pole shields was needed to withstand elevated load and remove excessive heat without melting. Design of the pole shield upgrade is described in detail in [1]. It includes molybdenum insert in the original copper plate. Removable insert is positioned in the area of the highest heat flux.
Upgrades for DIII-D neutral beams designed by PPPL are presented on Fig. 1. The upgrades include: new pole shields [1], calorimeter, and absolute collimator [2]. These upgrades allowed neutral beam power increase from 2.6 MW to 3.2 MW per source. Common features defining the design of these devices are: pulsed high heat flux impact, uneven spatial distribution of the heat load, reliance on water cooling system. These aspects defined the design features common for each of the upgrade: geometrical shaping, uneven heat load accommodation, and peripheral cooling system design, which will be described in detail for each upgraded component in the following sections. 2. Geometrical shaping 2.1. Pole shields Water cooled 12.7 mm thick copper pole shields were used in DIII-D neutral beams original design. Theses pole shields showed localized melting and fatigue cracks during the operation with 2.6 MW maximum
⁎
2.2. Calorimeter Copper is chosen for the upgraded calorimeter plates, which is the same material used in the original plates. The upgraded calorimeter should be capable to withstand a spectrum of pulses up to 6.3 MW per beam source. The requirement is to determine the maximum pulse lengths the calorimeter can withstand for each level of loading to qualify the calorimeter for a 100,000 cycle minimum design fatigue life. Additionally, a maximum pulse length will also be determined for a 7.5 MW pulse. Accordingly, a maximum front surface plate temperature that can achieve the desired life will be calculated. Cooling needs to be sufficient to permit a 3 min repetition rate for the spectrum of defined
Corresponding author. E-mail address: [email protected] (A. Khodak).
https://doi.org/10.1016/j.fusengdes.2019.02.047 Received 8 October 2018; Received in revised form 9 February 2019; Accepted 11 February 2019 Available online 05 March 2019 0920-3796/ Published by Elsevier B.V.
Fusion Engineering and Design 146 (2019) 1233–1236
A. Khodak, et al.
Fig. 1. DIII-D Neutral beam upgrades designed by PPPL.
3. Heat load accommodation
pulses. The repetition rate will also be determined for the aforementioned 7.5 MW pulse (which can exceed 3 min). Original calorimeter model had two opening angles of the heated surface leading to excessive heat flux on the front areas of the calorimeter. Changing the model to one opening angle allowed 20% reduction of the peak temperature as shown on Fig. 2. New plates were designed to fit into the same mounting halls, so original bracket design can be used.
3.1. Pole shields Ten segment molybdenum insert is fitted into the pole shield copper plate using loose tongue and groove pattern. 0.254 mm gaps between the segments, and between the segments and the plate, accommodate deformation of the segments due to non-uniform thermal expansion. Analysis of this design presented in [1] shows significant reduction of thermal stresses due to loose segmented design. At this point four pole shields are installed and operated for a year. Inspection of the pole shields, revealed no visible change. Fig. 3 shows one of the pole shields in the neutral beam opened for the planned maintenance, after a year of successful operation
2.3. Collimator DIII-D Neutral beam collimator was designed to shape two neutral beams at 4.33° each. Initial shape is modified to accommodate peak heat loads at an angle. So heat flux is spread over the surface. Threedimensional shape optimization allowed using copper for high heat flux areas. Interchangeable inserts are designed to reduce stresses. Details of the design are presented in [2].
3.2. Heat load accommodation In the pulsed operation heating of the calorimeter plate can be estimated using relations for the semi-infinite domain presented on Fig. 4: ∂T
ρcp ∂t =
∂q ; ∂x
∂T
q = − λ ∂x
(1)
where: T [℃] – temperature; q [W /m2] – heat flux; λ[W /(mK )] – thermal conductivity; cp [J /(kgK )] – heat capacity; ρ [kg /m3] – density; t [s] – time; x [m] – distance from the wall. Solution of (1) for constant heat flux can be found in [3]:
Fig. 2. Calorimeter plate shape modification.
Fig. 3. Installed pole shield after a year of operation. 1234
Fusion Engineering and Design 146 (2019) 1233–1236
A. Khodak, et al.
Fig. 4. Semi-infinite domain heating.
2 q π w
T − T0 =
x −⎛ 2 ⎝ ⎜
t ⎛ x exp ⎜⎛−⎛ λρcp ⎜ 2 ⎝ ⎝ ⎝ ⎜
ρcp ⎞ ⎟
λt ⎠
x erfc ⎜⎛ ⎛ 2 ⎝⎝ ⎜
ρcp ⎞2⎞ ⎟
⎟
λt ⎠ ⎠
ρcp ⎞ ⎞ ⎞ ⎟ λt ⎠ ⎠ ⎟ ⎠ ⎟
(2)
Fig. 6. Damage observed on GA calorimeter plates.
For wall temperature at x = 0 :
Tw − T0 =
2 q π w
Tc =
t λρcp
(3)
⎛x −⎜ 2 ⎝
Formula (3) was used in [4] to get limiting temperature of copper as shown on Fig. 5. Fig. 5 also shows GA shots data superimposed on the melting curves. Several shots exceeded melting conditions leading to some damage of the calorimeter plates as shown on Fig. 6. Formula (3) with copper properties was used as a guidance to determine calorimeter pulse power and duration. Assuming almost semi-infinite domain heating during the pulse, strain range is close to thermal strain range. At each pulse strain range is proportional to the peak surface temperature:
Δε ∼ α (Tw − T0) =
2α q π w
t λρcp
t − tp ⎛ ⎛ ⎛x exp ⎜−⎜ λρcp ⎜ 2 ⎝ ⎝ ⎝ ρcp ⎛⎛ x ⎞ erfc ⎜ ⎜ λ (t − tp ) ⎟ 2 ⎠ ⎝⎝
ρcp
2
⎞⎞ λ (t − tp ) ⎟ ⎟ ⎠⎠ ρcp ⎞⎞⎞ ; t > tp λ (t − tp ) ⎟ ⎟ ⎟ ⎠⎠⎠
(6)
Total thermal solution can found by adding (2) and (6) which for the wall x = 0 gives:
Tt − T0 =
2qw πλρcp
( t −
max (t − tp, 0) ) (7)
Temperature distributions presented on Fig. 7 shows that formula (7) allows accurate estimation of maximum wall temperature of the calorimeter during cooling period as well as the pulse itself
(4)
3.3. Collimator
Strain range obtained using relation (5) was used to define fatigue cycle limits of the design for various levels of pulse power and duration. Semi-infinite domain heating assumption can be expanded to the cooling period after the pulse. For the pulse of duration tp assume additional problem with
qwc = −qw ; t > tp
2 q π wc
As in the pole shields design collimator inserts we attached using loose tongue and groove pattern. 0.254 mm gaps between the inserts and the main body, accommodate deformation of the segments due to non-uniform thermal expansion. Analysis of this design presented in [2] shows significant reduction of thermal stresses due to loose segmented design.
(5)
4. Cooling system
Solution for the setup (5) can be found using the same procedure described in [3]:
4.1. Pole shields Cooling system of the pole shields includes a stainless steel tube
Fig. 5. Strongly focused GA ion source shots since 2009 Superimposed on melting of different materials depending on heat flux and pulse duration [4].
Fig. 7. Calorimeter cooling system with four straight gun drilled holes and four plugs. 1235
Fusion Engineering and Design 146 (2019) 1233–1236
A. Khodak, et al.
the new collimator design, with only minor changes. It includes stainless still conduit routed at the periphery of the main collimator frame. Analysis presented in [2] confirmed efficiency of such system. 5. Conclusions Geometrical shaping of the modified neutral beam components, allowed qualification at elevated requirements, by redistributing heat load on the wider surface area for calorimeter and collimator, or by positioning molybdenum insert in the high heat flux zone. For the pulsed device semi-infinite domain solution provide accurate estimation for the peak temperature and strain in the heated component, allowing fatigue assessment for different pulse power. Gaps between the components, allowed relieve of the stresses due to different thermal expansion. Peripheral channel routing creates robust and efficient cooling system. In all upgraded component this system relies on high thermal conductivity copper, and leads to thermal stress reduction.
Fig. 8. Calorimeter cooling system with four straight gun drilled holes and four plugs.
embedded into a pole shield copper plate groove using plasma spraying. Major design feature of the upgraded pole shields was peripheral routing of the cooling tube, which allows reduction of the effect of different thermal expansion of copper and stainless steel. Analysis presented in [1] show that cooling efficiency of is not affected by the peripheral location of the cooling pipe due to the high thermal conductivity of copper.
Acknowledgments This manuscript is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, and has been authored by Princeton University under Contract Number DE-AC02-09CH11466 with the U.S. Department of Energy. The publisher, by accepting the article for publication acknowledges, that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.
4.2. Calorimeter The existing NB210 Calorimeter is not using water cooling because of systemic water leaks in the stainless steel cooling tube brazed into the calorimeter two-inch thick copper plate. This leak occurred after 30–40 years of operating time. An upgraded calorimeter cooling plate set is required to replace the failed units with a more robust design, additional thermocouple instrumentation, and upgrading the cooling tube design with gun drilling of the water passages, if feasible. Peripheral routing was again used in the cooling system design as shown on Fig. 8. Geometrical modification of the calorimeter plate allows using four straight gun drilled holes to form a cooling system. Results of numerical analysis confirmed the efficiency of this cooling system.
References [1] A. Khodak, et al., dIII-D neutral beam pole shields design including copper plate with removable molybdenum insert, Fusion Sci. Technol. 68 (2) (2015) 373–377. [2] W. Wang, et al., Shaping the aperture of the absolute collimator in DIII-D neutral beam line upgrade, Presentation at TOFE 2018 to be published in Fusion Science and Technology, (2018). [3] H. Carslaw, J. Jaeger, Conduction of Heat in Solids, Oxford University Press, 1947. [4] M.A. Abdou, et al., Technical Assessment of the Critical Issues and Problem Areas in High Heat Flux Materials and Component Development Vol. 2 (1984) UCLA/ PPG—815 DE85 001155.
4.3. Collimator Existing DIII-D collimator cooling system consists was transferred to
1236