Effects of plasma equilibrium parameters on the alpha particle loss with the toroidal field ripple based on the CFETR steady-state scenario have been numerically investigated by the orbit-following code GYCAVA. It is ...Effects of plasma equilibrium parameters on the alpha particle loss with the toroidal field ripple based on the CFETR steady-state scenario have been numerically investigated by the orbit-following code GYCAVA. It is found that alpha particle losses decrease and loss regions become narrower with the plasma current increasing or with the magnetic field decreasing. It is because the ripple stochastic transport and the ripple well loss of alpha particle are reduced with the safety factor decreasing. Decrease of the plasma density and temperature can reduce alpha particle losses due to enhancement of the slowing-down effect. The direction of the toroidal magnetic field can significantly affect heat loads induced by lost alpha particle. The vertical asymmetry of heat loads induced by the clockwise and counter-clockwise toroidal magnetic fields are due to the fact that the ripple distribution is asymmetric about the mid-plane, which can be explained by the typical orbits of alpha particle. The maximal heat load of alpha particle for the clockwise toroidal magnetic field is much smaller than that for the counter-clockwise one.展开更多
Axial piston pump with pre-compression volume(PCV) has lower flow ripple in large scale of operating condition than the traditional one. However, there is lack of precise simulation model of the axial piston pump wi...Axial piston pump with pre-compression volume(PCV) has lower flow ripple in large scale of operating condition than the traditional one. However, there is lack of precise simulation model of the axial piston pump with PCV, so the parameters of PCV are difticult to be determined. A finite element simulation model for piston pump with PCV is built by considering the piston movement, the fluid characteristic(including fluid compressibility and viscosity) and the leakage flow rate. Then a test of the pump flow ripple called the secondary source method is implemented to validate the simulation model. Thirdly, by comparing results among the simulation results, test results and results from other publications at the same operating condition, the simulation model is validated and used in optimizing the axial piston pump with PCV. According to the pump flow ripples obtained by the simulation model with different PCV parameters, the flow ripple is the smallest when the PCV angle is 13~, the PCV volume is 1.3 ~ I0-4 m3 at such operating condition that the pump suction pressure is 2 MPa, the pump delivery pressure 15 MPa, the pump speed 1 000 r/min, the swash plate angle 13~. At the same time, the flow ripple can be reduced when the pump suction pressure is 2 MPa, the pump delivery pressure is 5 MPa,15 MPa, 22 MPa, pump speed is 400 r/min, 1 000 r/rain, 1 500 r/rain, the swash plate angle is ll~, 13~, 15~ and 17~, respectively. The finite element simulation model proposed provides a method for optimizing the PCV structure and guiding for designing a quieter axial piston pump.展开更多
The flow ripple, which is the source of noise in an axial piston pump, is widely studied today with the computational fluid dynamic(CFD) technology development. In the traditional CFD modeling, the fluid compressibi...The flow ripple, which is the source of noise in an axial piston pump, is widely studied today with the computational fluid dynamic(CFD) technology development. In the traditional CFD modeling, the fluid compressibility, which strongly influences the accuracy of the flow ripple simulation results, is often neglected. So a compressible sub-model was added with user defined function(UDF) in the CFD model to predict the flow ripple. At the same time, a test rig of flow ripple was built to study the validity of simulation. The flow ripple of pump was tested with different working parameters, including the rotation speed and the working pressure. The comparisons with experimental results show that the validity of the CFD model with compressible hydraulic oil is acceptable in analyzing the flow tipple characteristics. In this paper, the improved CFD model increases the accuracy of flow ripple rate to about one-magnitude order. Therefore, the compressible model of hydraulic oil is necessary in the flow ripple investigation of CFD simulation. The compressibility of hydraulic oil has significant effect on flow ripple, and the compression ripple takes about 88% of the total flow ripple of pump. Leakage ripple has the lowest proportion of about 4%, and geometrical ripple leakage ripple takes the remnant 8%. Besides, the influence of working parameters was investigated through the CFD simulations and experimental measurements. Comparison results show that the amplitude of flow ripple grows with the increasing of rotation speed and working pressure, and the flow ripple rate is independent of the rotation speed. However, flow ripple rate of piston pump grows with the increasing of working pressure, because the leakage ripple will increase with the pressure growing. The investigation on flow ripple of an axial piston pump using compressible hydraulic oil provides a more validity simulation model for the CFD analyzing and is beneficial to further understanding of the flow ripple characteristics in an axial piston pump.展开更多
The current research about the flow ripple of axial piston pump mainly focuses on the effect of the structure of parts on the flow ripple. Therein, the structure of parts are usually designed and optimized at rated wo...The current research about the flow ripple of axial piston pump mainly focuses on the effect of the structure of parts on the flow ripple. Therein, the structure of parts are usually designed and optimized at rated working conditions. However, the pump usually has to work in large-scale and time-variant working conditions. Therefore, the flow ripple characteristics of pump and analysis for its test accuracy with respect to variant steady-state conditions and transient conditions in a wide range of operating parameters are focused in this paper. First, a simulation model has been constructed, which takes the kinematics of oil film within friction pairs into account for higher accuracy. Afterwards, a test bed which adopts Secondary Source Method is built to verify the model. The simulation and tests results show that the angular position of the piston, corresponding to the position where the peak flow ripple is produced, varies with the different pressure. The pulsating amplitude and pulsation rate of flow ripple increase with the rise of pressure and the variation rate of pressure. For the pump working at a constant speed, the flow pulsation rate decreases dramatically with the increasing speed when the speed is less than 27.78% of the maximum speed, subsequently presents a small decrease tendency with the speed further increasing. With the rise of the variation rate of speed, the pulsating amplitude and pulsation rate of flow ripple increase. As the swash plate angle augments, the pulsating amplitude of flow ripple increases, nevertheless the flow pulsation rate decreases. In contrast with the effect of the variation of pressure, the test accuracy of flow ripple is more sensitive to the variation of speed. It makes the test accuracy above 96.20% available for the pulsating amplitude of pressure deviating within a range of ~6% from the mean pressure. However, with a variation of speed deviating within a range of ±2% from the mean speed, the attainable test accuracy of flow ripple is above 93.07%. The model constructed in this research proposes a method to determine the flow ripple characteristics of pump and its attainable test accuracy under the large-scale and time-variant working conditions. Meanwhile, a discussion about the variation of flow ripple and its obtainable test accuracy with the conditions of the pump working in wide operating ranges is given as well.展开更多
This paper introduces four PWM modes used in the sensorless brushless DC motor control system, analyzes their different influences on the commutation torque ripple in detail, and selects the best PWM mode in four give...This paper introduces four PWM modes used in the sensorless brushless DC motor control system, analyzes their different influences on the commutation torque ripple in detail, and selects the best PWM mode in four given types to reduce commutation torque ripple of Brushless OC(BLDC) motors. Simulation and experimental results show that the selection is correct and practical.展开更多
In order to deal with torque pulsation problem caused by traditional control method for brushless DC (BLDC) motor and to achieve high precision and good stability, a novel control strategy is proposed. Compared with...In order to deal with torque pulsation problem caused by traditional control method for brushless DC (BLDC) motor and to achieve high precision and good stability, a novel control strategy is proposed. Compared with the traditional control scheme, by using phase voltage as a control objective and making waveform of phase current approximately quasi-sinusoidal, torque ripple of BLDC motor is reduced from the original 14% to 3.4%, while toque is increased by 3.8%. Furthermore, by detecting zero-crossings of back electromotive force (BEMF) with non-conducting phases, sensorless control is realized. The new control strategy is simple. It can minimize torque ripple, increase torque, and realize sensorless control for BLDC motor. Simulation and experiments show good performance of BLDC motor by using the new control method.展开更多
In the flow on a mobile bed in an open channel, sand ripple often appears after the sediment begins to move. Different scholars have different views on the formation of sand ripples. This paper holds that as the rippl...In the flow on a mobile bed in an open channel, sand ripple often appears after the sediment begins to move. Different scholars have different views on the formation of sand ripples. This paper holds that as the ripple in general is very small, its formation is due to the instability of the laminar flow or the evolution of the small-scale coherent structures in the sublayer adjacent to the wall of the open channel. When the shear stresses caused by the disturbing waves or the coherent structure near the bed surface boundary and the water flow itself are greater than the shields stresses, responses on the bed surface appear and the sand ripple forms. If the frequency of the shear stress caused by the disturbance is close to the natural frequency of the sand grains that produced resonance, such a phenomenon is called the 'detection property' of the sediment. It is at this point that the maximum resonance appears and the sand ripple develops rapidly.展开更多
A peculiar first orbit loss type was found apart from the normal ones when we use ORBIT code to simulate fast ion orbits in the EAST tokamak. Fast ion orbits were studied in the presence of toroidal field (TF) rippl...A peculiar first orbit loss type was found apart from the normal ones when we use ORBIT code to simulate fast ion orbits in the EAST tokamak. Fast ion orbits were studied in the presence of toroidal field (TF) ripple and magnetohydro- dynamic (MHD) perturbations. We analyzed the properties of the drifted orbits in detail and compared their differences, finding that the combined effects of ripple and magnetic islands are much greater than the effects of either one of them alone. Then we investigated the orbitdeviations as a function of pitch angle in different radial positions. The modeling results demonstrate that the loss of trapped particles is mainly caused by the ripple, while MHD'perturbation mainly plays an important role in the passing particles. Furthermore we modeled the loss rate using different equilibriums. Results prove that a higher beta can indeed improve the confinement of fast ions, while a little change in the q profile can make the topologies of magnetic islands become quite different and results in quite different total particle losses.展开更多
The evolution of an initially flat sandy bed is studied in a laboratory wave flume under enoidal waves and acoustic Doppler velocimeter (ADV) was utilized in the detailed velocity measurements at different positions...The evolution of an initially flat sandy bed is studied in a laboratory wave flume under enoidal waves and acoustic Doppler velocimeter (ADV) was utilized in the detailed velocity measurements at different positions. The ripple formation and evolution have been analyzed by CCD images and the asymmetric rippled bed is induced by the nonlinear wave flow. The flow structure and a complete process of vortex formation, evolvement and disappearance were observed on the asymmetric rippled bed under cnoidal waves. With the increasing nonlinearity of waves, which is an important factor in the sand ripple formation, the vortex intensity becomes stronger and shows different characteristics on both sides of the ripple crest. The vorticity and wave velocity reach their maximum values at different phase angles. The vortex value reaches the maximum value at a small phase angle with the increasing Ursell number. The near bed flow patterns are mainly determined by the ripple forms and the averaged longitudinal velocity over a wave period above the ripple trough and crest are positive, which indicates the possibility of significant onshore sediment transport and a corresponding ripple drift. The phase averaged vertical velocity has noticeable positive values near the bottom of the ripple crest and trough. Sediments may be lifted from the ripple surface, picked up in suspension by the local velocity, and deposited over the crest and on the lee of the ripples.展开更多
A flux linkage compensation field oriented control (FOC) method was proposed to suppress the speed and torque ripples of a brushless wound-field synchronous motor in its starting process. The starting process was anal...A flux linkage compensation field oriented control (FOC) method was proposed to suppress the speed and torque ripples of a brushless wound-field synchronous motor in its starting process. The starting process was analyzed and the model of wound-field synchronous electric machine was established. The change of field current of the electric machine was described mathematically for simplified exciter and rotate rectifier. Based on the traditional field control, the flux linkage compensation was introduced in d-axis current to counteract the flux ripple. Some simulation and preliminary experiments were implemented. The results show that the proposed method is feasible and effective.展开更多
The efficiency of energetic ion confinement is reduced in a tokamak plasma by the non-axisymmetric field, namely the ripple field. The ripple field is produced by a finite number of toroidal field coils. It is affecte...The efficiency of energetic ion confinement is reduced in a tokamak plasma by the non-axisymmetric field, namely the ripple field. The ripple field is produced by a finite number of toroidal field coils. It is affected by the non-axisymmetric finite beta effect. The three-dimensional MHD equilibrium calculation code VMEC is used to analyze the non-axisymmetric finite beta effect in a ripple tokamak. In the VMEC code, the flux coordinates are used, so the calculation region is limited to the area of plasma. To calculate the orbit outside the plasma, we develop a field calculation code, which is based on the Biot-Savart law. The details of the method and results are described in this paper.展开更多
Predictions on the ripple loss of neutral beam fast ions on EAST are investigated with a guiding center code, including both ripple and collisional effects. A 6% to 16% loss of neutral beam ions is predicted for typic...Predictions on the ripple loss of neutral beam fast ions on EAST are investigated with a guiding center code, including both ripple and collisional effects. A 6% to 16% loss of neutral beam ions is predicted for typical EAST experiments, and a synergistic enhancement of fast ion loss is found for toroidal field (TF) ripples with collisions. The lost ions are strongly localized and will cause a maximum heat load of - 0.05 MW/m^2 on the first wall.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12175034 and 12005063)the National Key Research and Development Program of China (Grant No.2019YFE03030001)the Fundamental Research Funds for the Central Universities (Grant No.2232022G-10)。
文摘Effects of plasma equilibrium parameters on the alpha particle loss with the toroidal field ripple based on the CFETR steady-state scenario have been numerically investigated by the orbit-following code GYCAVA. It is found that alpha particle losses decrease and loss regions become narrower with the plasma current increasing or with the magnetic field decreasing. It is because the ripple stochastic transport and the ripple well loss of alpha particle are reduced with the safety factor decreasing. Decrease of the plasma density and temperature can reduce alpha particle losses due to enhancement of the slowing-down effect. The direction of the toroidal magnetic field can significantly affect heat loads induced by lost alpha particle. The vertical asymmetry of heat loads induced by the clockwise and counter-clockwise toroidal magnetic fields are due to the fact that the ripple distribution is asymmetric about the mid-plane, which can be explained by the typical orbits of alpha particle. The maximal heat load of alpha particle for the clockwise toroidal magnetic field is much smaller than that for the counter-clockwise one.
基金supported by National Key Technology R&D Program of the Eleventh Five-year Plan of China(Grant No.2011BAF09B03)National Natural Science Foundation of China(Grant No.51075360)
文摘Axial piston pump with pre-compression volume(PCV) has lower flow ripple in large scale of operating condition than the traditional one. However, there is lack of precise simulation model of the axial piston pump with PCV, so the parameters of PCV are difticult to be determined. A finite element simulation model for piston pump with PCV is built by considering the piston movement, the fluid characteristic(including fluid compressibility and viscosity) and the leakage flow rate. Then a test of the pump flow ripple called the secondary source method is implemented to validate the simulation model. Thirdly, by comparing results among the simulation results, test results and results from other publications at the same operating condition, the simulation model is validated and used in optimizing the axial piston pump with PCV. According to the pump flow ripples obtained by the simulation model with different PCV parameters, the flow ripple is the smallest when the PCV angle is 13~, the PCV volume is 1.3 ~ I0-4 m3 at such operating condition that the pump suction pressure is 2 MPa, the pump delivery pressure 15 MPa, the pump speed 1 000 r/min, the swash plate angle 13~. At the same time, the flow ripple can be reduced when the pump suction pressure is 2 MPa, the pump delivery pressure is 5 MPa,15 MPa, 22 MPa, pump speed is 400 r/min, 1 000 r/rain, 1 500 r/rain, the swash plate angle is ll~, 13~, 15~ and 17~, respectively. The finite element simulation model proposed provides a method for optimizing the PCV structure and guiding for designing a quieter axial piston pump.
基金supported by National Key Technology R&D Program of the Eleventh Five-year Plan of China (Grant No. 2006BAF01B01, Grant No. 2006BAF01B04)Open Foundation of State Key Laboratory of Mechanical System and Vibration of China (Grant No. MSV-2009-02)
文摘The flow ripple, which is the source of noise in an axial piston pump, is widely studied today with the computational fluid dynamic(CFD) technology development. In the traditional CFD modeling, the fluid compressibility, which strongly influences the accuracy of the flow ripple simulation results, is often neglected. So a compressible sub-model was added with user defined function(UDF) in the CFD model to predict the flow ripple. At the same time, a test rig of flow ripple was built to study the validity of simulation. The flow ripple of pump was tested with different working parameters, including the rotation speed and the working pressure. The comparisons with experimental results show that the validity of the CFD model with compressible hydraulic oil is acceptable in analyzing the flow tipple characteristics. In this paper, the improved CFD model increases the accuracy of flow ripple rate to about one-magnitude order. Therefore, the compressible model of hydraulic oil is necessary in the flow ripple investigation of CFD simulation. The compressibility of hydraulic oil has significant effect on flow ripple, and the compression ripple takes about 88% of the total flow ripple of pump. Leakage ripple has the lowest proportion of about 4%, and geometrical ripple leakage ripple takes the remnant 8%. Besides, the influence of working parameters was investigated through the CFD simulations and experimental measurements. Comparison results show that the amplitude of flow ripple grows with the increasing of rotation speed and working pressure, and the flow ripple rate is independent of the rotation speed. However, flow ripple rate of piston pump grows with the increasing of working pressure, because the leakage ripple will increase with the pressure growing. The investigation on flow ripple of an axial piston pump using compressible hydraulic oil provides a more validity simulation model for the CFD analyzing and is beneficial to further understanding of the flow ripple characteristics in an axial piston pump.
基金Supported by National Basic Research Program of China(973 Program,Grant No.2014CB046403)National Key Technology R&D Program of the Twelfth Five-year Plan of China(Grant No.2013BAF07B01)
文摘The current research about the flow ripple of axial piston pump mainly focuses on the effect of the structure of parts on the flow ripple. Therein, the structure of parts are usually designed and optimized at rated working conditions. However, the pump usually has to work in large-scale and time-variant working conditions. Therefore, the flow ripple characteristics of pump and analysis for its test accuracy with respect to variant steady-state conditions and transient conditions in a wide range of operating parameters are focused in this paper. First, a simulation model has been constructed, which takes the kinematics of oil film within friction pairs into account for higher accuracy. Afterwards, a test bed which adopts Secondary Source Method is built to verify the model. The simulation and tests results show that the angular position of the piston, corresponding to the position where the peak flow ripple is produced, varies with the different pressure. The pulsating amplitude and pulsation rate of flow ripple increase with the rise of pressure and the variation rate of pressure. For the pump working at a constant speed, the flow pulsation rate decreases dramatically with the increasing speed when the speed is less than 27.78% of the maximum speed, subsequently presents a small decrease tendency with the speed further increasing. With the rise of the variation rate of speed, the pulsating amplitude and pulsation rate of flow ripple increase. As the swash plate angle augments, the pulsating amplitude of flow ripple increases, nevertheless the flow pulsation rate decreases. In contrast with the effect of the variation of pressure, the test accuracy of flow ripple is more sensitive to the variation of speed. It makes the test accuracy above 96.20% available for the pulsating amplitude of pressure deviating within a range of ~6% from the mean pressure. However, with a variation of speed deviating within a range of ±2% from the mean speed, the attainable test accuracy of flow ripple is above 93.07%. The model constructed in this research proposes a method to determine the flow ripple characteristics of pump and its attainable test accuracy under the large-scale and time-variant working conditions. Meanwhile, a discussion about the variation of flow ripple and its obtainable test accuracy with the conditions of the pump working in wide operating ranges is given as well.
文摘This paper introduces four PWM modes used in the sensorless brushless DC motor control system, analyzes their different influences on the commutation torque ripple in detail, and selects the best PWM mode in four given types to reduce commutation torque ripple of Brushless OC(BLDC) motors. Simulation and experimental results show that the selection is correct and practical.
基金Project supported by the Shanghai Leading Academic Discipline Project (Grant No.T0103)
文摘In order to deal with torque pulsation problem caused by traditional control method for brushless DC (BLDC) motor and to achieve high precision and good stability, a novel control strategy is proposed. Compared with the traditional control scheme, by using phase voltage as a control objective and making waveform of phase current approximately quasi-sinusoidal, torque ripple of BLDC motor is reduced from the original 14% to 3.4%, while toque is increased by 3.8%. Furthermore, by detecting zero-crossings of back electromotive force (BEMF) with non-conducting phases, sensorless control is realized. The new control strategy is simple. It can minimize torque ripple, increase torque, and realize sensorless control for BLDC motor. Simulation and experiments show good performance of BLDC motor by using the new control method.
文摘In the flow on a mobile bed in an open channel, sand ripple often appears after the sediment begins to move. Different scholars have different views on the formation of sand ripples. This paper holds that as the ripple in general is very small, its formation is due to the instability of the laminar flow or the evolution of the small-scale coherent structures in the sublayer adjacent to the wall of the open channel. When the shear stresses caused by the disturbing waves or the coherent structure near the bed surface boundary and the water flow itself are greater than the shields stresses, responses on the bed surface appear and the sand ripple forms. If the frequency of the shear stress caused by the disturbance is close to the natural frequency of the sand grains that produced resonance, such a phenomenon is called the 'detection property' of the sediment. It is at this point that the maximum resonance appears and the sand ripple develops rapidly.
基金Project supported by the JSPS-NRF-NSFC A3 Foresight Program in the Field of Plasma Physics(NSFC Grant No.11261140328)
文摘A peculiar first orbit loss type was found apart from the normal ones when we use ORBIT code to simulate fast ion orbits in the EAST tokamak. Fast ion orbits were studied in the presence of toroidal field (TF) ripple and magnetohydro- dynamic (MHD) perturbations. We analyzed the properties of the drifted orbits in detail and compared their differences, finding that the combined effects of ripple and magnetic islands are much greater than the effects of either one of them alone. Then we investigated the orbitdeviations as a function of pitch angle in different radial positions. The modeling results demonstrate that the loss of trapped particles is mainly caused by the ripple, while MHD'perturbation mainly plays an important role in the passing particles. Furthermore we modeled the loss rate using different equilibriums. Results prove that a higher beta can indeed improve the confinement of fast ions, while a little change in the q profile can make the topologies of magnetic islands become quite different and results in quite different total particle losses.
基金The study was financially supported by the National Natural Science Foundation of China under contract Nos 50479015 and 10202003also supported by Program for New Century Talents Excellent Talents in University(NCET-05-0710).
文摘The evolution of an initially flat sandy bed is studied in a laboratory wave flume under enoidal waves and acoustic Doppler velocimeter (ADV) was utilized in the detailed velocity measurements at different positions. The ripple formation and evolution have been analyzed by CCD images and the asymmetric rippled bed is induced by the nonlinear wave flow. The flow structure and a complete process of vortex formation, evolvement and disappearance were observed on the asymmetric rippled bed under cnoidal waves. With the increasing nonlinearity of waves, which is an important factor in the sand ripple formation, the vortex intensity becomes stronger and shows different characteristics on both sides of the ripple crest. The vorticity and wave velocity reach their maximum values at different phase angles. The vortex value reaches the maximum value at a small phase angle with the increasing Ursell number. The near bed flow patterns are mainly determined by the ripple forms and the averaged longitudinal velocity over a wave period above the ripple trough and crest are positive, which indicates the possibility of significant onshore sediment transport and a corresponding ripple drift. The phase averaged vertical velocity has noticeable positive values near the bottom of the ripple crest and trough. Sediments may be lifted from the ripple surface, picked up in suspension by the local velocity, and deposited over the crest and on the lee of the ripples.
基金Sponsored by the NSFC General Project (51177135)the Key Project of Natural Science Foundation of Shaanxi Province (2011GZ013)
文摘A flux linkage compensation field oriented control (FOC) method was proposed to suppress the speed and torque ripples of a brushless wound-field synchronous motor in its starting process. The starting process was analyzed and the model of wound-field synchronous electric machine was established. The change of field current of the electric machine was described mathematically for simplified exciter and rotate rectifier. Based on the traditional field control, the flux linkage compensation was introduced in d-axis current to counteract the flux ripple. Some simulation and preliminary experiments were implemented. The results show that the proposed method is feasible and effective.
基金performed with the support and backing of the NIFS Collaborative Research Program
文摘The efficiency of energetic ion confinement is reduced in a tokamak plasma by the non-axisymmetric field, namely the ripple field. The ripple field is produced by a finite number of toroidal field coils. It is affected by the non-axisymmetric finite beta effect. The three-dimensional MHD equilibrium calculation code VMEC is used to analyze the non-axisymmetric finite beta effect in a ripple tokamak. In the VMEC code, the flux coordinates are used, so the calculation region is limited to the area of plasma. To calculate the orbit outside the plasma, we develop a field calculation code, which is based on the Biot-Savart law. The details of the method and results are described in this paper.
基金supported by National Natural Science Foundation of China (Nos.10975160,11175211)
文摘Predictions on the ripple loss of neutral beam fast ions on EAST are investigated with a guiding center code, including both ripple and collisional effects. A 6% to 16% loss of neutral beam ions is predicted for typical EAST experiments, and a synergistic enhancement of fast ion loss is found for toroidal field (TF) ripples with collisions. The lost ions are strongly localized and will cause a maximum heat load of - 0.05 MW/m^2 on the first wall.