1Department of Physics, The University of Burdwan, Burdwan-713 104, INDIA
Abstract - Gyro-devices like Gyrotrons are used in the TOKAMAK system for plasma heating. Hence thermal temperature distribution of Gyrotron is so important. Mainly the Magnetron Injection Gun (MIG), interaction cavity and collector deals with high thermal loading. The operating mode of 200kW CW, 42GHz Gyrotron is TE0,3 . Thermal analysis of this Gyrotron cavity has been carried out using ANSYS software and discussed in the paper. Heat generated at inner cavity wall due to cavity Ohomic wall loss has been cooled using liquid turbulent flow at 290K. Water has been used as coolant liquid for cooling purposes. After cooling of the cavity, thermal distributions along with cavity structure are shown. Calculated wall loss at the cavity wall is less than critical limit i.e. less than 1x104 kW/m2. Cooling arrangement of this cavity has been suggested with fins on the outer surface of the cavity.
Microwave tubes like Gyrotron generates very high power at very high frequency [1]. In INDIA 42GHz 200kW (CW) gyrotron has been initiated for an Indian TOKAMAK system for plasma heating. Main parts of Gyrotron consist of MIG, RF interaction cavity, collector, and output window. When the gyrating electron beams generated from MIG moves through the beam tunnel and interaction cavity, they will interact with RF in the resonator cavity and finally get collected at collector, while high power grown in the cavity has been taken out axially (conventional Gyrotron) from the device through output window. The power dissipated as heat flux. The wall loading of the 42GHz, 200kW Gyrotron for TE0,3 can be evaluated as 229.933kW/m2. The Ohmic wall loss [1] can be calculated from the formula mentioned bellow:
Ohmic wall loss,2 2 2
2
( )out D
mp
P QdP
dA m L
πδλ χ
=−
One can find diffractive quality factor using the
formula,2
2
4D
LQ
πλ
=
So, dP
dA=229.933kW/m2
Conductivity of copper (σ) is 5.8x107mho/m and wavelength of the wave (λ) at frequency 42GHz is 0.007142 m. Cavity length (middle section), L2=0.044 m. Where as ,m pχ = 0,3χ =10.173 and skin depth of oxygen free high conductive copper (OFHC-Cu) i.e. δ =1.0197e-007m at 42GHz. This wall load or heat flux has been applied on the inner wall of the cavity for simulation in commercially available ANSYS software [2].
II. GYROTRON CAVITY STRUCTURE
The dimensions of the Gyrotron cavity structure [3] are shown in Fig. 1. Inner dimension of the cavity have been decided from theoretical calculation as well as RF analysis in the various available softwares. The operating mode for this Gyrotron is TE03 and for this operating mode total cavity length (L) has been selected as 0.12m, which consist of three parts (Fig.1) as input down taper (L1)=0.03 m & input taper angle (θ1)=2°, uniform part (L2)=0.044m and output up taper (L3)=0.046 m & output up taper angle (θ3)=3°.
The cavity is made up with OFHC copper. For the thermal analysis the properties of the OFHC Copper has been used through out the simulation in ANSYS software.
Fig. 1. Total cavity structure with three sections (L1, L2, L3) along with taper angles and its symmetry about its axis. (All dimensions are in 10-3m)
INTERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL TECHNOLOGY
VOL.4, NO.1,JANUARY 2009
The final thickness of the cavity has been optimized after the thermal analysis and cooling effect [4]. For the better thermal stability of the cavity, radial fins in the middle part of the cavity, has been analyzed. Concept of fins in the middle part reduces the thermal loading effects. Radial fins having 0.001m thickness, 0.003 m height and 0.001m spacing in between, gives the better result. The structure of the cavity with radial fins has been shown in the Fig. 2.
III. HEAT TRANSFER METHOD
Heat has been transferred [5] from cavity inner wall to the cavity outer wall by the method of conduction whereas heat is transferred from outer cavity wall to the water by convection method. When fins are used the surface area increased and the increased surface area increases the water contact area with the cavity. This cavity is made up with OFHC copper, which is highly thermal conductive (conductivity is about 340 W/m.K), which helps to better heat conduction process.
Now, if the generated heat is large enough due to thermal heat flux at the inner surface, it can cause to melt the metal. This further causes to change the dimensions of the cavity. Change in cavity dimensions changes the resonator cavity mode and other parameters. Due to this Gyrotron will suffer to pursue its best performance. To maintain a specific temperature at the cavity, cooling arrangement is required. Normally, water-cooling system [3-4] has been used to achieve this. The detail thermal analysis is as follows.
IV. THERMAL ANALYSIS
ANSYS software has been used to study thermal analysis for the interaction cavity of Gyrotron. Total heat flux has been applied at the inner surface of the L2 part. Where as, the thermal film coefficient has been applied at the outer surface of the cavity. The result is quite satisfactory and shown in the Fig. 3. Then the cavity outer surface is modeled by using fins to increase the water contact surface area. The middle part with the fins is shown in Fig. 2. The interaction cavity has symmetry about its axis. This helps to simplify the simulation. Means instead of complete 3D structure, symmetry part of the structure can be studied. The water-cooling system is designed such that cavity outer surface is directly exposed to the water flow. For convective heat transfer from cavity surface to water, thermal heat film coefficient is required to specify how much heat flux has to be transferred from unit area having unit temperature difference. The thermal heat film coefficient (h) is calculated [3] and applied to the
water-cavity surface. Thermal heat flux, thermal heat film coefficient and liquid (Water) initial conditions are required to start the simulation. Calculations of different parameters for simulation for a typical case is discussed for the sake of example/ convenience are as follows:
Inner surface area of the L2 is 0.0032m2. Ohmic loss at the Gyrotron cavity wall has been found as 229.933kW/m2, which is with in the limits (<1x104 kW/m2). This wall loss has been used as wall load of the cavity and hence used in the thermal analysis. Equivalent thermal heat flux is 229.933kW/m2 .
Now, Reynolds number (Re) is required to determine the flow of water whether it is laminar, transient or turbulent. Re is a non-dimensional parameter. At the same time parameters like water mass flow (m*), viscosity of water (µ) and hydraulic diameter (Dh) are used for calculation. Reynolds number is calculated as,
Re=4.m*/(π. µ. Dh) (i)
Where, Mass flow (m*)=ρ. V. A (ii) Dh is hydraulic duct radius (=0.01m) and at 290K water
viscosity (µ)=0.00108 N.s/m2 & Water density (ρ)= 999.009kg/m3
Here, value of Re has been found greater than 4000. It indicates water flow is turbulent, for fully developed condition L/Dh ≥ 10.
Above initial inlet water thermal properties, water thermal conductivity (k) along with Re, Nusselt number (Nu) and Prandtl number (Pr) are required to find the value of heat film coefficient (h).
Nu=0.023(Re) 0.8(Pr) 0.4 (iii)
As, Nu=h L/k (iv)
So, one can find,
h=0.023 k (Re) 0.8(Pr) 0.4/Dh (v)
Here, Prandtl number (Pr) is equal to 7.56 for water at 290K and water conductivity (k)=0.598 W/m. K So, heat film coefficient, h (W/m2. K), has been calculated (using equations i to v) for fluid flow of 15 lit./min.
Another case also has been studied when the heat of about 10 % of the total output power (200kW) is dissipated in the uniform section of the cavity i.e. 20kW power in the 0.0032m2 area. This gives as result, heat flux of 6253kW/m2. This heat flux also dissipated in the inner surface of the cavity. Results are shown in the Fig 4. Due to high heat flux the fins on the outer surface are required to minimize the thermal effects on the cavity. When fins are exposed to the water flow then heat flux has been applied to the whole external surfaces.
INTERNATIONAL JOURNAL OF MICROWAVE AND OPTICAL TECHNOLOGY
VOL.4, NO.1,JANUARY 2009
V. RESULTS AND DISCUSSIONS
As mentioned above, in ANSYS the 3D Gyrotron cavity structure made-up with OFHC-Cu has been modeled and all heat loads are applied. Water-cooling system has been used here. After the steady sate analysis the minimum surface temperature becomes 290.07 K where as maximum becomes 306.12 K, when film coefficient 11615 W/m2. K and water bulk temperature 290 K is considered (Fig. 3). The wall thickness of the cavity is 0.005m. Fig. 2. Cavity with fins in the middle uniform part (L2)
Fig. 3. Temperature variation on the cavity for h=11615 W/m2. K, water flow rate equals 15litre/min at 290 K bulk water temp.
In the above result, the surface temperatures are within the limits. Another simulation has been done for higher heat flux in the cavity (Fig. 4). If 10% of the total output power has been dissipated on the cavity wall having inner cavity surface area 0.0032m2 i.e. power dissipated will be 20kW. This power when dissipated in the middle part of the cavity (L2) then heat flux becomes 6253 kW/m2. This wall load becomes high enough though it is with in the
limits (<1x104 kW/m2). Another approach to minimize the thermal loading at the surfaces groves can be used. The heat film coefficient has been chosen as 17000W/m2. K, when coolant is at 290K.
Fig. 4. Temperature variation on the cavity for h=17000 W/m2. K, water flow rate equals 15litre/min at 290 K bulk water temp.
From the above result shown in figure, outer cavity surface temperature is about 350K.
VI. CONCLUSION
Among the various simulated results the water flow has been chosen as 15lit/min at 290K. For this water flow, after cooling arrangement, cavity surface temperature maintained within the critical limit.
ACKNOWLEDGEMENT
Authors are grateful to the Director, CEERI, Pilani, for permission to publish this paper. Thanks are due to Dr SN Joshi, Dr. V Srivastava and gyrotron team members for their continuous support and encouragement. Also thanks to the HOD of the Department of Physics, The University of Burdwan.
REFERENCES
[1] C. J. Edgecombe, Gyrotron Oscillators, Taylor & Francis, London, 1993.
[2] ANSYS help guide, ANSYS Inc. [3] Jyotirmoy Koner, A. Bera, A. K. Sinha, Thermal analysis of
200kW(CW), 42GHz Gyrotron cavity, NCEE-2008, 9-11 Feb, 2008, West Bengal, INDIA.
[4] A. W. Scott, Cooling of Electronic Equipment, John W & S [5] F. P Incropera and D. P. Dewitt, “Introduction to heat
