STUDIES ON SINGLE AND TWIN PRIME MOVER TRAVELLING WAVE THERMOACOUSTIC SYSTEMS

Experimental and Simulation studies on single prime mover travelling wave thermoacoustic system have been performed for various working fluids such as Argon, Helium etc. at different operating pressures. Then simulation study on twin prime mover travelling wave thermoacoustic system is performed using DeltaEC software where resonators, regenerators, cold heat exchangers, ambient heat exchangers, hot heat exchangers and stack ducts are modeled. The system performance is studied at various operating pressures for various working fluids such as pure gases and binary mixture of helium and Argon. The newly modeled twin prime mover system has better performance in terms of pressure amplitude and resonance frequency when compared to that of a single prime mover travelling wave system. The studies on Helium/Argon mixtures in various proportions as a working fluid in twin prime mover travelling wave system are performed. The helium/Argon mixture at 60/40 ratio proves to be more efficient as its Prandtl number is less. The pressure amplitude of 0.1224 Mpa and frequency of 30 Hz at 1 Mpa operating pressure is recorded at He/Ar 60/40 ratio mixture. Keyword DeltaEC, Heat engines, multistage prime movers, Prime movers, Thermoacoustics.


II. STUDIES ON SINGLE PRIME MOVER SYSTEM
The experimental set up of the Single prime mover system is as shown in Fig 1. The system consists of two parts, a feedback loop and resonator with the buffer. Heater, ambient heat exchanger, stack (made of stainless steel wire mesh), cold heat exchanger, and the compliance tubes are housed in the feedback loop. The heater provides heat energy required to the hot heat exchanger and the cold heat exchanger is circulated with ambient water that can take heat from the other end of the stack. This creates a temperature gradient across the stack, which generates thermoacoustic oscillations. The traveling wave loop is attached with a resonator tube along with the buffer.
To understand the behaviour, the developed travelling wave thermoacoustic prime mover is experimented and performance of the same is studied for various working fluids. The system with similar configuration is modelled using DeltaEC software, the results are compared. Fig 2 shows resonance frequency of the system measured with different working fluid at different operating pressures. The resonance frequency of the traveling wave system depends on the working fluid. The resonance frequency is independent of operating pressure for a working fluid. As the frequency of oscillation for traveling wave thermoacoustic prime mover is directly proportional to the speed of sound in particular working gas. It is expressed as, "ƒ=a/4L", where 'a' is speed of sound and is given by, a = √(γ(P/ρ)). γ is the ratio of specific heats, P is the pressure, ρ is the density of working fluid. Increasing the operating pressure correspondingly increases the density of the working gas in the system. So the ratio of working pressure and density remains nearly constant. Hence, the frequency of oscillation is nearly constant with the increase in working pressure. Also Helium shows highest frequency, since the density of gas within the constant volume varies according to the molecular weight. The molecular weight of Helium is low and Argon is high.  The pressure amplitude is directly proportional to the operating pressure. This can be attributed as, according to linear thermoacoustics (Swift, 1988) the momentum, continuity and energy equations the pressure amplitude is directly proportional to velocity amplitude by the inertance and viscous resistance. Both inertance and viscous resistance of working gas depend upon the mean density of working gas in the system.
As the operating pressure of the working gas in the system is increased, the density increases correspondingly which leads to the increase in pressure amplitude. Also it is observed that, the pressure amplitude is the highest for Argon, the lowest for Helium. This is because the pressure amplitudes depend on the density of the working gas, and as higher the molecular weight, higher the density causes highest pressure amplitude for Argon as working gas and lowest for Helium due to its lowest density.
Argon shows the highest pressure amplitude at the lowest frequency of ~ 23 Hz at an average pressure of 0.51 MPa. On the other hand, Helium shows the lowest pressure amplitude at the highest frequency of ~73Hz. The reasons for the variation of pressure amplitude with the working fluid have been already explained. The variation in frequency among the working fluids is due to the difference in their molecular weights, which modifies the sound velocity of the fluid. III. DESIGN CONSIDERATIONS FOR MODELLING OF TWIN PRIME MOVER SYSTEM  A tube of 50mm inner diameter and 57mm outer diameter is used for the modelling of the system.  Initially DeltaEC program is developed for single prime mover system and later extended to desired twin prime mover layout.  For the purpose of design of independent component, the operating pressure of 10 Mpa is set, with pure Argon as the working fluid.  Necessary parameters such as porosity of heat exchangers, regenerators, thickness of ducts, length of feedback loop, outline of loops etc. are initially assumed suitably and then modified as per the requirements.  All specifications such as porosity, radius, gap between the plates in case of heat exchangers, type of meshes in case of regenerators, heat input etc. is exactly similar in both the prime movers. To ensure generation of one single wave with single resonance frequency and pressure amplitude, absolute similarity between the prime movers is required.  The two prime movers are arranged in series configuration.

IV. INITIAL PARAMETERS FOR MODELLING IN DELTAEC SOFTWARE
The following dimensions or specifications are initially used to develop the program of single prime mover system.

A. Design of resonator tube
The resonator tube is the important component, by varying which both the resonance frequency as well as pressure amplitude varies. The resonator tube material is selected as stainless steel. The inner diameter of the resonator is taken as 50mm. The outer diameter is 57mm, with 3.5mm wall thickness. This decides cross sectional area of resonator through which fluid can flow. The Srough is inner surface roughness of the tube or duct, whose value is 6e-4 for turbulent dissipation of fluids. The appropriate length for the resonator has to be arrived. The variation of pressure amplitude and resonance frequency with the resonator length is plotted as shown in fig 4. The pressure amplitude of the system increases almost linearly with resonator length and reaches maximum value of 0.1498 MPa at 2.6 m then the pressure amplitude decreases. The frequency decreases with increase in resonator length and at 2.6 m length its value is about 19.5 Hz. The Pressure amplitude has to be as high as possible with minimum resonance frequency for the best performance of the engine. Thus the resonator length of 2.6m is arrived from the above graphs.

B. Design of cold heat exchangers
The cold heat exchangers are placed right below the regenerator. The working fluid moves inside small cylindrical holes of given porosity. It is made of copper, as it is a good conductor. There are two cold heat exchangers in twin prime mover system. A water jacket arrangement is made externally to circulate water at room temperature around the heat exchangers. The water pumping arrangements are made for continuous circulation of water. The diameter of the heat exchanger remains same as that of the inner diameter of the resonator tube; the length of the heat exchangers has to be determined. The graph shows the variation of pressure amplitude and frequency with heat exchanger length. The pressure amplitude increases with the length of cold heat exchanger, reaches a stable value at 0.055 m length and then drops. The frequency remains almost constant, with the order of 19-20 Hz. Thus the cold heat exchanger length is taken as 0.055 m.

C. Design of hot heat exchangers
This heat exchanger adds heat energy to the working fluid. The twin prime mover system has two hot heat exchangers made of copper. Heater of known power is used externally to supply heat energy. As the heat exchanger length increases, the heat transfer to the working fluid becomes better because of large area of contact, but the pressure amplitude decreases as it acts as the obstruction to the beginning of wave oscillation. So the suitable length has to be selected such that the pressure amplitude is not too less and at the same time the operating temperature of the heat exchanger should be less than the melting point of the copper. The graph shows the variation of pressure amplitude and frequency with respect to the length of hot heat exchanger. Ambient heat exchangers are required to stabilize flow of the working fluid and to reduce the temperature of working fluid, thus preventing the temperature rise of the working fluid and the system. The two ambient heat exchangers are used in twin prime mover system. The graphs show the variation of pressure amplitude and frequency with length of ambient heat exchanger.

E. Design of regenerator
The twin prime-mover system contains two regenerators of wire mesh type. The regenerators are made of stainless steel mesh. As the length of the regenerator increases pressure amplitude increases and frequency remains constant. The temperature gradient is maintained across the regenerators. The regenerator is placed between cold and hot heat exchangers, whose lengths are 0.055 m and 0.065 m respectively. From the above graph, the appropriate length of regenerator is taken as 0.05 m. The other parameters are mesh type N=30, Porosity= 0.74, and hydraulic radius Rh=199.2e-6 m.

F. Design of stack duct
This duct decides the position of the prime movers and ambient heat exchangers. Increase in the length of this corresponds to increase in pressure amplitude and frequency remains almost constant. But the temperature of hot heat exchanger increases. The graphs show the variation of the amplitude and frequency with the length of stack. From the above graphs the appropriate value for the length of stack duct appears to be 0.1m. The wall area is 8.64e-4 m 2 corresponds to the wall thickness of 0.05 m.

V. DESIGN PARAMETERS ARRIVED FROM DELTAEC SOFTWARE
From DeltaEC software, specific design dimensions for twin prime mover system are arrived as shown.  The Fig 11 and 12 show variation of resonance frequency and pressure amplitude with operating pressure respectively, for pure gases and binary mixtures of helium and Argon. The resonance frequency is independent of operating pressure. The pressure amplitude increases with operating pressure. The frequency of helium gas is higher than argon because of its low molecular weight. The pressure amplitude of Argon is higher, as it has higher molecular weight than helium. From the above graphs, it is evident that the pressure amplitude is high for Argon with low resonance frequency, but the required temperature gradient across the regenerator for the beginning of the oscillation is very high. On other hand helium requires low temperature gradient to produces low pressure amplitude and high resonance frequency waves. A mixture of helium and argon in appropriate proportion will result in good pressure amplitude and frequency, operating at less temperature gradient when compared to pure gases. The pressure Amplitude and frequency of binary mixtures are plotted and it is evident from the graphs that the He/Ar mixture of 60/40 ration is optimum. The fluids with very low value of Prandtl number acts as best thermoacoustic fluid. The Prandtl number for He-Ar mixture of 60-40 ratio is least among all other mixtures thus acts as the best thermoacoustic working fluid. The same can be even visualized by simulation results.

VII.
CONCLUSIONS The Delta Ec modelling and simulation has been performed for single prime mover system, the results fairly matched with the experimental results. Then simulation study on twin prime mover system has been performed. The frequency of working fluid is almost independent of operating pressure. The pressure amplitude increases with operating pressure attains maximum value and then decreases. The DeltaEC successfully predicts the values of pressure amplitude and frequency, but fails to predict the T begin value. Among all the working fluids, binary mixture of He/Ar at 60/40 ratio acts as the best fluid due to its low Prandtl number, gives an intermediate optimum frequency and with considerably good pressure amplitude.

HX
Heat exchanger HHX-1 Hot heat exchanger of first prime mover CHX-1 Cold heat exchanger of first prime mover STK-1 Regenerator of first prime mover AHX-1 Ambient heat exchanger of first prime mover HHX-2 Hot heat exchanger of second prime mover CHX-2 Cold heat exchanger of second prime mover STK-2 Regenerator of second prime mover AHX-2 Ambient heat exchanger of second prime mover Delta T1 Temperature gradient across regenerator-1 Delta T2 Temperature gradient across regenerator-2