1、4780 Th Studies on Gas-Stack Heat Transfer for Hot Reservoir Research and Development of the Thermoacoustic Refrigerating System Emmanuel C. Nsofor, PhD, CEng Member ASHRAE ABSTRACT Thermoacoustic refrigeration is an environmentally safe technology that uses sound energy to pump heat. It offers seve
2、ral bene$ts, which include use of environmentally safe working fluids, no significant moving parts, and continuous capacity control. The thermoacoustic process results from thermal interactions between the oscillating gas and the stack surfaces in the system. This paper reports on studies involving
3、design, construction, operation, and experiments on the gas- stack heat transfer in the system. The results show that the heat transfer and Streaming Reynolds number increase with drive ratio and that the stackplate losses signijcantly dominate the total energy loss. It was also found that for the p
4、arallel plate stack arrangement, the use of an advanced engineering ther- moplastic stackmaterial wouldsignijcantly reduce the energy loss in the system compared to the stainless steel that has been favored in many studies. INTRODUCTION Concern for the environment has become increasingly important i
5、n the design and development of refrigeration systems. To eliminate the use of environmentally hazardous refi-igerants, research efforts have focused partly on the devel- opment of altemative refi-igerants and partly on alternative refrigeration technologies. One promising approach in the category o
6、f alternative technologies is thermoacoustic refrig- eration. The process by which sound is produced from cooling could be reversed so that cooling is produced from sound. This is the principle of thermoacoustic refrigeration. Figure 1 is a schematic of a simple thermoacoustic refrigeration system w
7、ith the work and heat flow directions. The system consists mainly of a resonance tube, a stack of parallel plates, and two Phani R. Gurijala heat exchangers. The acoustic driver (not shown in the diagram) located at the left end of the resonator tube supplies the energy necessary to pump heat from t
8、he low-temperature side to the high-temperature side of the system. Fluid inside the resonance tube interacts thermally with the plates, which, in turn, affects the standing waves that are being supported by the fluid. This results in the absorption of acoustic power and heat flux near the surface o
9、f the plates along the direction of the acoustic vibration. The plates are aligned parallel to the direction of vibration of the standing waves. A temperature gradient is produced along the length of the stack. The two major effects resulting from the communication between the sound waves and the so
10、lid boundary of the plates are (1) the absorption of acoustic power very close to the surface of the / Heat Exchanger / Heat Exchnaer TQ Tc I ColdReservoir 1 Figure 1 Schematic of a simple thermoacoustic refrigeration system. Emmanuel C. Nsofor is an assistant professor in the Department of Mechanic
11、al Engineering and Energy Processes, Southern Illinois Univer- sity, Carbondale, Illinois. Phani R. Gurijala is a systems engineer at General Electric Energy Services, Minden, Nevada. 41 6 02005 ASHRAE. plates and (2) a heat flux at the surface of the plates in the direc- tion of acoustic vibration.
12、 The mechanism for thermoacoustic heat transfer can be explained by considering the oscillation of a single gas parcel as it moves from one end of the tube to the other along the thin stack plate. Ideally, the plate is a poor conductor ofheat and is initially at a uniform temperature. The acoustic d
13、river generates an acoustic wave that excites the working fluid in the resonator tube. During displacement of the gas parcel to the left, it experiences an adiabatic compres- sion causing its temperature to increase above the temperature of the plate very close to it. Heat transfer thus occurs from
14、the parcel to the plate. Similarly, during the displacement of the parcel to the right, it experiences an adiabatic expansion that causes its temperature to fall below the local stack tempera- ture. Heat transfer consequently takes place from the stack to more research is required. Belcher et al. (1
15、999) reported that the best working gases for thermoacoustic refrigeration should have high ratios of specific heats and low Prandtl numbers. This was based on studies related to working gases suitable for use in thermoacoustic systems. Gurijala and Nsofor (2003) reported on preliminary experimental
16、 tests associated with this topic. This paper presents a summary of studies on the operation, analysis, design, construction, and experiments related to the gas-stack heat transfer in the system. Results of the studies identified some important parameters that influence fabrication, perfor- mance, a
17、nd gas-stack heat transfer in the thermoacoustic refngerating system. GOVERNING EQUATIONS the gas. The result of all this is that during each cycle, the gas the left end and heat transfer occurs between the gas and the plate. Due to a similar behavior by the remaining parcels of gas in the resonator
18、, there is a net heat transfer from the cold heat exchanger to the hot heat exchanger. The stack is regarded as the “heart” of this refrigerating to the stack by the gas particles. The thermal property of the stack material is important as it is required to provide the heat capaciSr for the desired
19、temperature gradient in the resonator. In the design of the stack, consideration was given to the fact parce1 some heat from the right end Of the stack to system. The heat generated in the working fluid is transferred Although this is a relatively new field, studies on the system have been undertake
20、n by a number of researchers. Swift (1 988) gave a review and in-depth description of ther- moacoustic physics in a comprehensive article. Studies related to this include Bai et al. (1998) that reported an experimental study on a thermoacoustic prime mover. The report discussed the effect of the wor
21、king fluid, resonator length, charging pres- sure, and heating temperature on the performance of the prime mover. Zhou and Matsubara (1998) ran experiments on a ther- moacoustic prime mover with stacks made of copper wire mesh. The influence of gas properties, frequency, mean pres- sure, mesh size,
22、and stack length on overall performance were measured and expressed in terms of normalized input power, heater temperature, and pressure amplitude. Herman and Wetzel (1999, 2000) studied the thermal interaction ,between a heated solid plate and acoustically driven working fluid by visualizing and qu
23、antifying the temperature fields in the neighborhood of the plate. The experiments combined holo- graphic interferometry and cinematography. The study looked at the thermoacoustic effects on a single stack plate. An eval- uation procedure that accounts for the influence of acoustic pressure variatio
24、ns on the refractive index was applied to accu- rately reconstruct the high-speed, two-dimensional, oscillat- ing temperature distributions. Worlikar and Knio (1996, 1999) and Worlikar et al. (1998) performed numerical studies on a thermoacoustic refrigeration system with emphasis on thermally strat
25、ified flow in the neighborhood of an idealized thermoacoustic stack, using a low Mach number model. Energy fux density around the heat exchangers was visualized and implications for heat exchanger design were examined. Herman and Wetzel (1995, 1996) developed a thermoacoustic model and worked on des
26、ign optimization of the models. The reports summarized the design steps and guidelines and pointed out areas in which that the stack plate material should have a low thermal conduc- tivity in order to reduce axial heat conduction along the plate and a high specific heat value to enhance relevant low
27、-temper- ature differential. Conduction perpendicular to the plate is also desirable. A number of stack arrangements are possible for this system. The types considered for use in this study included parallel plate stack, plastic roll stack, wire mesh stack, metal or ceramic honeycombs with square or
28、 hexagonal channel sections, and pin array stack arrangement (Swift 1993). The pin-arrayed stack consists of a hexagonal array of pins aligned with the wave propagation and has the advantage of a convex surface that gives the pin stack a greater ratio of thermoacous- tic area to viscous area. The mo
29、st common type of stack arrangement is the parallel plate. It has the advantage of being easy to fabricate. The fabrication techniques available for this study favored the choice of the parallel plate arrangement. Figure 2 shows the geometry with the stack plates arranged in parallel inside the cyli
30、ndrical resonator tube. The oscillating gas flows in the spaces between the plates. The location of the center position of the stack inside the resonator is between the pressure node and pressure antinode of the standing wave but more toward the pressure antinode. Recommendations in the study by Wet
31、zel and Herman (1997), applied in this design, assumed stratified flow and used normalized parameters, defined as 27c 5, = yx, to calculate coefficient of performance (COP) for the system. It showed that the closer the stack is located to the pressure antinode, or the acoustic dnver, the higher will
32、 be the COP achieved by the system. The desired spacing between the plates is two times the thermal penetration depth. To improve the performance of the system, the energy loss caused by the ASH RAE Transactions: Research 41 7 Stack Plates / The amount of heat carried by a gas particle from the cold
33、 side to the hot side of the stack plate is given by the relation Stack Holder/Re sonator Tub e Figure2 Geometry of the parallel plate stack arrangement. stack that is related to the flow in the resonator should be kept as low as possible. An important geometrical dimension that influences the flow
34、in the resonator and is related to this energy loss is the blockage ratio (BR), defined as 2yo 2y0+t, BR = - Swift (1988) gave substantial valuable information on the thennoacoustic theory. The heat and work transfer rates are some of the important parameters in the gas-stack heat trans- fer. The ti
35、me-averaged heat flux in the resonator along the axial direction is given by Yo Q = IpuTsdy. (3) O From the ideal gas relation p = p/RT and S = S, + Cp In (TIT,) - R In (pip,), Equation 1 can be written for a single plate in a standing wave as The thermal penetration depth is a measure of how far he
36、at can diffuse laterally during a time interval on the order of tJn. It is measured perpendicular to the direction of motion of the gas and is given by the equation 6k = The viscous penetration depth 6, is a measure of how far momentum can diffuse laterally during a time interval on the order of tin
37、. It is given by the equation 6, = Jz-;r/Op . It is to be noted that Equation 4 was derived neglecting axial conduc- tion in the working fluid and in the stack plates. The axial conduction in the fluid and the plates is (5) 2 - -LGkPA(r - I) 4P,C Qhyd - 7 where the gradient ratio (r) is defined as d
38、T/dx - - dT/dxc r= (dT/dx), O. c P (7) The work added or work flux is in the form of acoustic power absorbed by the fluid. For a single plate in a standing wave, this is given by the equation Equation 8 gives the work absorbed from the acoustic power to pump thermal energy from the low-temperature t
39、o the high-temperature side. The rest of the acoustic power is dissipated in different forms that include the increase of the amplitude of the standing wave. The drive ratio is a measure of the strength of the acoustic field and is defined as (9) Dynamic Pressure Amplitude Mean Pressure Dr = Another
40、 parameter related to the heat transfer in the system is the Streaming Reynolds number. Streaming is a time-averaged mechanism that occurs in thermoacoustic systems, and it plays a crucial role in the heat transport behav- ior. It helps in understanding the details of the fluid flow in the region ar
41、ound the stack. Streaming Reynolds number (R,) depends on parameters such as frequency and pressure ratio and is defined as Rs = ($($)*. The major heat losses related to the gas-stack heat transfer in the system were considered to be from two sources, the stack plates and the working fluid. The stac
42、k plate losses are defined by the equation The heat losses from the working fluid, called the fluid losses, are given by dTm Q, = 2LkS - dx The total heat loss is, thus, the sum of the plate losses and fluid losses as shown in Equations 11 and 12. Uncertainty analysis was performed for the experimen
43、ts based on the methods described by Coleman and Steele (1 999) and Moffat (1 988). For example, for the plate losses given by 41 8 ASHRAE Transactions: Research . / t Figure 3 Assembly of the system. Equation 1 1, the general uncertainty analysis expression is given by the equation For the bias lim
44、it, the uncertainty analysis expression is &)2 = e)2 + e)2 + (:)+ rz)2 + (x) , (14) and for the precision limit, the uncertainty analysis expression is p)2 = ()2+)2+()2+)2+(x) Ax . (15) QP, The uncertainty in the plate loss was obtained by combin- ing the bias and precision limits using the root-sum
45、-square model (RSS), with experimental data estimated at 95% confi- dence level as EXPERIMENTAL SETUP AND PROCEDURE Figure 3 shows the main features of the thermoacoustic refhgeration system used in this study. It consists of five major components-the acoustic driver, resonator tube, a stack, two he
46、at exchangers-and the working fluid, which in this case was helium gas. There are other auxiliary compo- nents, such as the audio frequency generator, power ampli- fier, pressure transducer, pressure gauges, an oscilloscope, thermocouples, and the data acquisition system. The resona- tor is a rigid
47、sealed tube filled with the gas that provides the medium for the propagation of the standing waves. A special type of resonator (Hofler 1986), which is a combination of two pipes of different diameters with a sphere on the oppo- site end of the acoustic driver, was adopted in this study. The large p
48、ipe, which is 150 rnm (6 in.) in diameter, houses the acoustic driver, the stack, and the two heat exchangers. The small pipe coupled to it had a diameter of 100 rnm (4 in.) with the end of the pipe capped off. The acoustic driver converts electric power to acoustic power and is responsible for crea
49、ting the oscillations of the gas inside the resonator. The stack is located in the larger diameter section of the resonator tube close to the pressure antinode. The choice of the gas used in the system for this study was based on the recommendations by Belcher et al. (1999). Choice of work- ing gas for the thermoacoustic system involves trade-offs between a number of factors, such as power, efficiency, availability, and other effects. High mean pressures and high sound speeds yield high power per unit volume of the hard- ware. The heat exchangers used in the system both have c
