EP1570214A1

EP1570214A1 - Heat exchanger for use with oscillating fluids in particular in a thermoacoustic cell

Info

Publication number: EP1570214A1
Application number: EP03796162A
Authority: EP
Inventors: Maurice-Xavier Francois; Emmanuel Bretagne
Original assignee: Universite Pierre et Marie Curie Paris 6
Current assignee: Universite Pierre et Marie Curie Paris 6
Priority date: 2002-12-04
Filing date: 2003-12-04
Publication date: 2005-09-07
Also published as: WO2004053405B1; WO2004053405A1; FR2848293B1; AU2003298414A1; FR2848293A1

Abstract

The invention concerns a heat exchanger (31 or 33) circulating an oscillating primary fluid, such as in a thermoacoustic cell (3, 7) for a thermoacoustic machine (1) wherein an acoustic wave propagates in said fluid, said exchanger of exchange surface S consisting of single-unit elements of characteristic dimension Lc, of heat exchange Ζ between the primary fluid at a temperature Tf and a secondary fluid determining a wall temperature Ts. The invention is characterized in that the dimension Lc and the exchange surface S are such that: Ζ/(Tf Ts) = S*C*A*F*Lcn, wherein F is a characteristic coefficient of the primary fluid, A is a characteristic coefficient of the acoustic wave present in the exchanger, C is a coefficient and n a superscript, both characteristic of the type of flow. The invention is, for example, applicable in the field of refrigeration or cryogenics.

Description

Heat exchanger for application to oscillating fluids in particular in a thermoacoustic cell

The present invention relates to the field of thermoacoustic machines and more generally to that of thermal machines operating with an oscillating fluid. It can be applied for example to a thermoacoustic wave generator, on a refrigerator or for the association of these two machines in a thermoacoustic liquefier. It relates in particular to a means making it possible to size the heat exchanger elements inside this type of machine having an industrial application.

Thermoacoustic energy conversion processes have been developed since the 1970s from work carried out by Peter Ceperley, the principle of which is found, for example, in US patents 4,114,380 or US4355,517. These processes are characterized by their relative simplicity of implementation. They arouse great interest in applications aimed at extracting heat. The aim is thus to liquefy gases, air conditioning, refrigeration or any other equivalent application.

Patents US3237421 from Gifford and US4489553 from Wheatley describe refrigeration machines, for the first a pulsed gas tube and the second a thermoacoustic refrigerator, operating on the thermoacoustic principle and whose mechanical energy source is either a mechanical piston or an electroacoustic source. This mechanical source can be replaced by a thermoacoustic wave generator operating from a thermal source. This gives a refrigeration system without moving parts, which thus has the advantage of significantly reducing the maintenance of these machines.

Patent US4953366, for example, by G. Swift describes a refrigeration machine consisting of a generator of thermoacoustic waves controlling a gas tube pulsed through a resonator tube. Another example of association is given by patent US4858441, where the pulsed gas tube is replaced by a thermoacoustic refrigerator. Among thermoacoustic machines, machines called "Stirling" are also concerned by the invention. The resonator of a thermoacoustic machine consists of a closed tube, generally of circular section, comprising parts of linear or toric shape depending on the operating mode. The tube contains a pressurized gas through which propagates an acoustic wave naturally brought into resonance. A transmitting means, operating according to a thermoacoustic energy conversion process, generates waves inside this tube which comprises at least one receiving means. The active parts, transmitter or receiver, are called thermoacoustic cells. In a thermoacoustic cell, the acoustic energy is partially converted into heat or conversely the heat into thermoacoustic energy. Thus in the receiving part (refrigerator), the acoustic wave allows the transport of heat from a cold source of heat to a second source at higher temperature.

The structure of a thermoacoustic cell results from the fact that an acoustic wave which propagates in a gaseous fluid in contact with a solid wall causes, as the case may be, an acoustic energy production or a transport of heat along it. this. This heat transport induces an axial temperature differential along the wall in the direction of wave propagation. The phenomenon depends on the local exchanges between the fluid and the wall and, located in the boundary layers, is of low energy. To make it meaningful, this surface is increased by multiplying the useful surfaces by stacking channels or walls. These stacks can be made from grids, a stack of plates or in a porous medium.

According to the aspect ratio δ _κ / R _h , where R _h is the hydraulic radius of the elementary channel, this stack of channels is called a stack or regenerator. Thus, for a stack, the distance separating them from each other is generally of the order of twice or 2.5 times the thickness of the thermal boundary layer δ _κ . For a regenerator, the aspect ratio is “1.

The thermoacoustic conversion mechanism is dependent on the phase relationship between the particle displacement xi and the dynamic pressure pi. The structure of the stack therefore depends on the acoustic field. There are two cases:

• when the sound field is stationary, the aspect ratio is less than or equal to 1 in order to control the phase relationship between heat exchange and pressure during particle displacement; • when the sound field is progressive, a maximum effect is however obtained on the one hand if the imposed wave is progressive and on the other hand if the aspect ratio is large.

In the case of a standing wave field, the energy conversion is based on the Brayton cycle; it is from Ericsson and sometimes from Stirling and therefore of a higher efficiency for a progressive wave field.

The heat transported per unit of time is proportional to the sound power as a first approximation.

Thus, within a stack in which an acoustic wave propagates, heat pumping is created, which results in a temperature gradient. Part of the acoustic energy is consumed to allow this pumping. The heat transport being directional, a thermal machine is obtained by combining two heat exchangers with the stack. The heat exchangers are shaped to achieve a uniform temperature field in a cross section of the stack of channels, these must operate as much as possible in parallel, in order to best match the 1D thermoacoustic modeling of the regenerators or stack.

The assembly formed by the stack of channels and two heat exchangers arranged on either side of the stack constitutes the thermoacoustic cell. It can be a wave generator or refrigeration.

In refrigeration mode, the stack of channels allows more generally the transfer of heat from an exchanger at a first temperature to the second exchanger at a second temperature. For operation in a thermoacoustic generator cell with transformation into acoustic energy, a large temperature gradient is created along the wall. It must be at least of the order of lOOOK / m. The phenomenon also takes place in the boundary layer of interaction between the solid wall and the oscillating fluid. The ambient acoustic noise is amplified and an acoustic wave of large amplitude and at the resonance frequency of the assembly is maintained by the temperature gradient. This gradient is generated by means of an appropriate heat source: gas burner, solar collector, etc. In liquefaction of natural gas for example, a mass fraction of this gas is used to supply the hot source, and the cold source, thus created in the resonator, is used to liquefy the unburned gas.

This technique has many advantages:

- it does not use any moving parts;

- its manufacture is easy;

- the reliability and longevity of the components entail a cost of an order of magnitude lower than that of conventional machines;

- the process being entirely thermal, its energy autonomy is easily guaranteed;

- the thermodynamic yields are satisfactory;

the working fluid present in the resonator is preferably helium gas which is an environmentally neutral gas, and

- The process, using thermal energy, is suitable for the use of solar energy for refrigeration plants or for air conditioning.

However, the process has so far remained in a laboratory development stage, for relatively low powers where the operating regimes respect the laws established by Rott. To the knowledge of the applicants, there is no application on an industrial scale commercially available. The known methods, making it possible to define the notably dimensional characteristics of the machines, do not take into account the phenomena which come into play.

The Rott equations are used to describe the parameters in an oscillating flow inside the regenerator. However, they assume that the exchanges at the heat exchangers are perfect.

The inventors have set themselves the objective of producing a machine adapted to industrial constraints.

The invention aims to determine the exchange surface of the heat exchangers, necessary in a cell, according to the power involved to supply or extract the primary fluid. Methods for manufacturing, but not dimensioning, specific exchangers dedicated to thermoacoustic applications can be found in patents US5339640 and US4516632. They are respectively a fin exchanger for gaseous primary fluids and a plate for liquids.

The invention also aims more generally to determine the surface of the exchangers traversed by an oscillating primary fluid. By oscillating fluid in the present application, one understands a perfect gaseous fluid effecting a periodic displacement in time around a mean position in space. Thus, the scope of the invention extends to heat exchanges in oscillating fluid flow: we can cite the control of combustion instabilities encountered for example in launchers and rocket engines, "dream pipes", cooling of electronic (MEM's) or electrical circuits ...

According to the invention, the heat exchanger traversed by an oscillating primary fluid, such as in a thermoacoustic cell for thermoacoustic machine where an acoustic wave propagates in said fluid, said heat exchanger of exchange surface S being composed of unitary elements of characteristic dimension L _c , of heat exchange Φ between the primary fluid at a temperature T _f and a secondary fluid determining a wall temperature T _s , is characterized in that the characteristic dimension L _c and the surface of exchange S are such that, Φ / (T _f - T _s ) = S _* C _* A _* F _* L _c ^π where

- F is a characteristic coefficient of the primary fluid;

- A is a coefficient characteristic of the acoustic waves present in the exchanger, and - C is a coefficient and n a power, both characteristics of the type of flow.

In particular, when the exchangers are made up of elements defining passages of dimension D for the oscillating fluid, such as a bundle of tubes of diameter D or of parallel plates spaced apart by a distance D, the coefficient C is between 1 , 6 and 3,4 and n equal to -1/2. In the description, the coefficient C will be taken equal to 2.06. L _c is equal to the length over which the heat exchange takes place, it is the minimum value between the length L of the exchanger and twice the particle displacement xl.

Preferably, the coefficient F is chosen so that it satisfies the relation F = λ _* Pr ^"1/6 , in which λ is the coefficient of thermal conductivity of the primary fluid and Pr its number of Prandtl.

Preferably again, the coefficient A is chosen so that it satisfies the relation A = 2 _* (uι) ^{1 2} / δ _k ω, where Ui is the particle velocity, ω the pulsation and δ _κ the layer thickness thermal limit along the walls of the exchanger. The power V relating to Ui is defined at more or less 1/5.

The field of validity of this law is in particular for Reynolds Re _Lc numbers between 3 _* 10 and 3 _* 10 and passage dimensions (the diameter D for tubes, the distance D between two parallel plates) very greater than the thermal boundary layer thickness δ _κ along the exchanger walls. In practice, this last condition corresponds to passage dimensions of the order of a millimeter or greater (that is to say between 0.5 and 4 mm) under the operating conditions of applications of thermoacoustic machines.

When the Reynolds number Re _Lc associated with F exchanger of characteristic dimension L _c is greater than 3 _* 10 ⁵ , and the passage dimensions D much greater than the thickness of thermal boundary layer δ _κ along the walls of F exchanger, we choose a coefficient C between 0.09 and 0.18 and n equal to -1/5. In the description, the coefficient C will be taken as 0.118.

We also choose a different exponent for the Prandtl number: F ≈ λJPf ⁷ ^'15 .

Similarly for the coefficient A we find different exponents: A is of the form A = 2 ^4/5 _* (uι) ^{4 / s} / δ _t ^{/ 5} _* ω ^4/5 . The power 4/5 relating to Ui is defined as more or less 1/5.

Thanks to the invention, the law for determining the heat exchange area required in a cell, depending on the power match Hence, one can determine the size of exchangers for _^ certain acoustic parameters fixed. Distance of particle travel (speed, frequency), average gas pressure, temperature difference. The invention relates in particular to exchangers consisting of a plurality of tubes through which the primary fluid passes. The heat exchange is carried out with a secondary fluid traversing the space between the tubes transversely to their axis. The invention also applies to heat exchangers made up of plates which are parallel to each other. The characteristic dimension is then the distance between the plates.

An embodiment of a machine according to the invention is described in more detail below, in relation to the appended drawings in which,

FIG. 1 schematically represents the various components of a thermoacoustic installation,

FIG. 2 represents a graph showing the relationship between the calculated and measured flows, FIG. 3 represents a first practical embodiment,

FIG. 4 represents a graph showing the linearity of the variation in the value of the flow measured as a function of the ratio ΔT / δ _κ for different gases,

- Figure 5 shows a graph showing the linearity of the variation in the value of the measured flux as a function of the ratio

(ΔT / δ _κ ) 2 * λ _* P ^{1 6} / (ω ^1/2 _* L _c ^1/2 ),

FIG. 6 shows the evolution of the thickness of the boundary layer along a plate on VA of acoustic period, and

- Figure 7 shows the representation of a heat exchanger.

A machine 1, such as an HDTR machine (Heat Driven Thermoacoustic Refrigerator), comprises a first thermoacoustic cell 3 which constitutes the generator of thermoacoustic waves. The cell 3 is, here, housed in a straight or U-shaped tube 5, closed near its end. The tube contains a gaseous primary fluid and constitutes a resonator for an acoustic wave passing through the primary fluid. At the other end, the tube comprises a second thermoacoustic cell 7, for refrigeration.

The first thermoacoustic cell 3 comprises, in a known manner, a regenerator placed between two heat exchangers: a hot 31 and a cold 33. A quantity of heat Q _h is supplied from the outside to hot exchanger 31 and a quantity of heat Q ₀ is discharged to the outside at the cold exchanger 33 by a secondary fluid FS. The cell delivers to the resonator 5 an acoustic power in which it is dissipated. The goal of the invention is therefore to generate a maximum acoustic power in a selected section of the resonator. This acoustic source appears as an oscillating gas piston for the part of the resonator where dissipation takes place.

On the other side of the resonator is the heat pumping cell 7.

An example of a heat exchanger 70 is shown in FIG. 7. It consists of small diameter copper tubes 72 mounted between two parallel plates 74 and surrounded by a circular collector 76. The collector is provided with tubular connections 78 for the secondary fluid supply. In operation, the primary fluid travels through the tubes 72 and the secondary fluid the space between the collector and the plates 74 at a temperature different from that of the primary fluid. Heat exchange occurs on the walls of the tubes 72.

The presence of the refrigeration cell inside the resonator influences the overall structure of the acoustic field and therefore the proportion of acoustic energy used for heat pumping or dissipated by visco-thermal effect on the different walls. The energy transmission between the gas piston and the refrigeration cell must be optimized.

Similarly, viscous dissipation must be reduced, which means that the resistive elements must be located near a knot of speed.

According to the invention, the dimensioning of the exchangers is such that the heat flow Φ between the primary oscillating gaseous fluid and the secondary fluid will be optimal or the temperature difference ΔT minimized.

The heat flow Φ is proportional to the difference in temperatures ΔT of the gaseous primary fluid (T _f ) and of the surface of the solid wall (T _s ) through which the heat is exchanged, to the surface S of this wall and to a coefficient h. This coefficient is itself a function of the characteristics of the gaseous fluid and of the conditions of the flow along this wall.

Φ = h * S "AT

In the embodiment shown, the exchangers consist of a bundle of parallel tubes arranged in the axis of the resonator tube or else of plates parallel to each other. The primary fluid therefore circulates inside, parallel to this axis.

In the case of tubes, the exchange surface is then proportional to the number of tubes and to the geometry of the tubes. S is therefore of the form

S — n _* π * D _{* c}

Where n is the number of tubes, D is the diameter of a tube if it is circular or an equivalent diameter if it is of another shape. For example, for oval section tubes, it is the diameter of a circle having the same area.

In the case of exchange surfaces in the form of plates, the surface is proportional to the distance separating two plates. D is then the value of this distance and S = n _* 2 (D + l) _* L _c where 1 is the average width of the plates.

It was surprisingly found that the flux could be determined experimentally from a formulation whose coefficients are valid for continuous laminar flows. Thus we found that the flux Φ was proportional to the square root of the Reynolds coefficient: Re and to the cube root of the Prandtl number: Pr.

To instruct how this law was obtained, tests were carried out with four different gases: helium, argon, nitrogen and SF6. The device includes a thermoacoustic generator cell with heat exchangers composed of 95 tubes each with a gas passage diameter of 3 mm. The cell is housed in a rectilinear resonator tube connected to an O-tube comprising a receiving cell. The tests were carried out with varying speed amplitudes, displacements and pressures.

FIG. 4 to which the value of the measured flux Φ _measured () is plotted as a function of the ratio ΔT / δ _κ shows for each gas the proportionality of the heat flux with the ratio ΔT / δ _κ . The values have been reported on this graph for each gas at different average pressures:

Helium 21, 11, 26 and 19 bars;

Argon 9, 15 and 25 bars;

Nitrogen 9.5 and 16 bars;

SF6 16, 11.5 and 9 bars. This proportionality was also underlined by GWSwift in the article Analysis and performance of a large thermoacoustic engine J. Acoust. Soc. Am., 92-1551-1563, 1992.

He interprets it as the manifestation of a conductive type exchange (proportionality of the heat flow with a temperature gradient) and has introduced in this form in his calculation code DeltaE, currently the most used in the thermoacoustic scientific community. See article by W. C. Ward and G.W. Swift, Design environment for low amplitude thermoacoustic engines (DeltaE) Manual, J. Acoust. Soc. Am. 95: 3671-3672, 1994,

The generality of the law (convective type exchange) claimed for all gases is demonstrated by Figure 5 where we see the perfect proportionality between Φ / S measured and (ΔT / δ _κ ) 2 _* λ _* Pr ^{"1 6} / ( ω ^1/2 _* L _c ^1/2 ). This last term corresponds to λ / L _* ΔT _* Pr ^1/3 _* Re _Lc ^1/2 / (uι ^1/2 ); hence what has been stated previously .

The model of this law (Φ / S _* ΔT) proportional to Pr ^1/3 _* Re _Lc ^1/2 is similar to that used for forced convective permanent flows of boundary layer in laminar regime. In fact, the passage dimension being much greater than the thickness of the boundary layer and the speed u (t) varying very little along the plate, because the length of the exchanger L is very small compared to the acoustic wavelength, may assume that at any time t, a boundary layer flow is developed along the wall. The evolution of the boundary layer thickness along the exchange zone is shown in Figure 6 for different times during a period.

Now for a permanent flow in forced convection, the usual exchange law is h = Nu _* λ / L = 0.66 _* Pr ^1/3 _* Re _L ^{1 2} _* λ / L for 0.6 <Pr <15 and Re _L <3 _* 10 ⁵ , where b is the average exchange coefficient over the length L. See the publication: FP Incropera, DP de Witt, Fundamental ofheat and mass transfer, Third edition, J. Wiley and Sons, Inc, 1990.

However, we theoretically expect to find h = 0.51 _* Pr ^{1 3} _* Re _L ^1/2 _* λ / L for an oscillating flow over a characteristic length L. This last result comes from the spatial and temporal mean of the formulation in permanent flow over an acoustic period and for all with

The possibility of transposing an established law into continuous flow for oscillating flows is therefore quite surprising since the assumptions of Igushi (M. Igushi, M. Ohmi, and K. Maegawa, Analysis of free oscillating flow in a U -shaped tube. Bull. JSME, 25: 1398, 1982.), allowing this, are only partially verified: the particle displacement is indeed always of the order of magnitude of the characteristic dimension D. In addition, one observes that the claimed relationship indicates that the effective transfer coefficient is 4.1 times greater than that which can be deduced theoretically. By analogy, for one is

For different primary fluids such as helium, argon, SF6 gas and nitrogen, tests were carried out using an installation as described above to measure the heat flux exchanged through The cold exchanger of the wave generating cell.

It was determined that the calculation of the heat flux from the value h satisfied the following formula h = C _{2 *} λ _* / L _{c *} (/ 2 _* Pr ^'1/6 / (δ _k ω) _* (u ₁ ) ^1/2 _* L ^{1 2} ) = C _{2 *} λ _* / L _* Pr ^1/3 _* Re _Lc ^1/2

C ₂ is a coefficient depending on the type of exchanger and is worth 2.06 for tabular exchangers in particular. The other coefficients are the thermal conductivity λ, the Prandtl Pr number, the thickness δ _k of the thermal boundary layer, the pulsation ω, the particle speed Ui.

L _c is the characteristic length, L _c = min (2xl, L)

As can be seen in the graph in FIG. 2, the abscissa of which measures the calculated values and the ordinate the measured values, for each configuration tested, the corresponding points are arranged substantially on a line of slope 1.

It is thus possible, thanks to the invention, to determine, from this relationship, the optimal value of the exchange surface and of the diameter of the unitary tube of the exchangers, in a given thermoacoustic application. A linear type wave generator has been shown. It is a standing wave generator operating according to a Brayton cycle where the resonator is a straight tube whose ends are closed. However, the invention applies to other types. The types are distinguished according to the topology of the resonator. The progressive wave generator has an O-tube resonator and operates on an Ericsson cycle. Hybrid generators have an essentially stationary sound field with the exception of the area of the thermoacoustic cell. We find a presentation of the different types of association in the thesis: E. Bretagne, Wave generators and thermoacoustic instability: application to energy conversion, PhD thesis, University of Paris VI, December 2001. Thus, for example, a thermoacoustic refrigeration machine powered by a thermal source can comprise a stationary or progressive wave generator cell associated with a stationary or progressive wave refrigeration cell.

The present invention is illustrated by the following two examples:

In a first case, a refrigeration installation is carried out on board a truck, the heat from the hot source of which can be borrowed at least in part from the engine exhaust gases.

As shown in FIG. 3, the machine comprises a linear resonator tube 100. Several machines are here provided for operating simultaneously in order to fulfill the functionality. Inside this tube containing the primary gaseous fluid, an acoustic wave generating cell 110 is placed at a first end and a receiving thermoacoustic cell 120 at the other end.

The generator cell includes a first heat exchanger 112 through which a secondary fluid passes. Heating can also be achieved by means of a resistive electric cable, heated to the temperature of the hot source. The second heat exchanger 114 is supplied with secondary fluid at ambient temperature and dissipates the heat transferred from the first exchanger 112. In between, the regenerator is composed of a stack of plates between which the primary fluid contained in the resonator tube can circulate. The structure of the regenerator is not part of the invention. It is constructed in accordance with the knowledge of a person skilled in the art.

The secondary fluid of the exchanger 112 is maintained at the required temperature by means of a heat exchanger 130 supplied with combustion gases which include in particular the vehicle exhaust gases. The secondary fluid of the exchanger 114 is maintained here at ambient temperature by means of a heat exchanger supplied with ambient air.

At the other end of the resonator, the second thermoacoustic cell 120, which is receptor, has been placed. It consists of a first exchanger 122 supplied with secondary fluid at room temperature and a second heat exchanger 124 supplied with heat transfer fluid at the temperature of the enclosure that is to be refrigerated. The heat transfer fluid circulates between the exchanger 124 and an exchanger housed in the enclosure to be refrigerated. The regenerator has for example the same structure as the previous cell but any regenerator capable of performing the function is suitable.

We set various data taking into account the conditions of use and the required thermal power.

To determine, for example, the dimensions to be provided for the cold exchanger of the generator cell, the following is fixed: The temperature of the surface of the cold exchanger 114: 293 ° K.

The characteristics of the resonator tube 100: the length, making it possible to fix the resonance frequency, for example is here 8 m. The diameter is 150 mm.

The primary fluid is helium at an average pressure P ₀ of 30 bars and the acoustic characteristics are:

Pressure amplitude, pi = 2.536 _* 10 ⁵ Pa. Speed = 10 ms ^_1 Oscillation frequency, 40Hz.

Knowing that we want to evacuate 22 kW at the cold exchanger 114, we determine the necessary exchange surface, and the coefficient h for a temperature difference T _r T _s of 24.5 ° h = 2120 W / m ² / ° KS = 0.42411 m ² Flux = 22022W Reynolds number Rg = 1.17 _* 10 ⁵ Then D = 0.003 m N = 1000 L≈ 0.045 m

The porosity, that is to say the ratio of the opening of the exchanger to the total section in which it is placed, must be as high as possible. However, technical constraints, such as the wall thickness of the tubes or their spacing, limit this to 50%. In practice, it is lower, between 20 and 40%, here 30%.

In another case, the invention was applied to the determination of the characteristics of a heat exchanger in a thermoacoustic machine for cryogenics. The power of the heat exchanger of the refrigeration part was fixed at 2 kW The values are as follows:

Wall temperature of the cold exchanger, 140 ° K

Po = 25 atm

Frequency 40 Hz Pl = 184,678 Pa

Speed = 6 ΠLS ^"1

Coefficient h = 2017 W / m7 ° K

Exchange surface S = 0.25023 m ²

Temperature difference, T _s -T _f = 4 ° K Heat flow exchanged through the walls 2016 W

Reynolds Re = 7.39 _* 10 ⁴

Tube length, L = 0.027 m Tube diameter, D = 0.0025 m Number of tubes, n = 1180.

The porosity was set at 0.3.

In the two previous examples, the ratio 2xl / L = 1.76. The power deduced by these laws is respectively 2.68 and 2.92 times greater than by a conductive law.

As an example, the following values are recommended for the coefficient C: - laminar case:

- helium C = 1.86 - argon C = 2.3

- nitrogen C = 2.3

- SF6 C = 2.82

- turbulent case:

- helium C≈ 0.107

- argon C = 0.131

- nitrogen C = 0.131

- SF6 C≈ 0.161

The user of the law may, depending on the value of the speed of sound in the gas he has chosen, approach the value of the coefficient C recommended for the preceding gases in which the speed of sound is known, or do any ad-hoc linear interpolation.

Claims

claims

1) Heat exchanger traversed by an oscillating primary fluid, such as in a thermoacoustic cell for thermoacoustic machine where an acoustic wave propagates in said fluid, said heat exchanger of exchange surface S being composed of unitary elements of characteristic dimension L _c , heat exchange Φ between the primary fluid at a temperature T _f and a secondary fluid determining a wall temperature T _s , characterized in that the dimension L _c and the exchange surface S are such that,

Φ / (T _r T = S _* C _* A _* F _* L _c ⁿ

OR

• F is a characteristic coefficient of the primary fluid;

• A is a coefficient characteristic of the acoustic wave present in the exchanger, and • C is a coefficient and n a power, both characteristics of the type of flow.

2) Heat exchanger according to the preceding claim, the associated Reynolds Re _{Lc number} is between 3 _* 10 and 3 _* 10, and the passage dimensions D much greater than the thickness of thermal boundary layer δ _κ along the walls of the exchanger.

3) Heat exchanger according to the preceding claim, consisting of a bundle of tubes of diameter D or parallel plates spaced by a distance D, and whose coefficient C is between 1.6 and 3.4.

4) Heat exchanger according to the preceding claim, whose power n is equal to -1/2.

5) Heat exchanger according to one of claims 2 and 3, wherein F = λ * Pr ^~ 1/6, where λ is the coefficient of thermal conductivity of the primary fluid and Pr its number of Prandtl.

6) Heat exchanger according to one e of claims 2, 3 and 4, whose coefficient A is of the form A or Ui is the speed particulate, ω the pulsation, the power ^l A relating to Ui being defined at more or less 1/5.

7) Heat exchanger according to claim 1, the associated Reynolds Re _{C number} is greater than 3 _* 10 ⁵ , and the passage dimensions D much greater than the thickness of thermal boundary layer δ _κ along the walls of the exchanger .

8) Heat exchanger according to the preceding claim, consisting of a bundle of tubes of diameter D or parallel plates spaced by a distance D, and whose coefficient C is between 0.09 and 0.18.

9) Heat exchanger according to the preceding claim, whose power n is equal to -1/5.

10) Heat exchanger according to one of claims 6 and 7, wherein F = λ * Pr ^~ 7/15, where λ is the coefficient of thermal conductivity of the primary fluid and Pr its number of Prandtl.

11) Heat exchanger according to l 'one of claims 6, 7 and 8, whose coefficient A is of the form A where Ui is the particle speed, ω the pulsation, the power 4/5 relating to a Ui being defined at more or less 1/5.

12) Thermoacoustic cell for a thermoacoustic machine where an acoustic wave propagates in an oscillating primary fluid, comprising at least one heat exchanger according to one of claims 1 to 9.