WO1996021230A1

WO1996021230A1 - A nonperiodically forced bubble fusion reactor

Info

Publication number: WO1996021230A1
Application number: PCT/US1995/015972
Authority: WO
Inventors: Mark J. Embrechts; Richard T. Lahey, Jr.; Robert I. Nigmatulin
Original assignee: Rensselaer Polytechnic Institute
Priority date: 1995-01-06
Filing date: 1995-12-11
Publication date: 1996-07-11
Also published as: AU4511896A

Abstract

A method of generating power comprising creating (12) and injecting gas bubbles of deuterium into a pressure vessel (10) of liquid, generating (14, 16) a pressure field in the liquid of the vessel for compressing the bubbles for a nonperiodic frequency which matches a non-linear resonance response of the bubbles in the liquid to the imposed energy. The resulting bubble oscillations then heat the bubbles to a sufficiently high temperature to cause fusion reactions which release heat into the primary liquid. The heated liquid is then circulated through a heat exchanger (24), and the heat from the heat exchanger is transferred to the secondary side where it is ultimately used to generate (28) electric power.

Description

A NONPERIODICALLY FORCED BUBBLE FUSION REACTOR FIELD AND BACKGROUND OF THE INVENTION

The present invention relates in general to power generation and in particular to a new and useful fusion reactor which utilizes some of the principles of sonochemistry.

The generation of usable power is one of the most pressing needs of modern technology. Fossil fuels have been the main source of this power from the beginning of the industrial revolution to the present day. As fossil fuels become increasingly scarce, alternate energy sources must be found. The most promising alternative to fossil fuel has been nuclear fission which rose to prominence as technology progressed, and then retreated as the problems of safety and waste disposal for radioactive material increased.

Although other alternative energy sources exist, such as geothermal, solar, wind and tide, the stale of technology is insufficiently developed to take full advantage of these sources.

The most promising area for satisfying an ever increasing demand for energy lies in the field of nuclear fusion. The most appealing fusion reactions, because they rely on a source of virtually unlimited fuel, ease of handling and inherent safety, are those reactions involving the heavy hydrogen isotopes deuterium ( H² _l ) or D, and those which involve tritium(H_3l ) or T. Deuterium is abundant, naturally occurring and in wide use as D₂O, or heavy water. Tritium is a radioactive isotope with a 12.3-year half-life and does not occur naturally in nature. Of the possible fusion reactions those involving deuterium are by far die most attractive.

The field of sonochemistry or acoustic-chemical reactions, involves the use of periodic ultrasonic waves to initiate chemical reactions. A good early discussion of this field can be found in an article appearing in the January 1976 issue of Russian Journal of Physical Chemistry, Vol. 50, No. 1 , 1 , "Modern Views on the Nature of Acoustic-chemical Reactions," by M.A. Margulis. On page 7 in that article, the author states that the possibility of achieving thermonuclear reaction temperatures using ultrasonically driven cavitation bubbles, is of practical as well as theoretical interest.

SUMMARY OF THE INVENTION

An object of the present invention is to provide a method and the apparatus for generating power which utilizes nonperiodically forced bubble fusion and pressurized water nuclear reactor technology for energy conversion. According to the invention, bubbles of deuterium are generated by electrolysis, or other means, at a size which is commensurate with the frequency characteristics of the equipment which is used to force bubble oscillations (e.g. , ultrasonic tiansducers). Bubbles consisting of deuterium, and possibly tritium, gas are oscillated violently by the externally forced pressure field until the temperature becomes sufficiently elevated for fusion to occur. Dy properly choosing the non-linear forcing so that it will reinforce bubble resonance, the bubble is made to collapse fast enough so that the energy is contained long enough for fusion to lake place. The power cycle of the reactor is based on a conventional Rankine steam cycle which is typical of a pressurized water nuclear reactor (PWR). In effect, according to the present invention the conventional fission-based nuclear reactor core of a PWR is replaced by the fusion reactor of the present invention. Additional information concerning known PWR technology can be found in Steam. Its generation and Use, 40th edition. Babcock & Wilcox, a McDermott Company, page 54-1.

By using deuterium fuel, little processing is required and the fuel itself is not radioactive. To further minimize environmental and handling hazards, circulating heavy water may be used as the coolant as well as the fuel. The bubble fusion reactor is inherently safe due to its dependence on the availability of nonperiodic forcing. The reactor will shut down immediately at any time by interrupting the power to the equipment used to force the bubble dynamics. Further, radiation and decay heat need not to be considered after shutdown. This is because there is neither the possibility of the continued reaction of fuel nor is there any appreciable radioactive decay in the reactor core after shutdown.

Later in this disclosure, it is demonstrated that the densities and temperatures within the oscillating bubbles are sufficiently high so that the fusion process works with deuterium-deuterium fusion, as opposed to the traditional proposals for deuterium-tritium fusion, which have some adverse features associated with the handling of radioactive tritium.

Accordingly, a further object of the present invention is to provide a method for generating power comprising: injecting gas bubbles of deuterium into the liquid in the pressure vessel; generating a nonperiodic pressure field* in the liquid in the vessel for oscillating and compressing the bubbles at a frequency which matches a non-linear resonance response of the bubbles in the liquid to the impressed pressure field, and for heating the bubbles to a temperature which is sufficiently high to cause fusion reactions in the hydrogen isotopes present, which, in turn, release significant heat into the liquid coolant.

A further objective of this invention is to provide a method which includes circulating the healed liquid though a heat exchanger, withdrawing the heat from the secondary side of the heat exchanger and using it to generate usable power in a Rankine cycle (i.e., with a steam turbine connected to an electric generator). This will involve the circulation of the coolant constituting the primary loop of a classical pressurized water nuclear reactor, but using fusion instead of a fission reaction, and the removal of heat from the heat exchanger via the secondary loop of the pressurized water nuclear reactor. As a consequence, existing technology can be utilized to allow for rapid commercialization of bubble fusion reactors.

Another object of the invention is to provide an apparatus for generating power comprising: means for generating gas bubbles of deuterium (and possibly tritium); a pressure vessel containing liquid; means for injecting the gas bubbles of deuterium into the liquid in the pressure vessel; a means of monitoring instantaneous bubble size; a pressure wave generator operatively connected to the vessel for generating a bubble size dependent nonperiodic pressure field in the liquid of the vessel, for compressing bubbles at a nonperiodic frequency which matches the non-linear resonance response of the bubbles in the liquid to the forcing energy, for healing the bubbles to a temperature which is

* The period of the inpressed pressure field must be coordinated with the instantaneous bubble size to achieve the required gas compression. sufficiently high to cause a fusion reaction in the deuterium which releases heal into the liquid.

A further objective of the invention is to provide such an apparatus wherein the liquid is circulated through the primary loop of a PWR type reactor using the fusion reaction as the power source, and a heat exchanger through which the heated liquid passes for discharging heat into a secondary loop for generating useful power.

The various features of novelty which characterize the invention are pointed out with particularity in the claims annexed to and forming a part of this disclosure. For a better understanding of the invention, its operating advantages, and specific objects attained by its uses, reference is made to the accompanying drawings and descriptive matter in which a typical embodiment of the invention is illustrated.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings:

Fig. 1 is a schematic representation of the bubble fusion reactor's core with other apparatus of the present invention;

Fig. 2 is a schematic representation of a pressurized water nuclear reactor type loop used for generating power according to the invention;

Fig. 3 is a three-part composite graph, plotting various calculated results for the non- linear oscillations of a hydrogen (H₂) bubble, originally at 300 K, and driven by a periodic acoustical field with frequency 10⁵ s^{- 1} and a pressure amplitude of 1.0 MPa;

Fig. 4 is also a composite graph showing calculated results of the non-linear oscillations of a similar hydrogen bubble driven by a nonperiodic pressure forcing with a Δp of 0.9 MPa, and coordinated with the sign of the bubble's radial velocity;

Fig. 5 is a composite graph similar to Fig. 4, but using a perfect gas equation of slate;

Fig. 6 is a qualitative schematic of the different stages of bubble compression for lhe n-th period of compression; and,

Fig. 7 shows the results of numerical evaluations in which all energy losses were included; gas temperatures exceeding 10⁸ K were achieved. DESCRIPTION OF THE PREFERRED EMBODIMENTS

The temperature levels which have been achieved in harmonically-forced sonoluminescence experiments are around 5000 K, as shown in the Margulis article and in numerous more recent articles. Nevertheless, much higher temperatures are possible using the techniques which are the subject of this patent. Indeed, the same basic phenomena can be used to obtain fusion in deuterium bubbles where it is necessary to achieve very high compression-induced temperatures (i.e. > 10⁸ K), according to the invention.

The invention uses a new non-linear, nonperiodic method of excitation of the kinetic energy of the liquid surrounding the bubble so that superhigh compression of the gas bubble takes place. This mode of excitation achieves very high gas bubble compressions and temperature peaks using modest pressure amplitudes (e.g., less than 10 bar) and frequencies (≅ 1 kHz). This mode of excitation involves nonperiodic liquid pressure oscillations with increasing periods of inertial expansion and compression of die bubble. This method is analogous to the method a basketball player used for gradually increasing the rebound of a basketball of the floor during dribbling. Instead of periodic impacts with the ball's motion, not impeding the ball when it is rising and impulsively pushing the ball downward when it is falling. When the amplitude of the rebound increases, the periods between the rebounds and the coordinated basketball player's impacts with the ball must increase too. What is happening, is that the basketball player "pumps" mechanical energy into the ball which is moving between the floor and the player's hand. This coordination may be treated as a non linear resonance forcing of the basketball.

When "pumping" kinetic energy into a gas-bubble/liquid system, the method used by a basketball player can also be employed. The non-linear coordinated multi-pulse resonance excitation method for external liquid pressure excitation of the invention operates as follows: At the moment of maximum gas bubble expansion, when the bubble's volume begins to decrease (because of over-expansion of the bubble) the liquid pressure must be quickly increased to reinforce the liquid's compression of the gas bubble. This new pressure must be maintained until the moment of the maximum compression of the bubble, whereupon the bubble begins to expand because of over-compression of the bubble. At this moment the liquid pressure must be dropped sharply to its minimum so as not to impede the liquid being radially accelerated due to bubble expansion and this low liquid pressure must be maintained until the subsequent end of bubble expansion. As the process continues, the liquid pressure oscillation periods must increase as the amplitude of the bubble's radius increases. Thus the key feature of this method of excitation is a correspondence of the non-harmonic oscillations of forced pressure in the liquid with the periods of expansion and compression of the gas bubble. As noted above, there is a direct analog with the method used for increasing the basketball's rebound by a basketball player.

This method of non-linear coordinated resonance excitation (which can be referred to as the "basketball dribbling regime", or BDR), allows one to achieve successively increasing compressions and superhigh gas temperatures in the gas bubble. These temperature peaks by far exceed the temperature peaks seen in sonochemistry experiments which use traditional harmonic excitation with fixed frequency, which is based on the linear resonance response for small amplitude bubble size oscillations.

The non-linear bubble forcing method described above is one of a family of non-linear forcing techniques (e.g., harmonic plus nonperiodic pulses) all of which are the subject of this invention. These proposed methods for obtaining superhigh temperatures are achieved using feedback between the liquid pressure and changes in bubble size.

Basic equations

The system of equations which describes the dynamics of the spherically symmetric flow of an incompressible liquid around a spherical bubble have been given by Nigmatulin, R.I., Dynamics of Multiphase Media, Vol. 1, Hemisphere Press ( 1990).

For a state of high gas bubble compression, the molecular volume should be taken into account in the equation of state for the gas. As a first approximation this influence may be taken into account using the high temperature approximation of the Van der Waals equation of state for the gas pressure, p_g , and for the internal energy, e_g :

here T_g and ρ_g , are the gas temperature and gas density, R_g and c_g are the gas constant and the constant volume heat capacity of the gas; 1/ρ* corresponds to the specific volume of the gas molecules, which is constant and determined by the critical density of the gas, (i.e., ρ* - 3_pα ).

The Van der Waals model of a gas is characterized by a gas constant, R_g , heat capacity, c_g , and the pressure, p_cr, and density, ρ_cr at the critical point. Van der Waals' model gives the temperature for the critical point as:

The difference in this value from the critical lemperatuie for a real substance is a measure of the errors inherent in the Van der Waals model. For instance, for hydrogen gas:

while the Eq. (2) gives, T_cr = 26.7 K. From the data of the critical point of hydrogen:

The internal energy equation for the gas bubble is:

where∇● q " is the divergence of the heat ilux vector due lo thermal conductivity, q_r"' is the gas energy loss density due to radiation. Equation (5) may be reduced to a gas pressure equation if the gas pressure is assumed to be uniform through the bubble (i.e., p = p_g(t); such a bubble may be named as a homobaric bubble), which is taken to be spherical in shape and of radius a. That is:

In Eq. (6) w is the radial velocity of the liquid on the bubble's surface, q is the total heat loss from the bubble, consisting of radial heat transfer, q _a , due to the conductive/convective heat losses through the bubble's interface and the energy losses due to radiation, is an averaged density of the gas and Y is the adiabatic exponent of

the gas.

The mass conservation law for the gas in the bubble without phase change is:

where ρ_g0 and a₀ aie the initial density and the initial radius of the bubble, respectively.

The momentum equation for the spherically symmetric flow of a non-compressible liquid is given by the well known Rayleigh Lamb-Plesset equation:

where p_l, μ_l , and σ are the density, dynamic viscosity of the liquid and the surface tension, respectively, and p_∞ is the forcing pressure (i.e., the external pressure impressed on the liquid far from the bubble).

The equations for the liquid and the gas temperature distribution around the bubble, which determines the inierfacial heat transfer, q_α , are known. Expressions for q_r include various kinds of gas or plasma radiation losses from the bubble. For details on the plasma losses see, e.g., Slacey, W. M., Fusion: An Introduction to the Physics and Technology of magnetic Confinement Fusion. John Wiley & Sons (1984). The principal results of the invention, however, are not strongly dependent on conductive, q_α, and radiation, q_r, losses, since, as can be seen in Fig. 6, the speed of the compression process is veiy fast, and thus the time available for energy loss is small.

Numerical Results

Figure 3 illustrates the non-linear oscillations of a hydrogen bubble in water (a₀ - 1 mm, p_ϋ = 0.1 MPa, Δp₀ = 1 MPa) which, as in classical sonochemistry experiments, is forced by a harmonic acoustical field of angular frequency, ω = 10⁵ rad/s, which corresponds to the linear resonance frequency of the bubble. The analysis assumes an adiabatic process in the gas (∇● q " = q_a = q_r = 0), and that the gas has a uniform pressure and temperature, and is undergoing an iscntropic process. Until the moment t = 0 the system was assumed to be at rest and in equilibrium (i .e. , iv = 0, p_∞ = p_g 2 σ / a .) In contrast, for t > 0 the pressure of the liquid far from the bubble, p_∞, is given by:

where p₀ and Δp are the initial liquid pressure and the pressure amplitude of the harmonic oscillations in the liquid far from the bubble. It is seen in Fig. 3 that even without dissipation there is no increase with time of the peak gas temperature (i.e.,≈ 5000 K). The disorder in the oscillations, even at the linear resonance frequency, is a result of the free oscillation period change due to non-linearities. Variations in the forcing frequency, ω , or the period of the acoustic field oscillations, do not change the essential results, which are typical of the response seen in harmonically-forced sonoluminescence experiments.

In contrast, Fig. 4 illustrates the dependence of the various bubble parameters for non-linear coordinated resonance forcing of the same bubble/liquid system of Fig.3. The solid lines are for the van der Waals equation, Eq. ( 1), and the dashed lines conespond to the perfect gas state equation,

It is seen that the corrections for molecular volume influences the bubble compression rate but do not influence the temperature peaks. This is a consequence of ignoring the influence of gas density on internal energy.

For the present invention, as illustrated in Fig. 4, during the time kinetic energy is being "pumped" into the bubble, dissipation, due to liquid viscosity, heat conductivity and radiation losses, have no significant influence. This is why it is possible to get useful results from considering the adiabatic case without viscosity. Indeed, the non-dissipate approximation greatly simplifies the mathematical investigation since it may be done analytically.

Figure 5 demonstrates the successive growth of the gas temperature peaks, which occur at the moment of maximum bubble compression. These calculations were made using the perfect gas law. The solid lines are calculated with dissipation and heat losses, while the dashed lines had neither. Below it is demonstrated that, for the non-dissipative (i.e., isentropic) case, these temperature peaks grow in accordance with a geometric progression. For every period of compression (or expansion) two sub-periods may be noted. They are: a sub- period of slow compression (or expansion) and a sub-period of very fast compression (or expansion) with a "sharpening" of the temperature - time dependence. The superhigh temperatures (i.e. T > 10⁴ K) and pressures take place during a short time interval when the bubble is at its minimum size. Some features of this interval are shown schematically in Fig. 6.

The dissipation, because of the liquid viscosity, μ_l , the thermal conductivity losses, q_a , and the radiation losses, q_r, must evolve asymptotically, after many non- harmonic oscillations, to a coordinated resonance regime of periodic oscillations with fixed frequency (depending on the pressure amplitude of the external forcing) where the amount of kinetic energy "pumped" into the system by the external forcing during the period is equal to the quantity of the energy dissipated due to viscosity, thermal conductivity and radiation during the same period.

It is important that the appearance of this stabilized periodic oscillation regime, involving superhigh compression of the bubble, is possible only after the nonperiodic resonance-intensified BDR regime which pumps-up the kinetic energy of the liquid in die oscillating system.

The practical realization of these periodic and nonperiodic regimes are associated with using feedback between the external driving pressure in the liquid, p_∞, and the bubble's transition from compression to expansion and back again according to the invention. These transitions are determined by the change of the sign of radial velocity, W , on the bubble's interface; when w < 0, the pressure p_∞ must be a maximum, while when W > 0, the pressure p_∞ must be a minimum.

Numerical calculations have been performed using the model just described including all relevant radiation loss terms. It can be seen in Fig. 7 that gas temperatures in excess of 10⁸ K were achieved using BDR non-linear forcing. Significantly, these temperatures are high enough to achieve thermonuclear fusion.

General Comments about the Invention

It should be stressed that to have "basketball dribbling regime" (BDR) type resonance forcing of kinetic energy into the two-phase system it is not necessary to have exactly a stepwise driving pressure, p_∞, with fixed Δp , stopping and initiating exactly at the moments of the maximum an minimum bubble radius, as was used in the calculations previously discussed. It is important only that the positive work of the external forces during the compression ( W < 0) time t_(c) for every step:

should exceed the negative work of the external forces during the expansion (IV > 0) time t_(e) for the same step:

togetherwith the dissipation during the time interval t_{( c)} + t_(e). Indeed, other nonperiodic forcing functions are possible and are part of this patent, but all involve coordinating the external forcing with the iiistanlaneous size of the oscillating bubble. For the proposed regime, which has coordinated liquid pressure forcing and oscillation of the bubble, the dissipation, and only the dissipation (viscous dissipation mechanisms, conductive and radiative heat losses, compressibility of the liquid), may impose a limitation on T_g and p_g . Moreover, these losses may cause the establishment of a periodic regime. In addition, evaporation of the liquid at the bubble's interface (during subcritical conditions of the liquid), ionization not only from the gas atoms but the liquid atoms too, diffusion of gas and liquid atoms through the interface, compressibility of the liquid with shock wave effects in both the liquid and the gas, and instability of the bubble's interface, may have a significant influence on the maximum temperature and pressure of the gas bubble. See Wn, C.C., and Roberts, P.H., Physics Review Letters. Vol. 70, No. 22, 3424 ( 1993). Nevertheless, the invention achieves superhigh gas bubble temperatures which should enable the commercial use of thermonuclear fusion for energy production.

Hardware of the Invention

Referring to Fig. 1 , the invention can be implemented in a pressure vessel (10) of conventional design and be used in PWR nuclear reactors. Unlike the conventional reactors however, the vessel ( 10) has a bubble generator ( 12) which generates deuterium bubbles (e.g., by electrolysis) that are injected into the liquid contained in the pressure vessel. Pressure transducers ( 14) and (16) are strategically located around the vessel and used to generate nonperiodic pressure waves inside the vessel, for example, standing waves or intermittently pulsed waves having a variable period and amplitude for compressing the oscillating deuterium bubbles, according to the invention, to increase their temperature to ultrahigh levels. A helium and tritium scrubber system ( 18) is connected to the outlet of the vessel ( 10) to remove helium and tritium from the now heated liquid stream.

Figure 2 illustrates a conventional PWR loop which replaces the fission reactor core with the nonperiodic forced bubble core of the present invention (see Fig. 1). The bubble generator (12) and scrubber ( 18), along with the pressure vessel (10) are provided on the primary circulating loop of the bubble fusion reactor, along with a main circulation pump (20) and a pressurizer (22), both of essentially conventional design. A heat exchanger (24) establishes a heat transfer link between the primary loop and a secondary loop which contains a steam turbine (26) connected to an electric generator (28) and a steam condenser (30) and circulating pump (32) for circulating the secondary loop water (H₂O) through the heat exchanger (24) for heating the water using the heat from the fusion reactions in the vessel (10).

Claims

WHAT IS CLAIMED IS:

1 . A method of generating power comprising:

a) injecting gas bubbles of deuterium (and possibly tritium) into a pressure vessel of liquid D₂O (or some other suitable liquid);

b) generating a nonperiodic pressure field in the liquid of the vessel for compressing the bubbles at a nonperiodic frequency which matches the nonlinear resonance response of the bubbles in the liquid by monitoring the instantaneous bubble size and using this information to set the forcing frequency, for compressing the bubbles and allowing the bubbles to expand repeatedly and heating the bubbles to a temperature which is sufficiently high to cause fusion reactions in the bubbles which releases heal into the surrounding liquid, the pressure forcing having a period which increases based on the instantaneous size of the oscillating bubbles; and,

c) circulating the heated liquid through a heat exchanger, from which heat is used to generate electric power.

2. A method according to Claim 1 wherein the nonperiodic pressure field is created within the pressure vessel.

3. A method according to Claim 2 including adjusting the pressure forcing function so that positive work is supplied to each bubble of deuterium during a compression phase which exceeds any dissipation and negative work of the bubble generated during an expansion phase of the bubble.

4. A method according to Claim 1 including adjusting the frequency of the external pressure field so as to use feedback between the external pressure around each deuterium bubble and the instantaneous bubble size as each bubble enters a transition phase between a period of expansion and a period of compression, during non linear resonance of the bubbles.

5. A method according to Claim 1 including using pressurized water nuclear technology having a circulation path containing a primary-to-secondary heat exchanger, a core which is located in a pressure vessel containing the pressure field forcing system hardware and injected bubbles of deuterium (and possibly tritium), and connecting to a secondary loop containing a turbine-generator and extending through the heat exchanger for powering the generator with energy from the heat exchanger to generate useful power.

6. An apparatus for generating power comprising:

a) means for generating gas bubbles of deuterium;

b) pressure vessel containing liquid;

c) means for injecting the gas bubbles of deuterium (and possibly tritium) into the liquid of the pressure vessel;

d) a device for creating the non-linear pressure field operatively connected to the vessel for generating a pressure field in the liquid in the vessel, for compressing the bubbles at a nonperiodic frequency which matches the non-linear resonance response of the bubbles in the liquid to the impressed pressure, to compress and expand the bubbles for healing the bubbles to a temperature which is sufficiently high to cause a fusion reaction in the deuterium gas which, in turn, releases heat into the liquid; and

e) circulating the healed liquid through a heat exchanger from which energy is removed and ultimately converted to electrical power.

7. An apparatus according to Claim 6 wherein the pressure vessel, the means for generating gas bubbles of deuterium (and possibly tritium) and the heat exchanger are in a primary loop typical of a pressurized water nuclear reactor, the apparatus including a secondary loop containing a turbine and generator for generating electrical power.

8. An apparatus according to Claim 7 wherein the device used to generate the imposed pressure field is positioned to generate a nonperiodic pressure in the liquid having a frequency with a period which increases for increasingly adding energy into the expanding and compressing bubbles.

9. An apparatus according to Claim 7 wherein the pressure field generator is positioned and structured to establish the required nonperiodic pressure field in the pressure vessel.