WO1988005223A1

WO1988005223A1 - Reciprocating free liquid metal piston stirling cycle linear synchronous generator

Info

Publication number: WO1988005223A1
Application number: PCT/AU1988/000001
Authority: WO
Inventors: Garrett Michael Sainsbury
Original assignee: Garrett Michael Sainsbury
Priority date: 1987-01-05
Filing date: 1988-01-04
Publication date: 1988-07-14
Also published as: AU1159288A; AU604295B2

Abstract

An electrical generator comprising two pairs of primary chambers, being a pair of hot chambers (11, 12) and a pair of cool chambers (15, 16) each containing a quantity of conducting liquid. A heat source (not shown) is provided for heating the hot chambers and a cooling means (not shown) is provided for cooling the cool chambers. The hot chambers (11, 12) are interconnected at their lower ends by a duct (13) incorporating an electrical generator unit (14). The cool chambers (15, 16) are interconnected at their lower ends by a duct (17) incorporating an electrical generating unit (18). The space (21) above the liquid in one of the hot chambers (11) is connected to the space (25) above the liquid in one of the cool chambers (15) to define a first working space. The space (21) above the liquid in the other hot chamber (12) is connected to the space (26) above the liquid in the other cool chamber (16) to define a second working space. The first and second working spaces are filled with an inert gas. Heat stores (22, 23) are provided in the working spaces to extract heat from gas flowing from the hot chambers and to heat gas flowing from the cool chambers.

Description

"RECIPROCATING FREE LIQUID METAL PISTON STIRLING CYCLE LINEAR SYNCHRONOUS GENERATOR"

THIS INVENTION relates to a electrical generator.

In one form the invention resides in a electrical generator comprising two pairs of primary chambers containing a quantity of conducting liquid, a heat source for heating one pair of primary chambers, a cooling means for cooling the other pair of primary chambers, each primary chamber of each pair being interconnected at their lower ends by a duct, each duct incorporating an electrical generating unit, the space above the liquid in one chamber of the one pair of chambers being connected to the space above the liquid of one chamber of the other pair of chambers to define a first working space, the space above liquid in the other chamber of the one pair of chambers being connected to the space above the liquid in the other chamber of the other pair of chambers to define a second working space, said working spaces being filled with an inert gas, a heat store provided in each working space between the spaces to extract heat from the gas flowing from the chambers of the one pair of chambers and to heat the gas flowing from the chambers of the other pair.

According to a preferred feature of the invention the electrical generating unit of the other pair of chambers being connected to the output of the electrical generating unit of the one pair of chambers for the supply of power when work is required to drive liquid in its movement between the other pair of chambers.

According to a preferred feature of the invention the flow of liquid between the chambers of a pair of chambers can be varied from zero to 90° out of phase relative to the flow of liquid between the chambers of the other pair of chambers in order to vary the power output of the generator.

According to a preferred feature of the invention the outputs of the electrical generating units are connected in an electrical circuit containing reactive elements.

According to a further preferred feature the reactive elements comprise capacitors and inductors.

According to a further preferred feature of the invention the two generators are connected adjacent each other and wherein the liquid flow therebetween is 180° out of phase such that the reaction forces created in each are in opposition.

According to a preferred feature of the previous features wherein the outputs of the two generators are connected in series.

According to a preferred feature of the previous two features a plurality of pairs of generators mounted in close proximity utilising a common heat source wherein the output of each pair are connected in parallel said pairs being out of phase by 360º n where n comprises the number of pairs of hydrodynamic generators.

According to a preferred feature of the invention the gas is introduced into the space in each chamber when flowing between spaces by being injected into the liquid.

According to a preferred feature of the invention a closed member having thermal insulating properties is slidably received in each duct to each side of the magnetic hydrodynamic cell. According to a preferred feature of the invention the gas pressure in the working spaces is caused to vary in a manner which causes the fluid columns to oscillate as a sinusoidal function of time.

According to a preferred feature of the invention means are provided to vary the volume of the working spaces to induce pressure therein to cause sinusoidal fluid flow between the chambers.

According to a preferred feature of the previous feature said means comprises a piston slidably supported to be movable into and out of the working spaces.

According to a preferred feature of the previous feature the piston is caused to move through the action of a rotating cam.

According to a preferred feature of the invention the generating unit comprises a solid armature slidably received in the duct and comprising a plurality of longitudinally spaced conducting elements associated with at least two magnetic poles of opposite polarity spaced longitudinally along the duct and capable of reciprocation past the holes as a result of the flow of liquid between the chamber connected by said duct conductive coils surrounding the duct in the region of the poles.

In another form the invention resides in a electrical generating unit comprising a duct communicating at either end with the liquid chambers of a electrical generator said duct being associated with, at least two magnetic poles of opposite polarity spaced longitudinally along the duct, an armature slidably received in the duct in the region of the poles said armature comprising a plurality of longitudinally spaced permeable elements formed of high magnetic permeable material each located opposite one or the other pole said armature being caused to reciprocate in the duct under the influence of hydrostatic pressures of the liquid chambers conductive coils being mounted in the poles adjacent the ducts.

According to a preferred feature of the invention the spacing between the permeable elements substantially equal the spacings between the poles plus the stroke of the armature.

According to a preferred feature of the invention the face of the poles adjacent the duct support a plurality of conductive coils which are connected in series.

According to a preferred feature of the invention a pair of ducts are positioned in parallel relationship.

According to a preferred feature, of the invention the poles are located adjacent one face of one duct and the ducts are separated by a spacer formed of material having a high magnetic permeability said spaces being in opposed relation to the poles, the other face of the other duct being associated wi th a yoke being located in opposed relation to the space occupied by the spacers.

According to a preferred feature of the invention the poles permeable elements, spacers and yokes are laminated.

The invention will be more fully understood in the light of the following description of an embodiment thereof. The description is made with reference to the following drawings of which:-

Figure 1 is a schematic diagram of the embodiment; Figure 2 is a graphical representation of the variation in the volume of the working spaces of the embodiment;

Figure 3 is a schematic diagram of the upper space of a hot chamber;

Figure 4 is a schematic diagram of the upper space of a cool chamber;

Figure 5 is a graphical representation of the instantaneous power requirement of the cold column linear motor and the buffer piston for one working spaces;

Figure 6 is a graphical representation of the compressor linear motor emf and current;

Figure 7 is a schematic circuit diagram of the connection between the compressor motor and engine generator;

Figure 8 is a plan layout of a multiple unit system;

Figure 9 is a sectional elevation of the multi unit system of figure 8;

Figure 10 is a sectional view of the combustion air preheater;

Figure 11 is a sectional view of a form of generator cell for use with the embodiment;

Figure 12 is a graphical representation of the power output of the embodiment before buffer piston induced pressure adjustments;

Figure 13 is a schematic diagram of one form of the means for varying gas pressure of the working spaces;

Figure 14 is a plan view of the cam of the form of varying gas pressure shown at figure 13; Figure 15 is a graphical representation of the power output after the buffer piston induced pressure adjustments;

Figure 16 is a graphical representation of the combined power at the shaft of the flywheel operating the buffer pistons shown at figures 8 and 9; Figures 17 and 18 show cyclic gas mass and temperature in the engine compressor and heat stores;

Figure 19 shows the corresponding engine pressure to the factors shown at figures 17 and 18;

Figure 20 shows cyclic engine volume compressor volume and combined volume; and

Figure 21 shows the volume of the compressor space.

The embodiment is directed to a electrical generator of similar form to that disclosed in International application number PCT/AU86/00101. The generator as shown at figures 1, 3, 4, 5 and 6 comprises a pair of generating circuits. One circuit comprises a pair of primary chambers 11 and 12 which are in heat exchange relationship with a combustion chamber (not shown) and are hereinafter referred to as the hot chambers. The lower end of the hot chambers 11 and 12 are interconnected by a cooled duct 13 which is associated with a electrical generator unit 14. The heat chambers 11 and 12 and duct 13 contain a quantity of liquid metal 10 which may comprise sodium, potassium or an alloy of sodium and potassium.

The second circuit comprises a pair of cool primary chambers 15 and 16 which are interconnected at their lower ends by a duct 17 which accommodates a electrical generator unit 18 acting as a motor. The cool chambers 15 and 16 and the duct 17 contain a quantity of liquid metal 19 such as an alloy of sodium potassium which is liquid at room temperature. The cool chambers are in heat exchange relationship with a cooling circuit containing a circulating cooling fluid.

The spaces 21 and 22 at the upper end of the heat chambers 11 and 12 respectively are connected to the spaces 25 and 26 respectively of the cool chambers 15 and 16 respectively through a heat store 22 and 23 respectively. The heat store contains a mesh of fine wires which can readily absorb and give up heat from the gas flowing between the interconnected spaces of the respective heat and cool chambers. The spaces 21, 22, 25 and 26 are filled with an inert gas such as helium.

The embodiment operates in accordance with the Stirling engine cycle whereby the liquid in the hot chambers flows therebetween through the duct 13 in a substantially sinusoidal manner and generates an electrical current in the generator 14 and define the engine. The liquid in the cooled chambers 15 and 16 flows between the chambers through an interconnecting duct 17 substantially in a sinusoidal manner and define a compressor. The flow of liquid in the engine is substantially 90° out of phase with the flow of liquid in the compressor when the generator is at full load, variable to substantially in phase at minimum load.

The volume of the two working spaces defined by the interconnected spaces 21, 25 and 26 and the respective heat stores 22 and 23 cyclically increase and decrease as shown graphically in figure 2. The bulk of the gas of each working space is in the respective hot chamber when expansion commences and the pressure therein is correspondingly high. Conversely the bulk of the gas is in the cold space when compression commences and the pressure is correspondingly low. The work exerted is a product of the change in a volume and pressure at which the change occurs and as the average pressure is higher during the expansive change of volume than it is during the compressive change of volume net positive work is performed during a complete cycle. The net positive work is equal to the difference between the heat added to the gas in the hot pipe and the heat rejected from the gas in the cold pipe. The heat stores improve the thermodynamic efficiency of the process by absorbing heat from the hot low pressure gas as it moves from the hot space to the cold space on the rise of the liquid level in the respective hot chamber and passes heat back to cold compressed gas as it moves from the cold space into the hot space as a result of a rise in the liquid level in cold chamber. The power extracted is the rate of doing works which is dependant upon the rate at which heat can be added to the gases in the hot chamber and extracted from the gas in the cold chamber.

The rate of heat transfer and hence power density is maximized by:

1. Using liquid metal with high thermal conductivity eg. sodium and potassium. The low density of these metals also aids power density by reducing the dynamic pressure required to accelerate the mass thus increasing frequency of oscillation. Lithium would be the ideal metal on the above criteria and it also has lower vapour pressure than sodium allowing higher temperature and thus more efficient operation but is expensive and difficult to contain at high temperatures.

2. Using gas with a high thermal conductivity, such as helium. Hydrogen has higher conductivity but is not compatable with the alkali metals.

3. Injecting the helium gas working fluid into the liquid metal so it is heated and cooled by direct contact heat exchange. The means of effecting this latter feature is shown in figure 3 for the hot chamber and figure 4 for the cold chamber.

As shown at f igure 3 the hot space 21 is connected to the respective heat store 22 through an inlet line 30 and outlet line 31 each having a non-return valve 32 and 33 respectively. The inlet line opens into an inlet manifold 34 which is provided with a plurality of tubes 15 which extend into the liquid metal 10 in the hot chamber 11. As a result the gas entering the hot chamber is injected into the liquid metal and is heated rapidly by direct contact with hot liquid metal. The gas expands and drives the hot liquid metal into the duct 13 and ultimately into the other hot chamber 12 until back pressure prevents the further flow of liquid in that direction. At this point the same action commences in the other hot chamber 12 to drive the liquid metal into the one hot chamber 11. The outlet line 31 in the one hot space connect into an exhaust manifold 38 located at the top of the hot space and connected to the space 21 by a set of exhaust parts 37 provided in the top of the space 21. On the liquid level in the one hot chamber 11 being raised low pressure gas is exhausted through the exhaust ports 37 the manifold 38 the outlet line 31 and non return valve 33 to the heat store 22 and then to the respective cold space .

The space at the top of the cold chamber is connected to the heat store 22 through an inlet line 40 and outlet line 41 which are each provided with a non return valve 42 and 43 respectively. The incoming gas enters from the inlet line 40 into a manifold 34 which is provided with a set of tubes 45 for the injection of gas into the liquid metal. The cold chamber 15 accommodates a central pipe 46 having an open lower end and is provided with apertures 47 in the upper end. The centrol pipe 46 is connected into the duct 17 and a non return valves 48 and 49 are provided in the centrol pipe 46 to each side of the connection to the duct 17. Cooling of the liquid metal is effected by cooling conducts 47 extending through the cool chamber 15 between a lower header 50 and upper header 51. The outlet line 41 opens into the upper end of the centrol pipe 46 through a set of exhaust ports (not shown) therein.

Gas entering the cool chamber through the injection tubes 45 is cooled by intimate contact with the cold liquid metal. Due to low pressure existing in the duct 17 liquid metal is forced into the central pipe 46 past the lowermost non return valve 49 therein and out through the duct 17 to the other cool chamber 16 until the back pressure prevents further place. At this point the same action commences in the other cool chamber 16 driving liquid metal back into the duct 17 and to the one cool chamber 15 where it enters the central pipe 46 passed the uppermost non return valve 48. As the level of liquid rises cooled compressed gas is driven from the cool chamber through the exhaust ports, outlet line 41 and non return valve 43 heat stove 22 to the hot space 21.

The flow of liquid into and out of the control pipe 46 is effectively uni-directional by virtue of the one way valves 47 and 48 therein and serves in ensuring the circulation of liquid metal in the chamber to prevent the development of hot spaces therein.

Transfer of Power to Generator

The engine generator 14 has positive power output at all times but the compressor generator 18 requires a power input at times during its cycle. Such power is derived from the engine generator 14. The instantaneous power converted in each compressor generator under full load is in the form shown in figure 5 from which the average power can be obtained (e.g. by numerical integrators).

The instantaneous current is obtained from

i = p/e

where

i = instantaneous current p = instantaneous power e = instantaneous emf

from which the maximum current I_max can be obtained (eg, numerically).

The maximum emf can be obtained from

E_max = E_ave

where

^Emax = maximum emf

E_ave = average emf = S/t * B * 1 S = armature stroke t = stroke period B = magnetic flux density

1 = combined length of active conductors connected in series

Figure 6 shows typical compressor generator emf and current curves corresponding to the power curve of figure 5 where negative power indicates the generator is drawing power from the system. It can be seen that the current and voltage are out of phase by an angle ∅ which can be obtained from the expression

P_ave = 1/2 * E_max * I_max cos ∅ ∅ = cos ^-1[2 * P_ave/(E_max * I_max)]

In order for the engine generator to transfer power to the compressor generator as required, some reactive elements must be introduced into the circuit as shown schematically in figure 7.

In the diagram,

G represents two engine generators of one phase connected in series

M represents two compressor generators of one phase connected in series

R₁ = internal resistance of G

R₂ = internal resistance of M

Z₁ & Z₂ represent impedance

E₂ = E_max<0°; voltage phasor

I₂ = I_max<∅; current phasor

E₁ = E _max <-90 ^º; voltage phasor for engine generator lags compressor generator voltage by 90°

I₁ = I¹ _max <- 90º; current phasor for engine generator, in phase with voltage ie ∅¹ = 0

E¹ _max is obtained in the same manner as E_max

I¹ _max is obtained from the expression V $

The term on the left is the power drawn from the engine generator and the first term on the right is the power converted in the compressor generator. The second term on the right is the power dissipated in the internal resistance of the compressor generator.

Reactance Z₂ is obtained from the phasor equation

E₂ = I₂ R₂ + (I₁ + I₂) Z₂ (i)

and the reactance Z is obtained from

E₁ = I₁ R₁ + I₁ Z₁ + (I₁ + I₂) Z₂ (ii)

In the case where 0 is positive, ie. compressor generator current leads the voltage, Z₂ is

Z₂ = (a - j b) ohms

The negative sign of the second term indicates that Z₂ includes a capacitor with

C₂ = 1/(b * 2 π * f)

where

C₂ = capacitance, farads b = numerical term obtained from the solution of phasor equation (i) f = frequency, hertz

The numerical term a represents resistance

a = resistance in series with capacitor C₂ Similarly, Z ₁ includes a capacitor with capacitance

c₁ = 1/(b¹ * 2π * f)

in series with a resistance a¹

Depending on the values involved it may be desirable to couple the generators to the circuit through transformers to increase the voltages thus reducing the size of the capacitors.

In a practical circuit the reactive elements include inductors as well as capacitors and are sized to make the real component of each reactance zero in all except one element which then represents the load resistance. Also, the capacitance and reactance are variable to accommodate different loads.

As shown at figures 8 and 9 a number of units of the form described above may be mounted in a common combustion chamber 60 having a pair of burners 61 and 62. The combustion chamber is formed with two recesses 63 and 64 in the upper walls which accommodate the compressor circuit of each end. The units are located in the combustion chamber such that they are arranged in 3 pairs wherein the movement of the liquid metal in the units of each pair are opposed in order that the reaction forces in one are balanced by substantially equal and opposite reaction forces in the other. The emf developed by one unit of a pair is 180 out of phase with the other unit and the output of each of the units of a pair of units are connected in series. The emf of the pairs of units are 120^º out of place with each other and their outputs are connected to provide 3 phase power. The hot chamber 11 and 12 of each unit is supported in the combustion chamber and is formed with a set of fire tubes 69 which open at their lower end into an exhaust 65 opening at the lower end of the combustion chamber. Combustion gases from the burners 61 and 62 circulate through the combustion chamber as shown by the broken lines in figure 9 and finally exhaust through the exhausts 65. The upper end of the fire tubes 69 connect into a header 66 interconnecting the fire tubes of all of the hot chambers. The header 66 communicates with a combustion air preheater 67 and thence to a stack 68.

The heated cooling fluid from the compression units exit the upper header 51 and flows through pipe 70 to a radiator 71 which is fan cooled. The cooled fluid returns to the lower header 50 through a return pipe 72.

It has been determined that the gas pressure available for conversion to electrical energy after dynamic pressure requirements and various losses associated with columns oscillating sinusoidally are taken into account is not itself a sinusoidal function of time whereas the power output from the generators should be if the velocity of the armatures of the generators is a sinusoidal function of time due to the influence of sinusoidally oscillating liquid metal columns. There is thus an imbalance between power available for conversion and the power produced. This is shown in figure 12 with the bottom curve representing the imbalance at different points during half a cycle.

Figure 12 is derived by first determining the variations in pressure in an engine space during a cycle according to the universal gas law for a perfect gas

p V = n RT

which is reasonably accurate for high temperature and low pressure

p = pressure, pascals v = volume, cubic metres n = mass of gas, moles

R = gas constant = 8.314 J/mol/K

T = temperature, degrees Kelvin

Applied to a working space comprising engine, compressor and regenerator space the gas law gives the mass of gas in each space at different points in the cycle from the relationships

nc = nt/{1 + Tc/Vc * [Ve/Te*(1 + PD) + Vr/Tr * (2 + PD)/2] } ne = nc * Tc/Te *Ve/Vc * (1 + PD) nr = nc * Tc/Tr * Vr/Vc * (2 + PD)/2

where

nc = mass of gas in compressor space ne = mass of gas in engine space nr = mass of gas in regenerator nt = total mass of gas

Tc = temperature of gas in compressor space Te = temperature of gas in engine space Tr = temperature of gas in regenerator Vc = volume of compressor space, inc. clearance Ve = volume of engine space, inc. clearance Vr = volume of regenerator space, (constant) PD = pressure drop in regenerator and liquid metal as a percentage This latter factor is undeterminable on theoretical grounds. A maximum value is assumed which applies when the volumetric rate of gas flow through the regenerator is maximum. At other points in the cycle the pressure drop is a fraction of the maximum equal to the ratio of the rate of flow to maximum rate of flow squared.

Knowing the mass of gas in each space at any time, the pressure can be determined from the relationships

Pe = ne * R * Te/Ve Pc = nc * R * Tc/Vc Pr = nr * R * Tr/Vr

The varying temperature of the gas in the engine and compressor spaces during the cycle for use in the above expressions is obtained as follows:

* Determine the point in the cycle mid way between the points of least and maximum combined volume.

* Assign the nominated engine and compressor liquid metal temperatures to the gas in these spaces at the above determined intermediate point in the cycle.

Use the expression

(n - 1)

to determine the temperatures at other points in the cycle. In this case n is a fraction of the ratio Cp/ Cv where

Cp = molar heat capacity of the gas at constant pressure

Cv = molar heat capacity of the gas at constant volume.

The fraction recognizes that expansion and compression cannot be entirely isothermal.

The process of determining the temperature of the gas in the regenerator at different points in the cycle is somewhat more involved.

It involves knowing the status of the gas flow in the heat store at each point during the cycle and the matrix temperature and range at each end. When gas is flowing through the heat stove its temperature Tr is taken as the mean of the temperatures at each end. The temperature at the inlet end is either that of the gas exhausting from the engine or compressor space depending on whether gas is flowing from the engine to the compressor (heat being stored) or the reverse (heat being recovered). The gas temperature at the outlet end is taken as being equal to the temperature of the matrix at that end which varies linearly with time during the period of through gas flow. AT the start of storage the outlet end matrix temperature starts at the temperature of the gas in the compressor and rises until at the end of the storage period it reaches the other end of its nominated range. At the same time the inlet end matrix temperature rises to equal the temperature of the gas leaving the engine space. The same process occurs in reverse during heat recovery. If gas is simultaneously flowing out of the engine and compressor space it is in effect being compressed in the heat store and the increase in mean temperature is determined from the relationship

given before. The sample applies when gas is simultaneously flowing out of the engine and compressor space.

It will be appreciated that the above relationships are quite implicit in nature and considerable iteration is involved to arrive at nominated levels of accuracy for the key parameters of start and finish of storage and recovery and regenerator volume Vr . The latter figure is obtained from the expressions:

Q = n * c *ΔT

where

Q = heat stored and released, Joules n = mass of matrix material, moles

C = molar heat capacity of matrix material , J/mol/º C ΔT = dif f erence between lowes t and highest means matrix temperature

and

Vr = n/d* * (1/v - 1) where

n = mass of matrix material d = mass density of matrix material v = ratio of solid to void in gross matrix volume

The heat Q transferred in the regenerator is the difference between the heat in the gas flowing out of the engine space and the heat in the gas flowing into the compressor space. These factors are obtained from the expression

U₂ - U₁ =ΔU = Q - W

where

U₁ = internal energy of gas, state 1 U₂ = internal energy of gas, state 2 ΔU = change in internal energy

Q = heat

W = work

The internal energy of a gas is the sum of the kinetic and potential energy of its molecules and for a monatomic ideal gas the molecular energy is wholly kinetic and is equal to

3/2 n . R . T = n. C_v . T

The work done by the gas is the product of its change of volume and the average pressure during the change. In each space the incremental changes in internal energy and work over a cycle are computed, giving incremental heat flows. The sum of the negative incremental heat flows for the engine space represents the heat in the gas exhausted from the engine space and the sum of the positive incremental heat flows for the compressor space represents the heat in the gas flowing into the compressor space from which the heat Q transferred in the regenerator is obtained.

The pressure developed in an engine space during the down (i.e. power) stroke of its liquid metal piston is balanced by

* Back pressure in opposing space.

* Dynamic pressure required to accelerate the liquid metal, heat buffer and generator armature.

* Pressure drop due to friction.

* Pressure drop due to shock or turbulence.

* Pressure drop due to electromagnetic forces developed in the generators.

* Static pressure due to imbalance of opposing liquid metal columns .

At the start of the stroke, when the piston velocity is zero, only the first two and the last factor are operative. Back pressure is known and static pressure (initially assisting) is

S * d * g

where

S = piston stroke d = liquid metal mass density g = acceleration due to gravity The pressure available to impart initial acceleration to the reciprocating mass is

pa - Pe ( 0 ) - Pe (Y/ 2 ) + pg

where

Pe (0) = pressure in an engine space at the beginning of a power stroke

Pe (y/2) = pressure in an engine space at the end of a power stroke (initial back pressure)

pg = static pressure

Dynamic (or inertial) pressure in a fluid is given by

pi = d . L . a

where

d = mass density of fluid

L = length of column of fluid a = acceleration

If the column of fluid is contained in a number of pipes of different cross sectional area then from the equation of continuity,

pi = d .

= a₁ * mass per unit area where

a₁ = acceleration of fluid in pipe 1

L₁ = length of pipe 1

L₂ = length of pipe 2

A₁ = cross sectional are of pipe 1

A₂ = cross sectional area of pipe 2 etc.

For a diffuser (ie. tapering pipe)

where

pi = infintesimal pressure drop over infintesimal length ΔL a_o = acceleration of fluid at entrance to diffuser

A₀ = area of entrance to diffuser f(L)=are of diffuser at point of infintesimal pressure drop Δ pi, expressed as a function of diffuser length L

The total pressure drop over the full diffuser length L is

pi = d . a₀ . A₀

From the equation of continuity

a₀=a₁ *

so pi (diffuser) = d . a₁ . ₁

For a diffuser with straight sides,

pi (diffuser) =

where

LD = overall length of diffuser

AD₂ = area of diffuser exit

AD₁ = area of diffuser entrance

Given the physical dimensions of the engine system and the mass density of the various reciprocating elements a factor equivalent to mass per unit area can be developed from the above relationships. From this the initial acceleration of the liquid metal piston can be derived

ie

a₁ = pa/mass per unit area where

pa = pressure available to impart initial acceleration a₁ to the piston

As the piston is to oscillate sinusoidally, the instantaneous acceleration at any point in the cycle is given by

a(N) = a₁ cos (N/Y . 2π )

where

N = any nominated pointed in the cycle Y = nominated total number of points in the cycle

= 1 + number of increments of equal duration in one complete cycle period

The instantaneous piston velocity is obtained from the expression

V(N+1) =

where

V(N+1) = final velocity V(N) = initial velocity

= zero at start of power stroke a = mean acceleration

= [a (N) + a(N+1)]1/2 d = distance piston travels in period from N to N+1

= stroke . (cos(N/Y . 2π ) - cos ((N+1)/Y . 2π)) The duration of any increment is given by

t = [v(N+1) - V(N)1]/

and is constant and the cycle period is

T = t * (Y-1)

and frequency = 1/_T hertz

Knowing the piston velocity, the full instantaneous power distribution in the system can be determined from

P(N) = p(N) * V(N) * A₁

where

P(N) = instantaneous power p(N) = pressure V(N) = velocity A₁ = piston area

and the average power from

∑p(N)/(Y-1)

Thus the power involved in accelerating the reciprocating mass is

mass/unit area * a(N) * a(N) * A₁

Power is consumed in the first half of the power stroke but is recovered in the second half as the reciprocating mass is slowed down by the gas cushion in the opposing cylinder. The net power involved in accelerating the reciprocating mass is therefore zero.

The pressure drop or shear stress due to friction in the fluid component of the reciprocating mass is determined for each fluid segment in the system in three steps.

* Determine Reynolds number

Rn = density * velocity * hydraulic diameter

dynamic viscosity

= velocity * hyd.diam.

kinematic viscosity

* Determine pipe coefficient from

f = 0.0008 +0.055/(Rn

.237)

This is one of a number of expressions valid for smooth circular pipes over the whole range of Reynolds numbers yet explored (from 3000 to 30,000,000)

* Determine pressure drop from

2 * f * (velocity)² * Ls * density/hydraulic diameter

where

Ls = length of segment

The pressure drop due to friction of the solid components is given by

[vd * V(N)/t_f * As]/Ax

where

vd = dynamic viscosity of "lubricant" (ie liquid metal), N.s/M V(N) = instantaneous velocity of component tf = thickness of lubricating film As = sliding surface area Ax = cross sectional area of component

The total pressure drop due to friction is the sum of the individual pressure drops of the fluid segments and solid components. From this the power consumed by friction can be computed.

The pressure drop due to separation or shock losses is the sum of drops at various points in the system grouped into the categories of entry, changes of section, changes of direction, and drag (due to flow around the fire tubes).

The losses are expressed in terms of the nominal velocity energy of the liquid d.V(N)²/2 where d = mass density and V(N) = velocity, and a coefficient of loss C depending on physical form. For example, in the case of the drag of the fire tubes C = 1.2, applicable to circular cylinders, axis normal to flow, length/diameter = 5 and with flow around the ends suppressed. The power consumed by shock losses is calculated in the usual manner.

The instantaneous power available for conversion in the generator is the algebraic sum of the instantaneous forward pressure, back pressure, dynamic pressure, friction pressure, separation pressure and static pressure times piston velocity times piston area and is plotted in figure 12. Superimposed on this is a sinusoidal power curve with the same average power which departs markedly from the former as noted before. Power surges would occur unless means were devised to maintain the compressor column in the correct phase relation with the engine column. (Any other phase relationship results in lower power output, one extreme being when the columns are 180° out of phase. Then, the power output is virtually zero because there is no change of volume in the working space. The other extreme is when the columns are in phase so that no transfer of gas between the hot and cold spaces occurs. This means no heat flow therefore no work. With regards to the compressor, exactly the same dynamic and thermodynamic factors apply as with the engine but they do not affect the situation depicted in figure 12. All that is necessary is to check that at no time in the cycle does the combined pressure drop due to acceleration, friction , separation and gravity for the reciprocating mass behind the compressor generator armature exceed the gas pressure on the back of the column when it is being driven forward by the armature thereby causing separation. This has never occurred during computer simulated operation, for sinusoidal oscillation. The net power output from the compressor generator is of course negative and is balanced by tapping some of the output of the engine generator).

Linear Synchronous Generator

A MHD generator is not particularly efficient due to the relatively high resistivity of liquid metal, even liquid sodium, compared with solid copper, and also because of eddy currents which occur where the liquid metal flow enters and leaves the magnetic field. This creates an effect similar to an eddy current brake and pressure is converted to heat within the liquid metal rather than useful electrical energy. Low voltage is also a difficulty.

To overcome such difficulty the embodiment utilises a linear synchronous generator as shown in figure 11 in place of the MHD generator. It works on the principle that an alternating electric current will be induced in a coil if a magnetic flux linking the coil is periodically reversed.

The motor/generator comprises a pair of ducts 80 and 81 of substantially rectangular cross-section in parallel relationship interposed in the duct 13 or 17 of the liquid circuits. The upper ducts is overlaid by a pair of magnetic pole shoes of opposite polarity 83 and 84 which are interconnected by a yoke 85. The pole shoes 83 and 84 are laminated in a direction parallel to the main axis of the duct and carry direct current field windings 86 and 87. The ducts are separated by laminated steel spacers located in opposed relation to the pole shoes 83 and 84. A laminated steel block 82 is located underneath the lower duct 81 in opposed relation to the pair of spacers and serves to complete the magnetic path. The faces of the pole shoes 83 and 84, the spacers 88 and 89 and steel block which are in opposed relation to the ducts are slotted to receive a total of 24 or more single loop coils a-a', b-b', c-c', ....... which are coplanar and parallel to the respective face of the duct and are stacked in layers of 2 above and below each duct. The coils are connected in series to form a single phase winding.

Each duct carries as an armature 90 which is slidable longitudinally in the duct in response to the movement of liquid between the primary chambers. Each armature comprises a pair of laminated steel blocks 91 maintained in spaced relation by a central spacer 92 and having an end spacer 93 at each end. The central and end spacers are formed of a hard non magnetic, non conducting material. The length of each steel block 91 is equal to the length of the slotted portion of each pole shoe plus the length of the stroke of the armature. The length of the central spacer is equal to the length of the stroke of the armature plus the pacing between the pole shoes. The length of the end spacers is equal to the length of the stoke of the armature. The axial length of each pole shoe is the length of the slotted portion plus twice the strokes of the armature. The overall length of the armature is

5 * S_A + 2 * L_s + P_s

where

S_A = armature stroke

L_s = slotted length of pole shoes

= N_s * W_s + (N-1) * (P_s-W_s) N_s = number of slots per pole shoe = N_c/ ( 2 * N_D * N_L) w_s = width of one slot

P_s = pitch of slots

N_c = number of coils

N_D = number of ducts

N_L = number of conductors per slot

P_s = spacing between poles

The overall duct length is equal to the armature length plus stroke. The slot width W_s and depth D_s is such that the cross sectional area w_s * D_s is between two and four times the combined cross sectional area of the conductors and insulating spacer blocks to allow adequate circulation of a cooling medium (eg. hydrogen). The cross sectional area of a conductor is such that the current density is between 2 and 3.5 amps per square millimetre. The magnetic components are dimensioned so that the maximum flux density is limited to about 1.4 tesla. The duct walls and armature cladding are formed of austenitic stainless steel which is compatable with liquid sodium and Na-K alloy and is non magnetic. In the case of the engine generator a cooling medium can be circulated through the elements to remove heat that is transmitted past an insulating block 95 (figure 3) provided in the ducts 14 to either side of the generator/motor. The insulating block 95 comprises a hollow steel block pressurized with low conductivity gas which reciprocates with the liquid sodium in the duct 14.

In operation the armatures 90 move back and forth in the respective duct, lubricated by a thin film of liquidmetal. As it does steel blocks 91 carry the magnetic flux with them due to their high permeability relative to the plastic spacers 92 and 93. Each coil is thus linked with a magnetic flux which changes direction with the movement of the armature. The instantaneous emf induced in each coil is

(Faraday's law)

where

E = emf and = = rate of change of magnetic flux linking the coil

dt The emf is also given by

E = V(N) . B . ℓ

where

V(N) = velocity of a conductor M/s, relative to a magnetic field when the orientation of the conductor and the direction of the magnetic field are mutually at right angles.

B = magnetic flux density, Tesla ℓ = length of conductor, metres = width of duct

For n single turn coils connected in series the total instantaneous emf is

E_n = 2 . n . V(N) . B . ℓ

which is the generator open circuit potential difference.

Controlling Gas Pressures

A means of controlling the gas pressures in the system to bring the two upper curves of figure 12 into correspondence has been devised. It acts indirectly on the column by varying the volume of the working space non sinusoidally (on the cool compressor side). The means of controlling gas pressure (as shown at figure 13) utilises a cam, solenoid or hydraulically actuated buffer piston in the head of each compressor cylinder which is caused to enter and withdraw from the compressor space 25 and 26 at appropriate times in the cycle to change the volume of the working space and thus adjust the pressures to the desired level. The pistons work on the gas only - at no time in the cycle do they penetrate the liquid metal surface. The arrangement shown at figure 13 shows a cam actuated system and one cam shape (not necessarily the optimum), is illustrated at figure 14. The cam effects adjustments in opposing compressor cylinders simultaneously in a fixed proportion, in each. This proportion can be constant, or it can be made a function of time, to give the best shape on mechanical considerations.

The embodiment shown at figure 13 comprises a buffer piston 100 which is slidably supported at the head 101 of each cool chamber 15 and 16 through seats 102. The piston 100 and head 101 can be made of any suitable material such as a zirconia ceramic to be able to withstand wear. Since the temperatures are not very high SEA gland packing of teflon plastic which as a very low coefficient of friction can be used to effect a tight gas seal. The upper end of the piston supports a cam follower 103 in the form of a roller which bears on the outer surface of a cam 104 of the form shown at figure 14. The cam is supported on a shaft 105 which in the case of the embodiment of figure 8 even carries four cams which act in buffer pistons 100 of the four cool chambers of a pair of power units which constitute one phase output of the generator. The three shafts 105 are coupled through gears 106 and 107 to a synchronous motor 108 which carries a flywheel 107 which in turn serves to even out the power draw on the synchronous motor.

As before, considerable iteration is required to achieve an acceptable degree of correspondence between instantaneous power available and produced while satisfying the basic dynamic and thermodynamic relationships given previoulsy to arrive at all points in the cycle. Figure 15 shows a typical result where the root mean square power difference has been reduced by a factor of 1200 compared with figure 12. Power input to the compressor is also a near sinusoidal function of time as shown at figure 5 which also shows instantaneous buffer piston power for one piston. Figure 16 shows the combined power at the shaft of flywheel 109 due to the twelve buffer pistons.

Figures 17 and 18 show cyclic gas mass and temperatures in the engine, compressor and heat store space and figure 19 shows the corresponding engine pressure. Figure 20 shows cyclic engine, compressor and combined volume (including heat store volume) and figure 21 shows the volume of the compressor space, split into "sinusoidal" and "buffer cylinder" components.

To determine the motion of the buffer piston convert the power differences of figure 12 to pressure differences and apply these in a nominated proportion (either constant or a function of time) to existing engine forward and back pressures to give a new set of engine pressures. Then use the relationships at a new set of instantaneous compressor volumes and subtract the original set to give the volume of a buffer "cylinder". This factor varies from positive to negative. When zero the buffer piston head is flush with the head of the compressor cylinder, when negative the piston projects into the cylinder, and when positive the piston is withdrawn into its sleeve. The instantaneous displacement of the buffer piston is

V/A_B

where

V = volume of buffer "cylinder" A_B = area of buffer piston head from which the cam shape is derived. A_B is selected so that the buffer piston never penetrates the liquid metal surface.

Claims

CLAIMS:

1. A electrical generator comprising two pairs of primary chambers containing a quantity of conducting liquid, a heat source for heating one pair of primary chambers, a cooling means for cooling the other pair of primary chambers, each primary chamber of each pair being interconnected at their lower ends by a duct, each duct incorporating an electrical generator unit the space above the liquid in one chamber of the one pair of chambers being connected to the space above the liquid of one chamber of the other pair of chambers, to define a first working space the space above liquid in the other chamber of the one pair of chambers being connected to the space above the liquid in the other chamber of the other pair of chambers to define a second working space said working spaces being filled with an inert gas, a heat store provided in each working space between the spaces to extract heat from the gas flowing from the chambers of the one pair of chambers and to heat the gas flowing from the chambers of the other pair.

2. A electrical generator as claimed at claim 1 wherein the electrical generator unit of the other pair of chambers being connected to the output of the electrical generator unit of the one pair of chambers for the supply of power when work is required to drive liquid in its movement between the other pair of chambers.

3. A electrical generator as claimed at claim 1 or 2 wherein the flow of conducting liquid between the chambers of a pair of chambers can be varied from zero to 90º out of phase relative to the flow of liquid between the chambers of the other pair of chambers in order to vary the power output of the generator.

4. A electrical generator as claimed at claim 1 or 2 or 3 wherein the output of the electrical generator units are connected in an electrical circuit containing reactive elements.

5. A electrical generator as claimed at claim 4 wherein the reactive elements comprise capacitors and inductors.

6. A electrical generator as claimed at any one of the preceeding claims wherein two electrical generator units are placed adjacent each other back to back and wherein the liquid flow therebetween is 180° out of phase such that the reaction forces created by the flow of liquid in each electrical generator unit cancel each other.

7. A electrical generator as claimed at claim 6 wherein the outputs of the two electrical generator units are connected in series constituting a single phase.

8. A electrical generator as claimed at claim 6 or 7 wherein a plurality of pairs of electrical generators are mounted in close proximity utilising a common heat source wherein the output of each pair are connected in parallel said pairs being out of phase by 360° n where n comprise the number of pairs of hydrodynamic generators.

9. A electrical generator as claimed at any one of the preceeding claims wherein the gas is introduced into the space in each chamber when flowing between spaces by being injected into the liquid.

10. A electrical generator as claimed at any one of the preceding claims wherein a closed member having thermal insulating properties is slidably received in each duct to each side of the electrical generator unit.

11. A electrical generator as claimed at any one of the preceeding claims wherein the gas pressure in the working spaces is caused to vary in a manner which causes the fluid columns to oscillate as a sinusoidal function of time.

12. A electrical generator as claimed at claim 12 wherein means are provided to vary the volume of the working spaces to induce pressure therein to cause sinusoidal fluid flow between the chambers.

13. A electrical generator as claimed at claim 12 wherein said means comprises a piston slidably supported to be movable into an duct of the working spaces.

14. A electrical generator as claimed at claim 14 wherein the piston is caused to move through the action of a rotating cam.

15. A electrical generator as claimed at any one of claims 1 to 14 wherein at least one cell comprises a solid armature slidably received in the duct and comprising a plurality of longitudinally spaced conductive elements associated with at least two fixed poles of opposite polarity spaced longitudinally along the duct said armature being capable of reciprocation past the poles as a result of the flow of liquid between the chambers connected by the duct, conductive coils surrounding the duct in the region of the poles.

16. A electrical generator substantially as hereindescribed.

17. A electrical generating unit comprising a duct communicating at either end with the liquid chambers of a electrical generator said duct being associated with at least two magnetic poles of opposite polarity spaced longitudinally along the duct, an armature slidably received in the duct in the region of the poles said armature comprising a plurality of longitudinally spaced permeable elements formed of a material having high magnetic permeability each located opposite one or the other pole said armature being caused to reciprocate in the duct under the influence of the hydrostatic pressure of the liquid chambers conductive coils being mounted in the poles adjacent the ducts.

18. A electrical generating unit as claimed at claim 17 wherein the spacing between the permeable elements substantially equal the spacings between the poles plus the stroke of the armature.

19. A electrical unit as claimed at claims 17 and 18 wherein the face of the poles adjacent the duct support a plurality of conductive coils which are connected in series.

20. A electrical generating unit as claimed at claim 17, 18 or 19 wherein a pair of ducts are positioned in parallel relationship.

21. A electrical generating unit as claimed at claim 20 wherein the poles are located adjacent one face of one duct and the ducts are separated by a spacer formed of material having a high magnetic permeability said spaces being in opposed relation to the poles, the other face of the other duct being associated with a permeable yoke being located in opposed relation to the spacers.

22. A electrical generating unit as claimed at claim 21 wherein the poles, permeable elements, spacers and yoke are laminated.

23. A electrical generating unit substantially as hereindescribed.