ENERGY THROUGH A CONVERGENT NOZZLE

INTRODUCTION

The invention relates to a method for providing a low-cost, commercial, base-load renewable energy production solution, by directly converting the thermo-pressure energy of fluids into fluid jet kinetic energy. This is done through the use of a positive displacement pump-driven converging nozzle which directly converts the thermal portion of the fluid enthalpy to kinetic energy at the nozzle throat, after which it converts the pressure portion of the fluid enthalpy at the vena contracta. This energy conversion takes place at relatively low fluid temperatures, a novel feat which has not been possible up to now.

BACKGROUND TO THE INVENTION

Modern society relies on the provision of energy in various forms to drive industrial production, fuel transport, communications, power convenience gadgets, etc. The bulk of this energy is fossil-based and derived from coal and oil, with only modest contributions from solar, hydro and wind. According to various lobby groups, climate change movements and environmental groups, the world is facing a real possibility that global demand and consumption of the earth’s limited natural, non-renewable energy resources are increasing at a rate that may result in these resources being exhausted within the foreseeable future. Various solutions are advocated, including a drastic increase in the use of renewable energy resources (e.g., wind, solar, hydro), limitation of consumption, use of energy efficient products, and so forth.

Conversion of fossil fuel heat energy to electricity or mechanical energy is limited by the so-called “Carnot efficiency” (i.e., the theoretical maximum efficiency achievable when a heat engine is operating between two temperatures) and the latent heat of phase change during conversion of water liquid to steam vapour. In general, utility scale coal power plants achieve between 30% - 37% efficiency, and 45% - 50% for combined cycle plants and super-critical boiler power stations. The same efficiency constraints apply for other technologies, such as nuclear plants and internal combustion engines (be they gas, or petroleum driven).

Conversion of renewable energy (solar, wind, geothermal heat) to electrical or mechanical energy suffers the same efficiency limits when steam is used. When direct photo-voltaic conversion is used, even lower efficiencies are achieved - i.e., 20% at best. Despite being massively hyped as a solution to the world energy problem, these systems have a mortal shortcoming of intermittent availability, leading to prohibitive storage costs. In hydropower facilities water pressure is converted to mechanical energy with much better efficiencies - i.e., around 90%. Unfortunately, suitable sites for hydropower generations are few.

Most practical energy conversion systems in use today, except for hydropower, suffer significant disadvantages of low efficiencies, high operating costs and generally negative environmental side effects. There is thus a need for a high efficiency, low operating cost, and environmentally friendly method of generating power. Prior art

Expansion of liquids and gasses through nozzles has historically been the subject of intensive study and there are literally hundreds of papers written on the topic. Most of the work on liquids has focussed on rotodynamic pump-fed convergent nozzles and convergent-divergent nozzles (de Laval nozzles) of flashing flow type (particularly in nuclear reactor power generation), and orifice flow in high-speed abrasive water jets. The success of the de Laval-type nozzles in the area of steam and jet-type gas engines appears to have engendered the belief that the application of these nozzles to flashing flows can achieve an efficient extraction of energy from low grade heat fluids, such as geothermal fluids and low-quality steam. To date this belief has met with disappointing results and the majority of experimental results show that this method of energy conversion is at best of marginal efficiency. [5] Akagawa et al (1988) and [6] Vahaji et al (2015) measured flashing flow nozzle efficiency and concluded that efficiency of extracting energy out of a two-phase steam flow decreases as steam quality decreases, i.e., use of de Laval nozzles to extract energy out of low-grade heat fluids in a two-phase flow appears to work moderately only with high quality steam and decreases significantly for low quality steam. Many researchers have concluded that the efficiency of expanding low grade heat thermal fluids through flash flow type convergent-divergent type nozzles is low.

A number of patents have been registered on nozzles that convert the energy of water high pressure to nozzle exit jet velocity. This prior art appears to be driven by the belief that high nozzle throat velocities are only possible if the liquid is first mechanically pressurised to very high-pressure values. The first publications on modern Abrasive Water Jets (hereafter “AWJ”) cutting were published in 1982 by Dr Mohamed Hashish et al, who was awarded USA patent number US4648215A on forming AWJ in 1987 [7], This patent effectively covers a method to convert a significantly high pressure of water to kinetic energy and entraining solid particles in the high velocity water stream to generate a high velocity/momentum abrasive fluid mixture that is capable of cutting hard materials, such as metals. To date, all inventions in this field essentially involve a method of first generating an extremely high-pressured water stream, mixing such high-pressure water stream with solid particles to form an abrasive jet, and ejecting such a mixture at high velocity through a nozzle/orifice durable enough to withstand the wear of the abrasive jet. None of the existing AWJ technologies envisage or teach converting liquid thermo-pressure energy to kinetic energy. By contrast, the current invention teaches that it is unnecessary to first create high pressure in order to obtain high jet velocities.

The invention proposed herein can be compared to Ocean Thermal Energy Conversion (hereafter “OTEC”) technology, in that both harvest water thermal energy at comparatively low temperatures. However, the invention is different in that it directly converts thermo-pressure energy of water to kinetic energy, at both low and high temperatures. By contrast, OTEC is an indirect process that uses a vapour compression cycle to convert water thermal energy to pressure energy, by extracting excruciatingly small amounts of thermal energy out of warm ocean surface waters, while using colder deep ocean waters as a heat sink to enable the process to be viable. OTEC is still in early stages of development, with the main hurdles to commercial viability being the availability of suitable sites, with correct temperature differentials of warm sea surface waters and not-so-deep cold waters; and the rough environment in which OTEC is expected to operate, which constitutes a serious obstacle to heat exchangers required by the process.

Fluid flow through a nozzle

Traditionally, it is understood that velocity of a jet through a nozzle or orifice is always the result of nozzle inlet pressure being converted to kinetic energy of the jet. This understanding is correct for rotodynamic and/or gravity driven flows. However, constant flow pump driven flow is different in that the observed nozzle inlet pressure is caused by nozzle resistance and not created by the pump. Fluid streamlines at the nozzle throat are curved, causing an increased pressure at the throat, i.e., the centrifugal effect of fluid flow past the nozzle throat causes a rise in pressure and this pressure is sensed by the pump as resistance. The reaction of the two flow types to the nozzle throat pressure results in dramatically different outcomes in the amount of kinetic energy in the exit jet, and this reaction is the principal basis of the invention.

Fluid flow through a nozzle or orifice is fundamentally a throttling process. The thermodynamics of this throttling process can be subdivided into three categories ¹ , viz:

(i) Constant flow pump driven flow through a converging nozzle or orifice. This flow is a constant pressure throttling process.

(ii) Dynamic pressure pump driven flow through a converging nozzle (rotodynamic pump). This flow is a constant temperature ² throttling process.

¹ There are really only two categories of fluid throttling, namely constant pressure and constant temperature. The 3 ^rd category is a special case of the second category (i.e., constant temperature), where fluid velocity after the vena contracta is reduced to zero and thus the kinetic energy gets converted to heat.

² This also holds true for compressible nozzle flow, although at first look it appears that the temperature varies. It is correct that the temperature at the nozzle throat drops, but this drop is not because the inlet temperature energy has converted to kinetic energy - it drops because the throat pressure has dropped and, as a result, the equation of state dictates that the temperature adjusts downwards. This difference (iii) Dynamic pressure driven flow through an orifice into a lower pressure chamber. This is the case of flow into a chamber where the kinetic energy of the flow is essentially reduced to zero. This flow is a constant enthalpy throttling process (which is really a special case of the constant temperature throttling). This is the throttling process employed in conventional vapour compression refrigeration.

The nozzle throttling flows described above are described by the enthalpy equation: wherein H = enthalpy, Cp = specific heat, T = temperature, P = pressure, p = fluid density.

The change in enthalpy is described by: wherein dp = 0 for incompressible fluids, such as water.

For a constant pressure positive displacement pump,_dP = 0 and dp = 0

. Hence dH = C _P *dT

. From the conservation of energy law, dH is converted to kinetic energy

. Hence

It is thus clear that the fluid auto-cools and the drop in temperature is converted to velocity energy of the flow while the pressure remains constant. This applies to converging nozzles and orifices. is subtle and, if not looked at carefully, may lead to the incorrect conclusion that temperature has contributed to kinetic energy at the throat. To the contrary, the inlet thermal energy does not vary. Hydrodynamic equations for adiabatic flow in converging nozzles and orifices

(i) Jet Contraction ³ ratio for a conical contraction (A): where: 9 = cone angle of nozzle; β = nozzle beta ratio = dt/di ; di inlet diameter; dt = throat diameter.

(ii) Pressure at the nozzle throat

The additional pressure induced by the vortex flow at the nozzle throat is:

(iii) Coefficient of discharge (Cd):

Cd = 1/λ

The coefficient of discharge (1/A) can be calculated from the above formulas ⁴ .

(iv) Boundary Laver Thickness (δ):

(v) The nozzle Q ratio (QR) :

The ability of the nozzle to transform the inlet thermo-pressure energy into kinetic energy at the vena contracta is given by Q ratio. The Q ratio is a measure of the

³ From the book: Pipe Flow: A Practical and Comprehensive Guide, First Edition, Chapters 9 - 10; Published 2012 by John Wiley &Sons Inc; authored by Donald C Fennels and Hobart M Hudson.

⁴ This is a completely new scientific discovery: the first formula to calculate the nozzle coefficient of discharge directly from fundamental physics. All of the known formulas available to date are empirical. In contrast, nozzle flow formulas published here, are based on the physics behind the vena contracta phenomenon. nozzle’s resonance, i.e. , the ratio of the jet exit kinetic energy to the input energy supplied by the pump. It is not a coincidence that this ratio is also found in electrical circuit resonance. wherein f = Moody friction factor and L _n = nozzle length.

As an example, a QR = 58 means that 1 unit of input energy will convert the thermal energy in the inlet fluid to 58 units of kinetic energy in the exit jet.

SUMMARY OF THE INVENTION

For purposes of this specification, the following terms shall be interpreted as follows:

(i) “fluid enthalpy” shall be interpreted to mean thermo-pressure energy of fluids.

(ii) “vena contracta” is the point in a fluid stream where diameter of the stream is the least and fluid velocity is at its maximum, such as in the case of a stream issuing out of a nozzle. Maximum contraction takes place at a section slightly downstream of the nozzle throat, where the fluid jet is more-or-less horizontal.

(iii) “radius curvature of the nozzle profile” (R _c ) is nozzle throat wall radius of curvature plus one quarter of nozzle throat diameter.

(iv) “beta ratio” is the ratio of a nozzle’s throat diameter to the nozzle’s inlet diameter.

(v) “contraction ratio” (A) is the ratio of a nozzle throat area to the vena contracta area. The contraction ratio is given by the square root of the sum of one plus the ratio of the throat static pressure energy to the throat kinetic energy. In other words A ² -1 = E _p /Ek, alternatively λ ² -1 = 2/Fr ² , wherein Fr = throat Froude number. According to a first aspect of the invention there is provided a method of converting fluid enthalpy to fluid jet kinetic energy, suitable for use in generating power, just behind the vena contracta, the method comprising the steps of - providing a pump for pumping the fluid; providing a convergent nozzle through which the fluid is pumped, wherein the convergent nozzle includes a nozzle inlet with an inlet diameter, a nozzle outlet with a throat diameter, and a curved profile between the nozzle inlet and outlet, and wherein the ratio of the nozzle throat diameter to the radius curvature of the nozzle profile is no more than 4; pumping the fluid through the convergent nozzle; and placing a power converter just behind the vena contracta for converting fluid jet kinetic energy to mechanical and/or electrical power.

The pump may be a positive displacement pump, reciprocating pump, rotary pump, vane pump, diaphragm pump, lobe pump, peristaltic pump, gear pump, screw pump, helical rotor pump, or progressive cavity pump. More particularly, the pump may be a positive displacement pump issuing a constant volume flow or constant mass flow discharge, and may include a positive displacement compressor where the fluid is a gas.

The nozzle further may be characterised therein that it has a nozzle beta ratio of 0.5 or less. The convergent nozzle may have an inlet diameter to throat diameter ratio of no less than 2. The nozzle may be profiled to minimise vena contracta induced throat pressure resistance, with the curved profile between the nozzle inlet and the nozzle outlet being concave, convex or linear. Particularly, the contour of a nozzle wall cross-section from the inlet to the nozzle throat may be curved in the shape of an ellipse, a circle, a hyperbola, a parabola, a straight line, or any combination of these shapes. More particularly - :

(a) an ellipse nozzle wall cross-section curve may have a shape parameter of no less than 0.6, wherein the shape parameter of the ellipse cross-section curve is specified as the sum of twice the ratio of the two radii of the ellipse and 0.5; and wherein the ratio may be computed as the major radius divided by the minor radius or vice versa;

(b) a circle nozzle wall cross-section curve may have a shape parameter of no more than 4, wherein the shape parameter of the circle cross-section curve is specified as the ratio of the nozzle throat diameter to the sum of the wall circle radius of curvature and one quarter (¼) times the nozzle throat diameter;

(c) a hyperbola wall cross-section curve and the parabola wall cross-section curve may have a shape parameter of no more than 4, wherein the shape parameter of the hyperbola/ parabola cross-section curve is specified as the ratio of the nozzle throat diameter to the sum of the wall hyperbola/ parabola radius of curvature and one quarter (¼) times the nozzle throat diameter;

(d) a nozzle wall cross section contour may be any combination of the cross-section curves described in anyone of (a) to (c) above; and

(e) a straight-line wall cross-section curve may have a shape parameter of no more than 0.12, wherein the shape parameter is specified by computing the ratio of the difference of the inlet diameter magnitude and the nozzle throat diameter magnitude to the axial length of the nozzle from inlet to the throat.

The nozzle may have a resonance (Q-ratio or QR) of at least 1.5, wherein QR is specified as the ratio of the square of the contraction ratio to the sum of the friction factor and the same square of contraction ratio reduced by 1 (one). In mathematic symbolic terms: wherein f means Moody friction factor, Φfr means friction factor, L _n means axial nozzle length, and di and dt mean inlet diameter and throat diameter respectively.

The nozzle may be fitted internally with an array of upright flat plate arrays structured in a honeycomb or geocell pattern, attached internally onto the nozzle wall perimeter, either perpendicular to or at an angle to the main axial fluid flow direction, in order to induce a reattachment wake flow regime between the plate arrays. The flat plates may have a minimum height of at least one fiftieth (1 /50 ^th ) of the nozzle throat diameter, while axial spacing between the plates may be no more than 12 times the plate height. The flat plate arrays may be constructed as an integral part of the nozzle, or they may be fabricated separately and fitted into the nozzle. The flat plate arrays or grooves may be fitted internally to the nozzle in the form of a honeycomb structure, such that the nozzle axial flow travels over the honeycomb structure.

The nozzle may define a narrow passageway, known as a thin or thick orifice, having an inlet that is sharp, bevelled or rounded. The nozzle may define a narrow contracting passageway, known as sudden contraction, sharp edged contraction, rounded contraction, conical contraction, bevelled contraction, smooth contraction, contracting pipe reducer, concentric pipe reducer, or eccentric pipe reducer.

The nozzle may include a non-contracting conduit fitted with an upright array of flat plates structured in a honeycomb or geocell pattern attached internally onto the nozzle wall perimeter in order to induce a reattachment wake flow regime between the plate arrays.

The power converter may be an impulse turbine / Pelton wheel, which drives an electric generator. The power converter may be situated 10 - 150 nozzle throat diameters after the nozzle, behind the vena contracta point. The region 10 - 150 nozzle throat diameters after the nozzle exit is the region where the exit jet stream has a constant velocity, and the jet velocity is at its maximum value.

The method may include the step of providing a geocell-lined fluid feed pipe which is arranged in fluid communication with the nozzle, wherein the pipe may be fitted internally with an array of upright flat plate arrays structured in a honeycomb or geocell pattern, attached internally onto the pipe wall perimeter, either perpendicular to or at an angle to the main axial fluid flow direction, in order to induce a reattachment wake flow regime between the plate arrays. The flat plate arrays may be constructed as an integral part of the fluid feed pipe, or they may be fabricated separately and fitted into the fluid feed pipe. The flat plate arrays or grooves may be fitted internally to the fluid feed pipe in the form of a honeycomb structure, such that the fluid feed pipe axial flow travels over the honeycomb structure. The dimensions of the geocell walls perpendicular to the flow direction are specified such that the ratio of a longitudinal gap between the walls to the cell height is less than 12. The geocell walls parallel to the flow direction are spaced such that they are at most 1/3 ^rd of the pipe circumference apart.

The method may include the step of heating the fluid. More particularly, the thermal part of the fluid enthalpy may be generated from extraneous heating sources, e.g., coal, oil, solar etc., or from the fluid’s own temperature / internal energy. The invention is compellingly suited to the efficient conversion of solar energy to useful forms such as electricity and mechanical motion. However, the invention is not limited to renewable energy, as it applies equally well to both renewable and non-renewable energy transformations. Temperature of the heated fluid may be in the range of -5°C to 100°C. Temperature of the heated fluid may be higher than 100°C.

The method may include the step of admixing solids with the pumped fluid to increase cutting ability of the fluid jet stream.

The method of the invention may be adapted to convert fluid enthalpy of water heated with waste heat from a boiler flue gas or heated with exhaust steam of fossil fuel fired boiler to fluid jet kinetic energy, the method then including the steps of using the waste heat to heat the cooling water to effect condensation of the exhaust steam to substantially the same temperature as the cooling water, returning the condensate to the boiler, while pumping the heated water with a constant flow pump through a convergent nozzle. The method may include the step of using the heat in process flue gasses and the heat in process exhaust steam to heat water to enable harvesting such heat through the method of the invention. According to a second aspect of the invention there is provided a convergent nozzle adapted for converting fluid enthalpy to fluid jet kinetic energy and suitable for use in the method according to the invention, wherein the nozzle includes a nozzle inlet with an inlet diameter, a nozzle outlet with a throat diameter, and a curved profile between the nozzle inlet and outlet, and wherein - the ratio of the nozzle throat diameter to the radius curvature of the nozzle profile is no more than 4; the nozzle has a nozzle beta ratio of 0.5 or less; and the nozzle has an inlet diameter to throat diameter ratio of no less than 2.

The nozzle may be profiled to minimise vena contracta induced throat pressure resistance, with the curved profile between the nozzle inlet and the nozzle outlet being concave, convex or linear. Particularly, the contour of a nozzle wall cross-section from the inlet to the nozzle throat may be curved in the shape of an ellipse, a circle, a hyperbola, a parabola, a straight line, or any combination of these shapes, as described hereinbefore.

The nozzle may have a resonance (Q-ratio or QR) of at least 1.5, wherein Q is specified as the ratio of the square of the contraction ratio to the sum of the friction factor and the same square of contraction ratio reduced by 1 (one). In mathematic symbolic terms: wherein f ⁵ means Moody friction factor, Φfr means friction factor measured at the nozzle throat, Ln means axial nozzle length, and di and dt mean inlet diameter and throat diameter respectively.

The nozzle may be arranged in fluid communication with a positive displacement pump issuing a constant volume flow or constant mass flow discharge through the nozzle.

According to a third aspect of the invention there is provided a geocell-lined fluid feed pipe which is adapted for converting fluid enthalpy to fluid jet kinetic energy and which is suitable for use in the method according to the invention, wherein the pipe is fitted internally with an array of upright flat plate arrays structured in a honeycomb or geocell pattern, attached internally onto the pipe wall perimeter, either perpendicular to or at an angle to the main axial fluid flow direction, in order to induce a reattachment wake flow regime between the plate arrays.

The flat plate arrays may be constructed as an integral part of the fluid feed pipe, or they may be fabricated separately and fitted into the fluid feed pipe. The flat plate arrays may be fitted internally to the fluid feed pipe in the form of a honeycomb structure, such that the fluid feed pipe axial flow travels over the honeycomb structure. The dimensions of the geocell walls perpendicular to the flow direction are specified such that the ratio of a longitudinal gap between the walls to the cell height is less than 12. The geocell walls parallel to the flow direction are spaced such that they are at most 1 /3 ^rd of the pipe circumference apart. None of the current state of the art teaches direct conversion of thermo-pressure energy to kinetic energy, or teaches that thermo-pressure energy of a fluid is efficiently and directly converted to kinetic energy by way of positive displacement pumps pushing fluids through appropriately contoured convergent passageways, of sufficient beta ratio, as a method to harvest the fluid thermo-pressure energy profitably. The energy conversion process of the invention has an efficiency in excess of 90%. Tests based on the invention method show that the quantity of jet kinetic energy produced exceeds the quantity of the input energy consumed to overcome the pumping pressure, connecting pipe flow friction, connecting pipe fittings energy losses, nozzle flow friction and internal pump energy losses.

SPECIFIC EMBODIMENT OF THE INVENTION

Without wishing to be bound thereto, the invention will now further be described and illustrated with reference to the following drawings and examples in which -

FIGURE 1 is a schematic flow map for fluid flowing through a converging nozzle of the invention, showing flow temperature and pressure variation along the nozzle axis (inlet values at 25°C/ 100kPa; exit to atmosphere Patm = 100kPa; Diniet/dn = 20.4) and nozzle exit temperature of 5°C.

FIGURE 2 illustrates an example of a different nozzle profile of the invention.

FIGURE 3 illustrates an embodiment of the invention where a conical convergent nozzle jet stream discharges onto a Pelton wheel, where the Pelton wheel typically drives an electrical generator (not shown).

FIGURE 4 illustrates the thermodynamic cycle according to the invention. FIGURE 5 illustrates a chart showing output power versus input power for a 25mm nozzle, from experimental tests conducted.

FIGURE 6 is a table illustrating the results of pumping tests that were conducted with a 30kW pump on a series of convergent conical nozzles.

FIGURE 7 is a sectional side elevation of a geocell-lined fluid feed pipe according to the invention.

FIGURE 8 is a perspective view of the geocell-lined fluid feed pipe of Figure 7.

The nozzle [12] of the invention directly converts fluid enthalpy (thermo-pressure energy) to kinetic energy, such conversion reaching a maximum at the vena contracta [18]. As a result, jet kinetic energy at the vena contracta [18] exceeds total pump [10] input energy, under specific conditions. This phenomenon is analogous to the series resonance condition in an electrical RLC ⁶ circuit and “Back EMF ⁷ ’’ in electric circuits, but to date this has not been understood in the field of fluid mechanics.

Referring to Figure 1 as a first example, the process of the invention is a cyclical process to convert thermal energy to kinetic energy. Water is first heated to about 25°C. A pump [10] produces a current flow of liquid, such as water [Q1 ]. The heated water [Q1 ] is then pumped by means of a positive displacement pump [10] through a convergent nozzle [12] having a 255mm nozzle inlet [14] and a 12,5mm nozzle throat [16], at an inlet velocity of 1 m/s. The nozzle [12] is characterised therein that it has

⁶ RLC means an electrical circuit in which a resistor, inductor and capacitor are connected in series and the same current flows through them.

⁷ a constant flow pump fed convergent nozzle develops a higher pressure at the nozzle throat, analogous to an inductor or capacitor. The throat pressure then accelerates the throat jet to the vena contracta, thus acting like a discharging capacitor or inductor. Nozzle friction is analogous to a resistor, and nozzle throat pressure is analogous to an inductor-capacitor series connection, but 180° out of phase with each other, thus cancelling each other’s impedance. an inlet [14] diameter to throat [16] diameter ratio of 20,4 (twenty comma four) and is profiled to have a contraction ratio A of 1 ,05. At this contraction ratio the throat pressure is 8,6 MPa. [Qi] exits into atmospheric air at nozzle throat [16], a nozzle throat jet velocity of 416m/s, forming a vena contracta [18]. At nozzle throat [16], Qi continues as an accelerated jet current reaching a maximum velocity of 437m/s at vena contracta [18], after which it continues at constant velocity through region [22]. A Pelton wheel [20] is situated within region [22], which may be anywhere between 10 - 150 nozzle throat diameters from the nozzle throat [16].

The exit jet temperature auto-cools to 5°C at the nozzle throat [16] and the pressure in the nozzle [12] is sensibly constant at ca 9 MPa (it reduces slightly from 10MPa at the nozzle inlet [14] to 8,6MPa at the nozzle throat [16]). The pressure reduction is consumed to overcome nozzle friction. The high velocity jet drives the Pelton wheel [20], thereby transferring all its kinetic to the turbine ⁸ [20]. Thus, the thermal energy of the liquid current [Q1] has been converted to kinetic energy of the liquid jet at Pelton wheel [20]. This process is, in contrast to the Carnot type heat engine, not limited by a temperature difference between the inlet and outlet ambient temperatures.

The exhaust jet at 5°C can then be heated again to 25°C and the cycle repeated. The liquid water serves as the working fluid to transform the thermal energy to kinetic energy and is itself not consumed in the process. Those skilled in the art will recognise

⁸ Note the extremely high jet velocity of 437m/s. At these velocities the Pelton turbine used will essentially be the same as a gas turbine, the only difference being that the Pelton turbine will operate at room temperature as opposed to 400°C. At a rotation speed of 12 OOOrpm, the turbine diameter will be a mere 300mm with an output power of 4.350MW. Such a hooped turbine can be fabricated out of a Ti- 17 alloy and will require a power transmission shaft of only 40mm diameter. It is clear that the high jet speeds will essentially enable aero turbines to be used as miniaturised hooped Pelton turbines operating at room temperature and delivering mega power. this as a “heat rejection” cycle, much the same as a refrigeration cycle in the conventional sense. The Coefficient of Performance (i.e., output energy divided by input energy) of the cycle ranges from 2,0 times to 5,1 times in the tests done with 80mm and 25mm throat diameter nozzles.

The input energy required to achieve the constant velocity jet in region [22], is total hydraulic resistance (being the sum of friction resistance, induced throat centrifugal pressure, and pipe fittings resistance losses), which energy must be supplied from a source external to the pump [10], such as an electrical power generator. Jet velocity at the throat [16] is determined by the nozzle beta ratio [fi = , the nozzle contraction ratio A, and the nozzle inlet temperature ti. The throat temperature tt is clearly limited to the freezing point of the liquid due to ice formation (which would effectively choke the flow).

At sufficiently low beta ratios, the power delivered by the exit jet at vena contracta [18] far exceeds the power required to overcome the total hydraulic resistance of the motor, pump, nozzle and pipe fittings.

In a preferred embodiment of the invention, hot water is pumped through a convergent nozzle with a beta ratio of 0.5 or less and a ratio of the nozzle throat diameter to the radius curvature of the nozzle profile of no more than 4. This arrangement, coupled with the appropriate nozzle profile that is optimised using the disclosed nozzle flow equations, ensures that the inlet thermo-pressure energy in the liquid is converted with high efficiency to kinetic energy by utilising the conical convergent nozzle, while the Pelton wheel [24] transmits that energy to an electrical generator at high efficiency (see Figure 3). The process of the invention is thus independent of how the water is heated - all that is required is that the feed water pumped must be at an elevated temperature suitably matched to the pump capacity, the nozzle beta ratio and the radius of curvature of the nozzle profile.

In other words, the invention enables extraction of heat out of inlet water into a nozzle, and simultaneously converting the heat to flow velocity at the nozzle throat. Past the nozzle throat, the throat pressure is converted to additional velocity at the vena contracta, and immediately after the vena contracta the total velocity energy is extracted by an impulse turbine, such as a Pelton Wheel. This outcome is enabled by a combination of a positive displacement pump and a convergent nozzle. The nozzle generates extremely high pressure, which have to be overcome by input pump power. These high pressures can be eliminated when the nozzle profile is correct. The velocities in the nozzle are extremely high and, as a result, the friction losses require substantial pump power.

Figure 2 illustrates an alternative embodiment of a nozzle used in the invention, schematically illustrating positioning of a flat plate array [26] and having the dimensions as illustrated on the drawing.

Examples

Referring to Figure 6, pumping tests were conducted with a 30kW helical screw pump on a series of convergent conical nozzles with outlet diameters of 80mm, 26.3mm and

25mm. (i) The pump was powered by a 34kVA Cummins Diesel Generator, driving a 22kW 8-pole electrical motor.

(ii) The nozzles were connected to an 8-inch supply pipe (205mm inner diameter). This resulted in nozzle beta ratios (3 (dt/ di) ranging from 0.39 to 0.12.

(iii) The electrical motor speed was controlled through a Variable Frequency Drive (VFD), capable of varying the pump speed from a minimum 438 RPM to a maximum 730 RPM. The power factor (pf) for the motor was 78% at 100% load, 74% at 75% load, and 63% at 50% load.

(iv) The pump had a flow capacity of 23.3 Litres/sec at 438 RPM and 37.6 Litres/sec at 730 RPM. The pump stator friction losses ranged from 3.1 kW at 438 RPM, 4.1 kW at 600 RPM and 5.1 kW at 730 RPM. A water meter was connected on the pump discharge side to measure the volumetric water flow.

(v) The pump was run at 438 RPM (VFD setting at 60% of full motor speed of 730 RPM), feeding convergent nozzles, one with 204.7mm inlet diameter and 26.3mm outlet, and the other with 194.0mm inlet diameter and 25.0mm outlet. Pump discharge flow was measured at 23.3L/S, measured by the water meter installed on the discharge side of the pump.

(vi) In order to enable the pump motor to cope with the power needed by the test nozzles, the flow into the nozzle line was reduced by splitting the flow from the pump discharge into two - i.e. , one flow through the nozzle, and the other flow bypassed to an open hydrant through a gate valve. The valve was used to vary the amount of by-pass flow. For each of the test runs the total pump discharge and the hydrant flow were measured, the flow through the nozzle being the difference of the two. The measured flows were cross checked with mass balance calculations. Flow in the 26.3mm nozzle

In this test run, the nozzle inlet pressure gauge reading was 560kPa, the generator power reading was 21 ,7kVA, total pump discharge was 23.3L/S, and hydrant discharge was 10.9L/s. Note that the 560kPa reading includes all nozzle resistance - i.e., friction, nozzle throat vena contracta resistance, and the boundary layer thickness effect. The boundary layer thickness was calculated with the applicant’s own physics-based boundary layer thickness formula. This was cross-checked with the formula of R Benedict [1 ] and the Schlichting turbulent boundary layer estimation formula. The results are in good agreement.

The 560kPa represents the total nozzle and hydrant line energy consumption of 13.1 kW, i.e., 560kPa x 23.34L/S. Net energy consumed due to vena contracta effect is then 13.1 kW minus 0.139 kW friction minus 6.0kW for hydrant bypass flow, equalling 6.9kW. This is equivalent to a net pressure of 554kPa.

The jet contraction ratio A of the nozzle is: A = 1 .180

• The results from this test show total input active power consumed by the pump is 16.1 kW (21.7kVA), of which: o Nozzle throat resistance due to Vena Contracta effect = 6.8kW o Screw pump internal resistance = 3.1 kW o Nozzle wall friction = 0.14kW o Pipe fittings losses = 0.07kW o Kinetic energy of water at inlet = 0.01 kW o Hydrant/By-pass line flow = 6.0kW o Pump Motor reactive power (at 74.1% pf) = 5.6kW

• Total exit nozzle jet power before the vena contracta is 17.3kW (i.e., jet power at nozzle throat), which exceeds the nozzle input power of 6.9kW. This clearly demonstrates the principle of the invention.

• Total exit jet power at the vena contracta is 24.1 kW, which exceeds the gross total pumping input power of 16.1 kW. This shows that the additional energy consumed to overcome the vena contracta effect of nozzle throat pressure increase is recovered as increased kinetic energy of the jet stream after the vena contracta. The 560kPa pressure read from a pressure gauge at the nozzle inlet represents total nozzle resistance, i.e., nozzle wall friction and vena contracta vortex flow pressure increase.

• As observed by Kotousov [3], the ratio of Total Exit Jet Kinetic Energy to Nozzle Inlet Pressure Energy is greater than 1 , ranging from 3.4 to 5.3 times for the test runs cited in this example (refer FIGURES 5 and 6). This demonstrates that the kinetic energy of the exit jet does not derive solely from the nozzle inlet pressure - all that the inlet pressure does is to avail energy to overcome the nozzle wall friction and the nozzle throat vortex pressure increase.

• In the current example of the 25mm nozzle test runs, the pump internal resistance is high at 3.1 kW. Other pump models may not have so much internal resistance. The pump internal resistance and motor reactive power consumption are not relevant to the pumping power consumed by the nozzle. These are specific to specific motor and pump model used, which will obviously differ according to particular manufacturers. The essential issue here is the actual energy consumed by the pipe fittings and the nozzle itself, is used in the analysis to compare input energy to output energy.

Figures 7 and 8 illustrate a geocell-lined fluid feed pipe [28] which is arranged in fluid communication with the nozzle [12], The pipe [28] is fitted internally with an array of upright flat plate arrays [30] structured in a honeycomb or geocell pattern, attached internally onto the pipe wall perimeter, either perpendicular to or at an angle to the main axial fluid flow direction [32], in order to induce a reattachment wake flow regime between the plate arrays [30]. The flat plate arrays [30] are constructed either as an integral part of the fluid feed pipe [28], or they may be fabricated separately and fitted into the fluid feed pipe [28]. The flat plate arrays [30] or grooves may be fitted internally to the fluid feed pipe [28] in the form of a honeycomb structure, such that the fluid feed pipe axial flow [32] travels over the honeycomb structure.

The effect is that the fluid flows over the edges of the geocells, and part of the fluid is trapped as little dams inside the individual geocells. The flow structure in each little dam is a bubble vortex that is trapped between the geocell walls. The dimensions of the geocell walls perpendicular to the flow direction are specified such that the ratio of the longitudinal gap between the walls to the cell height is less than 12. This ensures that the flow remains “laminar” and does not become turbulent and unstable. The geocell walls parallel to the flow direction are spaced such that they are at most 1 /3 ^rd of the pipe circumference apart, i.e., they can be anything less than 1/3 ^rd pipe circumference apart. The function of these walls is to constrain the bubble vortices in the direction perpendicular to the flow and to suppress the secondary vortices that will otherwise disrupt the flow. The flow in the centre of the pipe [28] (i.e. , outside the little geocell dams) is as illustrated in Figure 7.

The key technical function of the geocell lining [30] is to eliminate pipe wall friction. How this structure eliminates friction is highly technical. Suffice it to say that the geocell lining [30] suppresses turbulence in the pipe flow, has the effect that the trapped bubble vortices in contact with the pipe wall have very low velocities, and hence result in low skin friction values. The main flow has no contact with the pipe wall and the fluid dams inside the geocells act like ball bearings. Because of the high flow velocities involved in the invention, pipe wall friction power consumption can literally run into tens of megawatts of power. Without the geocell lining [30] the pump power requirements could be formidable.

Although the invention has been described in simple terms and demonstrated using water as the working fluid, the method is by no means limited to the few examples used. It will be clear to a person sufficiently skilled in the art that through suitable modifications the method can be used to harvest thermal energy of fluids (gasses included) in various ways.

REFERENCES

1. Donald C. Rennels and Hobart M. Hudson: Pipe Flow: A Practical and Comprehensive Guide, First Edition, Chapters 9 - 10; Published 2012 by John Wiley & Sons Inc.

2. P. R. Bullen, D. J. Cheeseman and L. A. Hussain: A study of turbulent flow in pipe contractions; Part E: Journal of Process Mechanical Engineering Vol 210, 1996

3. L. S. Kotousov: Measurement of the Water Jet Velocity at the Outlet of Nozzles with Different Profiles, Technical Physics Vol 50, No. 9, pp. 1 112 - 1118. Translated from Zhurnal Tekniskoi Fiziki, Vol 75, No. 9, 2005, pp. 8 - 14

4. A. J. Schmidt: A quantitative measurement and flow visualisation of water cavitation in a converging-diverging nozzle, Kansas State University 2012, A Thesis

5. K. Akagawa, T. Fujii, J. Ohta, K. Inoue and K. Taniguchi: Performance characteristics of Divergent-Convergent Nozzles for subcooled hot water, JSME International Journal, Series II. Vol 31 , No. 4 1988

6. S. Vahaji, A. Akbarzadeh et al: Study on the efficiency of a Convergent- Divergent Two-Phase Nozzle as a Motive Force for Power Generation from Low Temperature Geothermal Resources, World Geothermal Congress 2015, 19-25 April 2015, Melbourne, Australia

7. M. A. Hashish, M. J. Kirby and Yin-Ho Pao: Method and apparatus for forming a high velocity Liquid Abrasive Jet, 1987; US Patent 4 648 215

8. F Kedziur, H. John, R. Roffel, J. Reimann: Experimental Investigation Of A Two-Phase Nozzle Flow, Institut fur Reaktorentwicklung/ Institut fur Reaktorbauelemente/ Laboratorium fur Isotopentechnik; Projek Nukleare Sicherheit, Kernforschungsentrum Karlsruhe GmbH, July 1980, pp 44 - 47

9. I. E. Idel’chik: A Handbook of Hydraulic Resistance, Coefficients of Local Resistance and Friction, published by The US Atomic Energy Commission and The National Science Foundation, Washington DC, 1966

10. R. Maddahien, B. Farhanieh, B. Firoozabadi: Turbulent Flow in Converging Nozzles, part one: boundary layer solution, Applied Mathematics and Mechanics (English Edition 32(5), 645-662 2011 ) - Sharif University of Technology, Tehran, Iran