Magneto Hydro Dynamic.doc (Size: 354.5 KB / Downloads: 613)
Magneto Hydro Dynamic power generation technology
The Magneto Hydro Dynamic power generation technology (MHD) is the production of electrical power utilising a high temperature conducting plasma moving through an intense magnetic field. The conversion process in MHD was initially described by Michael Faraday in 1893. However the actual utilisation of this concept remained unthinkable. The first known attempt to develop an MHD generator was made at Westing house research laboratory (USA) around 1936.
The efficiencies of all modern thermal power generating system lies between 35-40% as they have to reject large quantities of heat to the environment. We need to improve this efficiency level as in all other conventional power plants like nuclear power plant, hydro-electric power plant, for which first the thermal energy of the gas is directly converted in to electrical energy. Hence it is known as direct energy conversion system. The MHD power plants are classified in to Open and Closed cycle based on the nature of processing of the working fluid. With the present research and development programmes, the MHD power generation may play an important role in the power industry in future to help the present crisis of power.
The MHD process can be used not only for commercial power generation but also for so may other applications. It is economically attractive from the design point of view and as far as bulk generation of power is concerned. The MHD process promises a dramatic improvement in the cost of generating electricity from coal, beneficial to the growth of the national economy. Not only that the extensive use of MHD can help in saving billions of dollars towards fuel prospects, lead to much better fuel utilization but the potential of lower capital costs with increased utilization of invested capital also provides a very important economic incentive in this case. The beneficial environmental aspects of MHD are probably of equal or even greater significance. The MHD energy conversion process contributes greatly to the solution of the serious air and thermal pollution problems faced by all steam - electric power plants while it simultaneously assures better utilization for our natural resources. The high temperature MHD process makes it possible to take advantage of the highest flame temperatures which can be produced by combustion from fossil fuel. While commercial nuclear reactors able to provide heat for MHD generators have yet to be developed, the combined use of MHD generators with nuclear heat source holds great promise for the future. In India, coal is by far the most abundant fossil fuel and thus the major energy source for fossil fuelled MHD power generation.
1. What is Magneto Hydro Dynamics?
Magneto Hydro Dynamics (magneto-fluid-dynamics or hydro-magnetics) is the academic discipline which studies the dynamics of electrically conducting fluids. Examples of such fluids include plasmas, liquid metals, and salt water. The word Magneto Hydro Dynamic (MHD) is derived from Magneto- meaning magnetic field, Hydro- meaning liquid , and Dynamics- meaning movement. The field was initiated by Hannes Alfven , for which he received the Nobel Prize in physics in 1970. The idea of MHD is that magnetic fields can induce currents in a moving conductive fluid, which create forces on the fluid, and also change the magnetic field itself. The set of equations which describe MHD are a combination of the Navier-Stokes equations of fluid dynamics and Maxwell's equations of electromagnetism. These differential equations have to be solved simultaneously, either analytically or numerically. Because MHD is a fluid theory, it cannot treat kinetic phenomena, i.e., those in which the existence of discrete particles, or of a non-thermal distribution of their velocities is important.
The simplest form of MHD, Ideal MHD, assumes that the fluid has so little resistivity that it can be treated as a perfect conductor. (This is the limit of infinite magnetic Reynolds number.) In ideal MHD, Lenz's law dictates that the fluid is in a sense tied to the magnetic field lines. To be more precise, in ideal MHD, a small rope-like volume of fluid surrounding a field line will continue to lie along a magnetic field line, even as it is twisted and distorted by fluid flows in the system. The connection between magnetic field lines and fluid in ideal MHD fixes the topology of the magnetic field in the fluid - for example, if a set of magnetic field lines are tied into a knot, then they will remain so as long as the fluid/plasma has negligible resistivity. This difficulty in reconnecting magnetic field lines makes it possible to store energy by moving the fluid or the source of the magnetic field. The energy can then become available if the conditions for ideal MHD break down, allowing magnetic reconnection that releases the stored energy from the magnetic field.
1.1 Ideal MHD Equations:
The ideal MHD equations consist of the continuity equation (mass), the momentum equation, Ampere's Law in the limit of no electric field and no electron diffusivity, and a temperature evolution equation. As with any fluid description to a kinetic system, a closure approximation must be applied to highest moment of the particle distribution equation. This is often accomplished with approximations to the heat flux through a condition of adiabaticity or isothermality.
Applicability of MHD to Plasmas:
Ideal MHD is only strictly applicable when:
1. The plasma is strongly collisional , so that the time scale of collisions is shorter than the other characteristic times in the system, and the particle distributions are therefore close to Maxwellian.
2. The resistivity due to these collisions is small. In particular, the typical magnetic diffusion times over any scale length present in the system must be longer than any time scale of interest.
3. We are interested in length scales much longer than the ion skin depth and Larmor radius perpendicular to the field, long enough along the field to ignore Landau damping, and time scales much longer than the ion gyration time (system is smooth and slowly evolving).
1.3 The importance of resistivity and kinetic effects:
In an imperfectly conducting fluid, the magnetic field can generally move through the fluid, following a diffusion law with the resistivity of the plasma serving as diffusion constant. This means that solutions to the ideal MHD equations are only applicable for a limited time for a region of a given size before diffusion becomes too important to ignore. One can estimate the diffusion time across a solar active region (from collisional resistivity) to be hundreds to thousands of years, much longer than the actual lifetime of a sunspot - so it would seem reasonable to ignore the resistivity. By contrast, a meter-sized volume of seawater has a magnetic diffusion time measured in milliseconds.
Even in physical systems which are large and conductive enough, simple estimates suggest that the resistivity can be ignored, resistivity may still be important: much instability exists that can increase the effective resistivity of the plasma by factors of more than a billion. The enhanced resistivity is usually the result of the formation of small scale structure like current sheets or fine scale magnetic turbulence, introducing small spatial scales into the system over which ideal MHD is broken and magnetic diffusion can occur quickly. When this happens, Magnetic Reconnection may occur in the plasma to release stored magnetic energy as waves, bulk mechanical acceleration of material, particle acceleration, and heat. Magnetic reconnection in highly conductive systems is important because it concentrates energy in time and space, so that gentle forces applied to plasma for long periods of time can cause violent explosions and bursts of radiation.
When the fluid cannot be considered as completely conductive, but the other conditions for ideal MHD are satisfied, it is possible to use an extended model called resistive MHD. This includes an extra term in Ampere's Law which models the collisional resistivity. Generally MHD computer simulations are at least somewhat resistive because their computational grid introduces a numerical resistivity.
Another limitation of MHD (and fluid theories in general) is that they depend on the assumption that the plasma is strongly collisional (this is the first criterion listed above), so that the time scale of collisions is shorter than the other characteristic times in the system, and the particle distributions are Maxwellian. This is usually not the case in fusion, space and astrophysical plasmas. When this is not the case, or we are interested in smaller spatial scales, it may be necessary to use a kinetic model which properly accounts for the non-Maxwellian shape of the distribution function. However, because MHD is very simple, and captures many of the important properties of plasma dynamics, it is often qualitatively accurate, and is almost invariably the first model tried. Effects which are essentially kinetic and not captured by fluid models include double layers, Landau damping, a wide range of instabilities, chemical separation in space plasmas and electron runaway.
Schematic view of the different current systems which shape the Earth’s magnetosphere
In many MHD systems, most of the electric current is compressed into thin, nearly-two-dimensional ribbons termed current sheets. These can divide the fluid into magnetic domains, inside of which the currents are relatively weak. Current sheets in the solar corona are thought to be between a few meters and a few kilometers in thickness, which is quite thin compared to the magnetic domains (which are thousands to hundreds of thousands of kilometers across). Another example is in the earth's magnetosphere, where current sheets separate topologically distinct domains, isolating most of the earth's ionosphere from the solar wind.
1.4 Applications :
MHD as a science has its application in geophysics as well in astrophysics. MHD is related to engineering problems such as plasma confinement, liquid-metal cooling of nuclear reactors, and electromagnetic casting, power generation (among others).
Magneto Hydro Dynamic Generator
The MHD (magneto-hydro-dynamic) generator or dynamo transforms thermal energy or kinetic energy directly into electricity. MHD generators are different from traditional electric generators in that they can operate at high temperatures without moving parts. MHD was eagerly developed because the exhaust of a plasma MHD generator is a flame, still able to heat the boilers of a steam power plant. So high-temperature MHD was developed as a topping cycle to increase the efficiency of electric generation, especially when burning coal or natural gas. It has also been applied to pump liquid metals and for quiet submarine engines. The basic concept underlying the mechanical and fluid dynamos is the same. The fluid dynamo, however, uses the motion of fluid or plasma to generate the currents which generate the electrical energy. The mechanical dynamo, in contrast, uses the motion of mechanical devices to accomplish this. The functional difference between an MHD generator and an MHD dynamo is the path the charged particles follow.
MHD generators are now practical for fossil fuels, but have been overtaken by other, less expensive technologies, such as combined cycles in which a gas turbine's or molten carbonate fuel cell's exhaust heats steam for steam turbine. The unique value of MHD is that it permits an older single-cycle fossil-fuel power plant to be upgraded to high efficiency. Natural MHD dynamos are an active area of research in plasma physics and are of great interest to the geophysics and astrophysics communities. From their perspective the earth is a global MHD dynamo and with the aid of the particles on the solar wind produces the aurora borealis. The differently charged electromagnetic layers produced by the dynamo effect on the earth's geomagnetic field enable the appearance of the aurora borealis. As power is extracted from the plasma of the solar wind, the particles slow and are drawn down along the field lines in a brilliant display over the poles.
MHD Power Generation (The Principle):
When an electrical conductor is moved so as to cut lines of magnetic induction, the charged particles in the conductor experience a force in a direction mutually perpendicular to the magnetic field (B) and to the velocity of the conductor (v). The negative charges tend to move in one direction, and the positive charges in the opposite direction. This induced electric field, or motional emf, provides the basis for converting mechanical energy into electrical energy
The Lorentz Force Law describes the effects of a charged particle moving in a constant magnetic field. The simplest form of this law is given by the vector equation.
• F is the force acting on the particle (vector),
• Q is charge of particle (scalar),
• v is velocity of particle (vector),
• x is the cross product,
• B is magnetic field (vector).
The vector F is perpendicular to both v and B according to the Right hand rule.
At the present time nearly all electrical power generators utilize a solid conductor which is caused to rotate between the poles of a magnet. In the case of hydroelectric generators, the energy required to maintain the rotation is supplied by the gravitational motion of river water. Turbo-generators, on the other hand, generally operate using a high-speed flow of steam or other gas. The heat source required to produce the high-speed gas flow may be supplied by the combustion of a fossil fuel or by a nuclear reactor (either fission or possibly fusion). It was recognized by Faraday as early as 1831 that one could employ a fluid conductor as the working substance in a power generator. To test this concept Faraday immersed electrodes into the Thames River at either end of the Waterloo Bridge in London and connected the electrodes at mid span on the bridge through a galvanometer. Faraday reasoned that the electrically conducting river water moving through the earth's magnetic field should produce a transverse emf. Small irregular deflections of the galvanometer were in fact observed. The production of electrical power through the use of a conducting fluid moving through a magnetic field is referred to as magneto-hydro-dynamic, or MHD, power generation. One of the earliest serious attempts to construct an experimental MHO generator was undertaken at the Westinghouse laboratories in the .period 1938-1944, under the guidance of Karlovitz. This generator (which was of the annular Hall type) utilized the products of combustion of natural gas, as a working fluid, and electron beam ionization. The experiments did not produce the expected power levels because of the low electrical conductivity of the -gas and the lack of existing knowledge of plasma properties at that time. A later experiment at Westinghouse by Way, OeCorso, Hundstad, Kemeny, Stewart, and Young (1961), utilizing a liquid fossil fuel-“seeded” with a potassium compound, was much more successful and yielded power levels in excess of 10 kW. Similar power levels were achieved at the Avco Everett laboratories by Rosa (1961) using arc-heated argon at 3000˚K –“ seeded” with powdered potassium carbonate. In these latter experiments- “seeding” the working gas with small concentrations of potassium was essential to provide the necessary number of free electrons required for an adequate electrical conductivity. (Other possible seeding materials having a relatively low ionization potential are the alkali metals Cesium and Rubidium.)Types of MHD generator systems:
During the decade beginning, about 1960 three general types of MHD generator systems evolved, classified according to the working fluid and the anticipated heat source. They are as follows:
• Open Cycle MHD generators: They operate with the products of combustion of a fossil fuel and are closest to practical realization.
• Closed Cycle MHD generators: They are usually envisaged as operating with nuclear reactor heat sources, although fossil fuel heat sources have also been considered. The working fluid for a closed cycle system can be either a seeded noble gas or a liquid metal. Because of temperature limitations imposed by the nuclear fuel materials used in reactors, closed-cycle MHD generators utilizing a gas will require that the generator operate in a non-equilibrium mode.
• Liquid Metal MHD generators: They operate basically with liquid metals, flowing through ducts, while the operating principle remains the same.
Typically for a large scale power station to approach operational efficiency in computer models, steps must be taken to increase the electrical conductivity of the conductive substance. The heating of a gas to plasma or the addition of other easily ionizable substances like the salts of alkali metals accomplishes this increase in conductivity. In practice a number of issues must be considered in the implementation of a MHD generator: Generator efficiency, Economics, and Toxic byproducts. These issues are affected by the choice of one of the three MHD generator designs. These are the Faraday generator, the Hall generator, and the disc.
• Faraday generator: The Faraday generator is named after the man who first looked for the effect in the Thames River. A simple Faraday generator would consist of a wedge-shaped pipe or tube of some non-conductive material. When an electrically conductive fluid flows through the tube, in the presence of a significant perpendicular magnetic field, a charge is induced in the field, which can be drawn off as electrical power by placing the electrodes on the sides at 90 degree angles to the magnetic field.
There are limitations on the density and type of field used. The amount of power that can be extracted is proportional to the cross sectional area of the tube and the speed of the conductive flow. The conductive substance is also cooled and slowed by this process. MHD generators typically reduce the temperature of the conductive substance from plasma temperatures to just over 1000 °C.
The main practical problem of a Faraday generator is that differential voltages and currents in the fluid short through the electrodes on the sides of the duct. The most powerful waste is from the Hall effect current. This makes the Faraday duct very inefficient. Most further refinements of MHD generators have tried to solve this problem. The optimal magnetic field on duct-shaped MHD generators is a sort of saddle shape. To get this field, a large generator requires an extremely powerful magnet. Many research groups have tried to adapt superconducting magnets to this purpose, with varying success.
• Hall generator: The most common answer is to use the Hall effect to create a current that flows with the fluid. The normal scheme is to place arrays of short, vertical electrodes on the sides of the duct. The first and last electrodes in the duct power the load. Each other electrode is shorted to an electrode on the opposite side of the duct. These shorts of the Faraday current induce a powerful magnetic field within the fluid, but in a chord of a circle at right angles to the Faraday current. This secondary, induced field makes current flow in a rainbow shape between the first and last electrodes.
Losses are less than a Faraday generator, and voltages are higher because there is less shorting of the final induced current. However, this design has problems because the speed of the material flow requires the middle electrodes to be offset to "catch" the Faraday currents. As the load varies, the fluid flow speed varies, misaligning the Faraday current with its intended electrodes, and making the generator's efficiency very sensitive to its load.
• Disc generator: The third, currently most efficient answer is the Hall effect disc generator. This design currently holds the efficiency and energy density records for MHD generation. A disc generator has fluid flowing between the center of a disc, and a duct wrapped around the edge. The magnetic excitation field is made by a pair of circular Helmholtz coils above and below the disk. The Faraday currents flow in a perfect dead short around the periphery of the disk. The Hall Effect currents flow between ring electrodes near the center and ring electrodes near the periphery.
Another significant advantage of this design is that the magnet is more efficient. First, it has simple parallel field lines. Second, because the fluid is processed in a disk, the magnet can be closer to the fluid, and magnetic field strengths increase as the 7th power of distance. Finally, the generator is compact for its power, so the magnet is also smaller. The resulting magnet uses a much smaller percentage of the generated power.
An MHD generator, like a turbo generator, is an energy conversion device and can be used with any high-temperature heat source-chemical, nuclear, solar, etc. The future electrical power needs of industrial countries will have to be met for the most part by thermal systems composed of a heat source and an energy conversion device. In accordance with thermodynamic considerations, the maximum potential efficiency of such a system (i.e., the Carnot efficiency) is determined by the temperature of the heat source. However, the maximum actual efficiency of the system will be limited by the maximum temperature employed in the energy conversion device. The closer the temperature of the working fluid in the energy conversion device to the temperature of the heat source, the higher the maximum potential efficiency of the overall system. A spectrum of heat source temperatures is currently available, up to about 3000˚K. However, at the present time large central station power production is limited to the use of a single energy-conversion scheme-the steam turbo-generator-which is capable of operating economically at a maximum temperature of only 850˚K. The over-all efficiencies of present central-station power-producing systems are limited by this
fact to values below about 42 percent, which is a fraction of the potential efficiency. It is clear that a temperature gap exists in our energy conversion technology. Because MHD power generators, in contrast to turbines, do not require the use of moving solid materials in the gas stream, they can operate at much higher temperatures. Calculations show that fossil-fuelled MHD generators may be capable of operating at efficiencies between 50 and 60 percent. Higher operating efficiencies would lead to improved conservation of natural resources, reduced thermal pollution, and lower fuel costs. Studies currently in progress suggest also the possibility of reduced air pollution.
The essential elements of a simplified MHD generator are shown below in the figure. This type of generator is referred to as a continuous electrode Faraday generator. A field of magnetic induction ‘B’ is applied transverse to the motion of an electrically conducting gas flowing in an insulated duct with a velocity ‘u’.