This application claims priority from U.S. provisional patent application No. 60/434,230, filed on day 12, month 16, 2002, and U.S. provisional patent application No. 60/517,359, filed on day 11, month 4, 2003.
Detailed Description
Introduction to the design reside in
Included herein is a method for accelerating technical processes and improving product quality in the metallurgical, foundry, and chemical industries. The method is based on the treatment of ultra-high agitation based in particular on the application of a mobile magnetic field intensification technique following an ultra-high wave pattern according to the ultra-high wave type activity described by Irving I.Darkik in the New theory of the great Law of the university, published in the 1994 month 3/4 (V.44, No.5) of the journal of Cycles. See also The article "The Law of Waves" by Irving i.dardik in "Cycles" journal v.45, No.3, 1995 and "Superwaves" by him on website www.dardikinstitute.org, 2002: the Realitythat existance ". Each of these articles is incorporated by reference in its entirety.
As pointed out in the Dardik article, it is scientifically accepted that everything in nature is made up of atoms that move around in a constant motion, attracting each other when the atoms are at a small distance and repelling each other once squeezed into another. In contradistinction, Dardik assumes that everything in the universe is made up of waves, the activity of which is called "hyper-fluctuation". The hyper-fluctuation is caused by and is a substance in motion (i.e., two changes simultaneously define substance-space-time).
Thus, in essence, the changes in frequency and amplitude of the waves are not independent and different from each other, and concurrently with each other, represent two different levels at the same time. Any increase in wave frequency establishes a new wave pattern for all waves that contain smaller waves and that contain varying frequencies therein, and cannot exist without the other.
Each wave necessarily contains smaller waves and is contained within larger waves. Thus each high amplitude low frequency main wave is modulated by a number of higher frequency low amplitude wavelets. Hyper-fluctuation is the process by which a wave is fluctuating within another wave, preferably sharing a quantile relationship with another wave.
FIG. 1 (adapted from Dardik) schematically illustrates the super-waving phenomenon. Fig. 1 depicts a low frequency main wave 11 modulated, for example, by wavelets 12 and 13. Wavelets 12 and 13 have incrementally higher frequencies (compared to main wave 11). Other wavelets of even higher frequencies may modulate the main wave but are not shown for simplicity. The same super-fluctuation phenomenon is described in the time domain in fig. 2.
This new principle of wave fluctuation indicates that the wave frequency and wave intensity (amplitude squared) are simultaneous and continuous. Two different types of energy (i.e., energy carried by a wave proportional to its frequency and energy proportional to its intensity) are also simultaneous and continuous, so that the energy is a fluctuating wave or "wave/energy".
This phenomenon can be studied using the electro-and hydrodynamic equations and empirical conclusions established in some experimental magnetohydrodynamics. Thus, the results of the ultrasonic studies in the metallurgical, foundry and chemical industries are expected to promote our understanding of the ultrasonic phenomenon in general.
The metallurgical, foundry and chemical industries are among the most energy-consuming branches of industry in developed countries. Thus, for example, the electrical energy consumption for the production of steel alloys in an electric arc furnace is about 400-500 kW h/ton (the figure relates only to the steel production process and does not include the electrical energy consumed in cast iron production and steel rolling). The production of one ton of magnesium alloy in the resistance furnace and one ton of copper alloy in the channel induction furnace also consumes approximately 400 kwh.
In order to produce high quality steel, it is very important to thoroughly stir the molten metal during casting. As will be explained later, the introduction of the stirring force by means of nonlinear ultra waves with amplitude and frequency modulation enhances the stirring and at the same time also significantly reduces the electrical energy consumption, thus significantly improving the economic efficiency.
The following simple calculation may give an overall idea of potential savings. Pricing of electrical energy in the united states is quite complex. The electricity prices vary from state to state. It also depends very much on the peak of energy consumption, with an average electricity price of about at least 15 cents/kwh. Thus, the cost of 500 kW hours/ton described above is $ 60-75 per ton of metal. The total cost of producing steel sheet and section steel is about $ 300/ton. This results in the cost of the electrical energy consumed in the furnace to produce the steel (i.e. the fraction of overhead that can be significantly reduced by the ultra-waves used for stirring) being in the range of about 20-25% of the total cost of metallurgical production.
The productivity of metallurgical and chemical plants producing, processing melts or electrolytic solutions is determined by the rate of the melting process or the rate of the dissolution process of the reagents added to the melt or solution and the rate of the chemical reactions in the melt or electrolytic solution. The rate of the above process depends, among other things, on the intensity of the stirring of the melt (or solution) in the technical equipment. This factor also determines the structure of the melt and the production of continuous, stable metal ingots and ingots during crystallization and thus their mechanical properties. The intensity of stirring the melt and the solution is a major factor determining the productivity of metallurgical and chemical plants, the energy consumption for producing metal products and various chemical materials and their quality.
Thus, the stirring intensity of the injection in the metallurgical, foundry and chemical industries seems to be comparableNaturally. An estimate of the average velocity of the turbulence rotating the MHD flow shows that this velocity is proportional to the square root of the electromagnetic force amplitude, which in turn is proportional to the slip (i.e. to the difference ω/p- Ω: where ω/p is the angular velocity of RMF rotation, p is the number of pole pairs, and Ω is the angular velocity of melt rotation). Thus, the results were obtained by the following "semi-formal Model of turbine rotation MHDFlogs" at the Proc.5 from E.Golblaikh, A.kapusta and B.MikhalivichthSimple expressions in internal pamir conf, ramatellel, France, Septermber 16-20, 2002, I-227-I-230 (which is also incorporated herein by reference in its entirety) determine the average angular velocity of rotation of a turbulent quasi-solid core:
Ω≈(Q/2)(√1+4/Q-1)ω, (2)
wherein Q ═ Ha2·δz/ReωCo; here, the
<math>
<mrow>
<mi>Ha</mi>
<mo>=</mo>
<mi>BoRo</mi>
<msqrt>
<mi>σ</mi>
<mo>/</mo>
<mi>η</mi>
</msqrt>
<mo>;</mo>
</mrow>
</math>
δ z is Zo/Ro; zo is the melt height; ro is the radius of the volume containing the melt; reω=ωRo2V is; ν is the kinematic viscosity of the melt; σ is the conductivity of the melt; and Co 0.018 is an empirical constant.
Evaluation of the effect of an ultra-wave modulated magnetic field on steel production
The temperature of the melt or electrolytic solution and the time required for their turbulent stirring to mix thoroughly uniformly is inversely proportional to the angular speed of rotation of the liquid. Thus, when the rotation speed is increased by about 1.5 times, the homogenization time is decreased at the same rate. Since the homogenization time is about 50% of the total casting time, this allows a reduction of the melting duration in the electric furnace by about 20% and an acceleration of the desulfurization and dephosphorization in the MHD plant by about 50% for the treatment outside the furnace.
Since the power of the MHD stirring installation is generally about 1 to 1.5% of the power of the furnace transformer, the reduction in the duration of melting saves electrical energy particularly significantly. A 1.5-fold reduction in the duration of melting in the electric arc furnace reduces the specific power consumption to 270-.
Evaluation of the Effect of applying an ultrasound modulated magnetic field during the crystallization of a Metal ingot
As demonstrated in Pestel et al, U.S. Pat. No. 2,963,758, which is incorporated herein by reference in its entirety, the optimum crystalline structure of a steel ingot is achieved under the following conditions:
ωB2R2≈5×10-3-11.3×10-3T2m2/s (3)
where ω is the magnetic field rotational angular velocity, radians/second; b is magnetic induction T; and R is the liquid pocket (crater) radius, meters. Thus, the necessary values of magnetic induction are:
B~0.04-0.06T. (4)
an inductor mounted on a continuous casting facility ("CCF") generates a magnetic field in the melt. The rotating (moving) magnetic field induces a current, the interaction of which with said magnetic field causes the appearance of an electromagnetic force that affects the melt. Depending on the CCF type and production rate, the power rating of the inductor is about 150-300 kilowatts (i.e., about 10-12 kilowatt-hours/ton) at specific power consumption. When amplitude and frequency modulated current is used, the ingot crystallization process is significantly accelerated at inductor-like power, which increases the productivity of the CCF. In addition, the strength characteristics of the cast metal are improved and the porosity is reduced.
In addition, as preliminary experiments have shown, the force action properties of the electromagnetic field on the melt change significantly when amplitude and frequency modulated currents are used, since the EMBF and the increase in the mean value of the EMBF (which increases the mean flow rate) together contribute to a strong pulse that causes the melt to vibrate. The combined effect of these factors results in a significant improvement in the quality of the continuous ingot.
Potential application of ultrasonic modulation magnetic field in chemical technology
In the chemical industry, stirring is performed in order to enhance heat and mass exchange and accelerate chemical reactions. In order to stir the liquid, as a rule, turbine type and impeller type stirrers are applied. In this case, homogenization of the concentration and temperature in the stirring stage is accomplished by circulation and turbulent diffusion. Using "Industrial Mixing Technology" available from Tatterson, g.b., calabree, r.v., and Penney, W.R: the following formula, obtained in Chemical and biological application ", AI chem. eng.pub.1994 (which is incorporated in its entirety by reference), makes an approximate calculation of the total homogenization time τ in turbulent mode for a device with a mechanical stirrer:
τ≈5V/nd3,(5)
wherein V is the equipment volume in cubic meters; n is the number of agitator revolutions; and d is its diameter.
Dimensionless EMBF versus relative frequency (where ω ═ μ)oσwRo 2) The dependence of (c) indicates that the EMBF is negligibly small for very small values of ω.
The amplitude of ω of the strong electrolytic solution was about 0.001 when RMF was applied at a frequency ω of 314 rad/sec in a 1 meter diameter vessel. The relative EMBF value at a radius of 0.4 m is equal to f ═ ω r/2 to 0.0002. Thus, no rotation is observed when an electrolyte (e.g., sulfuric acid) is placed in a sufficiently strong RMF having a magnetic induction of about 0.07T, so that the RMF excited by a low-frequency current does not actually affect the electrolytic solution. However, if the current density turning field is inductively introduced into the electrolyte, the interaction of the field and RMP can excite a strong enough EMBF field to rotate the electrolyte at high angular velocities. BMF and current density field modulation significantly improve the efficiency of electromagnetic stirring elements, which modulation can be beneficially applied in the chemical industry to replace conventionally applied mechanical stirrers when making corrosive materials such as concentrated acids and bases.
Physical machine with frequency and amplitude ultrasonic modulation magnetic field force influenceSystem for making
The force effect by the non-modulated RMF rotating at a fixed angular velocity about the axis of the container with the sensing liquid and energized by the permanent magnet is now described. The magnetic field B, which rotates at the same angular velocity on the immobile liquid, excites an axial current in the inductive liquid, which rotates at the same velocity. The interaction of the induced current and the magnetic field produces an EMBF that is rotationally aligned with the magnet. These forces have a fixed component and an unfixed component, the latter varying periodically at a double frequency 2 ω and an amplitude equal to the fixed component. Under these forces, the liquid starts to rotate at a certain angular velocity Ω < ω, where the induced current density is proportional to the slip, i.e., (ω - Ω).
If the angular velocity of the magnet is not fixed (i.e. it varies periodically with time), this additional motion induces an additional current, the interaction of which with the modulated magnetic field generates an additional force on the liquid. As a consequence of this effect, the average angular velocity of the liquid rotation increases and two-dimensional vibrations occur, which automatically agitate the liquid. Of course, if the angular speed of rotation of the magnet is not fixed, a certain amount of additional work is required to achieve its rotation at the same principal speed ω.
The proposed method is implemented as follows.
The mold in which the melt is poured is placed in the nonmagnetic gap of an m-phase inductor and the current modulated by the method is applied to the windings of the inductor. These currents generate a frequency and amplitude modulated magnetic field that moves helically (in particular, rotates and moves axially) in the melt, which in turn induces an m-phase current system modulated by the method in the melt.
In general, as a result of the interaction of the current and the magnetic field, a three-dimensional EMBF field appears, which m is composed of a constant component and a set of complex pulsations and oscillations with different amplitudes, frequencies and initial phases.
The amplitude dependence of the azimuthal component of the dimensionless EMBF on dimensionless time is shown in fig. 3, where 1-is excited by amplitude and frequency modulated current; 2-no modulation is present. The dependence of the radial component of the amplitude of the dimensionless EMBF on dimensionless time is shown in fig. 4, where 1-is excited by the amplitude and frequency modulated current; 2-no modulation is present.
Under the effect of this EMBF field, a spatial structure remains complex in the melt and naturally in the vicinity of the crystallization front with turbulence which is forced to oscillate with a frequency depending on the frequency spectrum of the EMBF field. The flow according to the invention is capable of completely suppressing the generation of columnar crystals, so that the ingot solidified in this state (ingot) preferably has an equiaxed, fine-grained dense structure.
In a continuous casting plant, the m-phase inductor can be placed below the crystallizer (see fig. 4A) (in the case of steel casting) or built into the crystallizer. In a preferred embodiment of the invention, the casting mold is made of a material that shields the magnetic field to a minimum.
The proposed installation shown in fig. 5 and 6 comprises a lining trough 21 with a receiving funnel 22, a ladle nozzle 23, an injection hopper 24 for reagents, and a stand 25. In the lining of the tank there is provided an inductor with a magnetic circuit 27 made of ferro-ceramic and a coil 28 (see e.g. fig. 9 and 10), the coil 28 being in the form of a ceramic box with a spiral pipe 29, the pipe 29 being filled with a liquid metal having a melting temperature well below the melting temperature of the melt to be treated but a boiling temperature much higher than the boiling temperature of the melt to be treated (e.g. tin may act as such metal). One tubular and the other solid electrode 30 is used to supply current to the coil and to pour metal into the pipe 29.
Fig. 7 and 8 show a second design of the installation, which comprises a lining channel 21 ', in which the poles 26' made of ferro-ceramic are arranged in the lining of the furnace, while the base 27 'of the magnetic circuit is made of laminated electrical steel and is fixed in an annular channel on the furnace jacket 23'. The poles 26 ' of the magnetic circuit are protected from the melt by a ceramic tube 31 ', the thickness of the tube 31 ' preferably being chosen such that the outer surface temperature of the tube does not exceed the curie temperature of the ferro-ceramic.
The proposed installation operates as follows. The liquid metal may be supplied to the tundish from a ladle furnace or a cupola furnace. The necessary reagents are continuously supplied from the injection hopper 24. The melt flows through the bath 21, in which the melt is influenced by the EMBF according to the invention, which intensively mixes the melt and the reagents. The treated melt was continuously discharged into a ladle. In the case of melts provided with certain agents (soda, lime or magnesium powder), these agents also melt and form a slag enriched with harmful impurities, which is removed from the melt before the metal is tapped from the ladle.
Thus, a method is provided for continuously alloying or purifying ferrous metal melts from unwanted impurities outside the furnace under the influence of a helical moving (i.e., moving in a helical motion to rotate the melt and simultaneously move axially along the longitudinal axis of the bath 21) magnetic field excited by an m-phase amplitude and frequency modulated current system, wherein the amplitude modulation depth as well as the frequency modulation offset vary along the axis of the long liner. The evaluation shows that in this case the peak value of the electromagnet force is higher than in the absence of modulation, which guarantees strong melt stirring, shortens the time required for total homogenization of the temperature and composition and significantly accelerates the rate of the chemical reaction of dissolution of the alloying additives and of the discharge of harmful impurities into the slag. Also provided is a design of a facility for carrying out the method for high temperature melts.
Another proposed method according to the invention involves strengthening of the melting and melt stirring process. The method of the present invention can significantly improve the melt stirring strength in the shaft, shorten the melting time and improve the quality of metals and alloys due to the enhanced reaction at the boundary of the metal and slag. In addition, the method can increase the capacity of the tank reactor by increasing the height of the furnace shaft without providing the power of the furnace transformer.
Although RMF excitation requires additional energy consumption, a significant reduction in melting time (e.g., 20%) can significantly reduce the energy consumption for producing metals and alloys in the channel induction furnace. As a rule, the electric arc furnaces of today are equipped with an arc stator manufactured by ASEA, swedish company, which is mounted below the furnace bottom. The stator windings are fed with a current having a frequency of about 0.35-1.50 hz depending on the capacity of the furnace. Stator power is typically about 2% of furnace transformer power and can reach 0.5MVA for large volume furnaces.
The method of the invention for enhancing melting and melt stirring in an electric arc furnace with a newly designed RMF inductor reduces the power consumption required for melt stirring and significantly enhances the melting process, which in turn results in a reduction of melting time, an increase in furnace output, a reduction in power consumption and a reduction in metal losses.
The RMF inductor is of a design that is significantly different from known designs used in metallurgy and casting. To this end, one method of the invention forms the magnetic circuit of the inductor from an iron ceramic (e.g., chamotte, magnesite, colored magnesite or high temperature concrete) representing a refractory material with an iron powder or cobalt powder filler. The size of the powder particles may be, for example, 1mm, and the powder content in the refractory material may depend on the type of refractory material used. After sufficient stirring, the material is produced in the form of individual elements whose shape depends on the design of the particular furnace, and then annealed. Below the curie temperature of the filler, the material retains its magnetic properties, is electrically non-conductive and has a sufficiently low heat transfer rate to act as both a magnetic circuit inductor and a liner for the facility. This design of the RMF inductor enables the RMF source to be positioned maximally close to the melt and reduces the power required by the inductor. In addition, the design significantly reduces the size of the non-magnetic gap between the liquid metal and the inductor thereby eliminating the weakening of the magnetic field caused by the furnace jacket. Since the inductor coils are also located in the high temperature zone, their design is also very different from the inductor coils conventionally used in metallurgical technology.
The method for strengthening the technical process of a channel induction furnace proposed by the present invention and the changes introduced in the furnace design make a significant contribution to the improvement of the technical installation.
By way of example, the figures show a single phase single slot induction furnace with the proposed structural changes to provide the above-mentioned advantages of the present invention.
Fig. 11 and 12 show a vertical section and a horizontal section of a first embodiment of the furnace of the invention. The furnace includes a lining 41. A slot section 42, a furnace transformer 43, a primary winding 44 of the transformer, a slot 45 and a stand 46. A magnetic circuit 47 made of iron ceramic is established in the lining of the shaft 41. A coil 48 in the form of a ceramic box with a helical duct (e.g. duct 29 of fig. 9 and 10) is connected to the poles of the shaft 41. The pipe 29 is filled with liquid metal having a melting temperature substantially lower than the temperature of the melt in the furnace and a boiling temperature substantially higher than the boiling temperature of the melt (for example tin may act as such metal).
Solid electrodes 30 in fig. 9, one tubular and the other solid, are introduced at the bottom of the relatively low temperature coil 48, through which electrodes current is applied to the liquid metal winding and the metal is poured into the slot 29. The poles of the magnetic circuit 47 are separated from the melt by an underlayer 51, the thickness of which is chosen such that the temperature on the outer surface of the layer 51 is lower than the curie temperature of the ferro-ceramic.
Fig. 13 and 14 show a furnace according to a second embodiment of the invention, in which the poles 47c made of iron-ceramic and the coils 48' are arranged in the furnace lining, while the bottom 47b of the magnetic circuit of the RMF inductor is made of laminated transformer steel and is fixed to the furnace casing.
Fig. 15 shows the furnace of the first embodiment of the invention shown in fig. 11 and 12 with an elongated shaft and a three-phase inductor. Such an inductor can excite a helical magnetic field RMF or a magnetic field moving along the furnace axis according to the change of the phase of the coils arranged in the vertical and horizontal directions. With such field amplitude and frequency modulation, the average velocity of each of the helical, rotating or vertical flow, and the pulsating velocity component of the forced high intensity turbulence spectrum that maintains the melt, are significantly increased (preferably by at least one order of magnitude). Thus, the melting time in a furnace of sufficiently large volume (e.g., 20%) is reduced.
The current in the slots can also be frequency and amplitude modulated as a result of the current fed to the primary winding of the furnace transformer. These currents and inherent magnetic field interactions result in the appearance of an additional, non-stationary rotating EMBF field that creates turbulence in the currents in the bath and enhances heat exchange with the metal in the shaft. In addition, the release of joule heating in the tank is also increased at the cost of some increase in furnace transformer power.
Fig. 16 and 17 show a high capacity (e.g. 200 ton capacity) melting chamber of an electric arc furnace of the present invention comprising a steel sleeve 61a, a cylindrical section bushing 62a, a bottom bushing 63a and a roof 64 a. An m-phase RMF inductor having a bottom 65a and a magnetic pole 66a, which is made of iron ceramic containing a cobalt filler, is embedded in the bottom bushing 63 a. The curie temperature of the ceramic is, for example, 1000 ℃. The design of the coil 67a may be the same as the design of the coil 28 (fig. 9) for a slot furnace inductor described above. Due to the low heat transfer rate of the ferro-ceramic and the fact that the coils can operate, for example, at temperatures in the range of 300-400 c, the poles of the inductor can be maximally close to the melt, thereby enabling a significant reduction in the power of the inductor and the use of frequency and amplitude modulated currents.
Also provided is a method of forcibly influencing a conductive medium with a helically moving (especially rotating and axially moving) magnetic field excited by a system of m-phase helical (especially axially or otherwise azimuthally) currents that periodically vary harmonically or non-harmonically in time, wherein the currents are in phase or synchronous and are amplified by a time periodic function and frequency and amplitude modulated in layers. With some choice of current modulation amplitude and frequency, the amplitude of the unfixed component of the EMBF is preferably increased by a factor of several tens compared to the fixed and unfixed EMBF components excited by the unmodulated magnetic field. The EMBF wave packet includes more frequency components, and thus the electromagnetic response of the medium may be highly nonlinear. The influence of this force field on the liquid medium results in a rapid and deep homogenization of the temperature and concentration of the medium. This method is more energy efficient than known methods and can be implemented with standard electrical systems that excite such fields.
The proposed method of forcing influence improves the stirring efficiency by an order of magnitude. And thus ensure deeper, faster homogenization of the melt. As an example, the electrokinetic processes in the conductive cylinder under the action of the amplitude and frequency modulation RMF are determined mathematically as follows.
In the cylindrical coordinates r,
It is convenient to describe these processes under the z system with the magnetically induced vector potential correlated by the ratio B-rotA and induction. In this case, the axial component of the current density is:
while the induced radial and azimuthal components are:
the azimuthal component of the EMBF was determined as:
and the radial component is determined as:
re is the real part of the complex variable.
The vector potential Az is described by:
wherein
Is the media velocity; mu.s
0=4π10
-7Hn/m is the permeability of the vacuum; σ is the conductivity of the medium; and t is time.
Solving equation (10) under the following boundary conditions:
where NI is a linear current load; omega2(t)=ω2[1+∈1sin(ω1t+γ)](ii) a And p is the number of pole pairs.
Using eigenvalues of vector potential, time, coordinate r and angle phi:
problems (10), (11) become dimensionless and under the conditions
The following were obtained:
wherein
Is the relative frequency;
a
zis the z-component of the dimensionless vector potential; τ is dimensionless time; and r below is a dimensionless coordinate.
The RMF may be superimposed and modulated with a dimensionless reference frequency of 1:
az=az1+ε2az2· (13)
approaches the solution of the problem (12) in the form of.
Substituting (13) into (12) yields:
problems (14) and (15) are obvious:
wherein
Is a bessel function of the first order type in the complex domain.
Usually a isz1Written as follows:
az1=(a11+ia12)(cos2πφ1+isin2πφ1),(18)
the questions (14), (16) have semi-analytic solutions, and a can be expressedz2Writing into:
az2=(a21+ia22)(cos2πφ2+isin2πφ2),(19)
wherein
<math>
<mrow>
<msub>
<mi>a</mi>
<mn>21</mn>
</msub>
<mo>=</mo>
<mi>Re</mi>
<mo>[</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mo>∞</mo>
</munderover>
<msub>
<mi>α</mi>
<mrow>
<mn>2</mn>
<mi>n</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>τ</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>J</mi>
<mrow>
<mn>2</mn>
<mi>p</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>β</mi>
<mi>n</mi>
</msub>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>θ</mi>
<mfrac>
<msup>
<mi>r</mi>
<mrow>
<mn>2</mn>
<mi>p</mi>
</mrow>
</msup>
<mrow>
<mn>2</mn>
<mi>p</mi>
</mrow>
</mfrac>
<mo>]</mo>
<mo>,</mo>
</mrow>
</math>
<math>
<mrow>
<msub>
<mi>a</mi>
<mn>22</mn>
</msub>
<mo>=</mo>
<mi>Im</mi>
<mo>[</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>n</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mo>∞</mo>
</munderover>
<msub>
<mi>α</mi>
<mrow>
<mn>2</mn>
<mi>n</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>τ</mi>
<mo>)</mo>
</mrow>
<msub>
<mi>J</mi>
<mrow>
<mn>2</mn>
<mi>p</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>β</mi>
<mi>n</mi>
</msub>
<mi>r</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>θ</mi>
<mfrac>
<msup>
<mi>r</mi>
<mrow>
<mn>2</mn>
<mi>p</mi>
</mrow>
</msup>
<mrow>
<mn>2</mn>
<mi>p</mi>
</mrow>
</mfrac>
<mo>]</mo>
<mo>,</mo>
</mrow>
</math>
<math>
<mrow>
<msub>
<mi>α</mi>
<mrow>
<mn>2</mn>
<mi>n</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>τ</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>χ</mi>
<mrow>
<mn>2</mn>
<mi>n</mi>
</mrow>
</msub>
<mo>+</mo>
<msubsup>
<mi>C</mi>
<mi>n</mi>
<mo>*</mo>
</msubsup>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mi>r</mi>
</mrow>
</msup>
<mo>,</mo>
</mrow>
</math>
<math>
<mrow>
<msubsup>
<mi>C</mi>
<mi>n</mi>
<mo>*</mo>
</msubsup>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>p</mi>
</mfrac>
<mfrac>
<mrow>
<msub>
<mi>β</mi>
<mi>n</mi>
</msub>
<msub>
<mi>J</mi>
<mrow>
<mn>2</mn>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>β</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mrow>
<mo>(</mo>
<msubsup>
<mi>β</mi>
<mi>n</mi>
<mn>2</mn>
</msubsup>
<mo>-</mo>
<msup>
<mrow>
<mn>4</mn>
<mi>p</mi>
</mrow>
<mn>2</mn>
</msup>
<mo>)</mo>
</mrow>
<msubsup>
<mi>J</mi>
<mrow>
<mn>2</mn>
<mi>p</mi>
</mrow>
<mn>2</mn>
</msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>β</mi>
<mi>n</mi>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>,</mo>
</mrow>
</math>
<math>
<mrow>
<msub>
<mi>χ</mi>
<mrow>
<mn>2</mn>
<mi>n</mi>
</mrow>
</msub>
<mo>=</mo>
<munderover>
<mi>Σ</mi>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mo>-</mo>
<mo>∞</mo>
</mrow>
<mo>∞</mo>
</munderover>
<msub>
<mi>k</mi>
<mrow>
<mn>2</mn>
<mi>ni</mi>
</mrow>
</msub>
<msup>
<mi>e</mi>
<mrow>
<mn>2</mn>
<mi>πdiτ</mi>
</mrow>
</msup>
<mo>,</mo>
</mrow>
</math>
Im is the imaginary part of the complex function,
it is clear that,
<math>
<mrow>
<msub>
<mi>Reb</mi>
<mi>r</mi>
</msub>
<mo>=</mo>
<mfrac>
<mi>P</mi>
<mi>r</mi>
</mfrac>
<mo>{</mo>
<msub>
<mi>a</mi>
<mn>11</mn>
</msub>
<mi>sin</mi>
<mn>2</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>12</mn>
</msub>
<mi>cos</mi>
<mn>2</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<mn>2</mn>
<msub>
<mi>ϵ</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>a</mi>
<mn>21</mn>
</msub>
<mi>sin</mi>
<mn>2</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>22</mn>
</msub>
<mi>cos</mi>
<mn>2</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>}</mo>
<mo>,</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>21</mn>
<mo>)</mo>
</mrow>
</mrow>
</math>
wherein
<math>
<mrow>
<msub>
<mover>
<mi>a</mi>
<mo>·</mo>
</mover>
<mi>ik</mi>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mrow>
<mo>∂</mo>
<mi>a</mi>
</mrow>
<mi>ik</mi>
</msub>
<mrow>
<mo>∂</mo>
<mi>τ</mi>
</mrow>
</mfrac>
<mo>;</mo>
<msub>
<msup>
<mover>
<mi>a</mi>
<mo>·</mo>
</mover>
<mo>′</mo>
</msup>
<mi>ik</mi>
</msub>
<mo>=</mo>
<mfrac>
<msub>
<mrow>
<mo>∂</mo>
<mi>a</mi>
</mrow>
<mi>ik</mi>
</msub>
<mrow>
<mo>∂</mo>
<mi>r</mi>
</mrow>
</mfrac>
</mrow>
</math>
The azimuthal component of the EMBF is:
<math>
<mrow>
<mo>+</mo>
<msubsup>
<mi>ϵ</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
<mo>[</mo>
<msub>
<mi>f</mi>
<mn>1</mn>
</msub>
<msub>
<mi>a</mi>
<mn>21</mn>
</msub>
<mo>+</mo>
<msub>
<mi>f</mi>
<mn>2</mn>
</msub>
<msub>
<mi>a</mi>
<mn>22</mn>
</msub>
<mo>+</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>a</mi>
<mn>21</mn>
</msub>
<msub>
<mi>f</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>22</mn>
</msub>
<msub>
<mi>f</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>sin</mi>
<mn>4</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>a</mi>
<mn>22</mn>
</msub>
<msub>
<mi>f</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<mi>a</mi>
<mn>21</mn>
</msub>
<msub>
<mi>f</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>cos</mi>
<mn>4</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>2</mn>
</msub>
<mo>]</mo>
<mo>+</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>23</mn>
<mo>)</mo>
</mrow>
</mrow>
</math>
<math>
<mrow>
<mo>+</mo>
<msub>
<mi>ϵ</mi>
<mn>2</mn>
</msub>
<mo>[</mo>
<msub>
<mi>a</mi>
<mn>11</mn>
</msub>
<mi>sin</mi>
<mn>2</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>12</mn>
</msub>
<mi>cos</mi>
<mn>2</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>1</mn>
</msub>
<mo>]</mo>
<mo>[</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>f</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mrow>
<mn>2</mn>
<mi>a</mi>
</mrow>
<mn>21</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>sin</mi>
<mn>2</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>f</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mrow>
<mn>2</mn>
<mi>a</mi>
</mrow>
<mn>22</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>cos</mi>
<mn>2</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>2</mn>
</msub>
<mo>]</mo>
<mo>}</mo>
<mo>,</mo>
</mrow>
</math>
wherein
The radial component of the EMBF is:
<math>
<mrow>
<msubsup>
<mi>ϵ</mi>
<mn>2</mn>
<mn>2</mn>
</msubsup>
<mo>[</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>f</mi>
<mn>2</mn>
</msub>
<msub>
<msup>
<mi>a</mi>
<mo>′</mo>
</msup>
<mn>21</mn>
</msub>
<mo>-</mo>
<msub>
<mi>f</mi>
<mn>1</mn>
</msub>
<msub>
<msup>
<mi>a</mi>
<mo>′</mo>
</msup>
<mn>22</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>f</mi>
<mn>1</mn>
</msub>
<msub>
<msup>
<mi>a</mi>
<mo>′</mo>
</msup>
<mn>21</mn>
</msub>
<mo>-</mo>
<msub>
<mi>f</mi>
<mn>2</mn>
</msub>
<msub>
<msup>
<mi>a</mi>
<mo>′</mo>
</msup>
<mn>22</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>sin</mi>
<mn>4</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>f</mi>
<mn>2</mn>
</msub>
<msub>
<msup>
<mi>a</mi>
<mo>′</mo>
</msup>
<mn>21</mn>
</msub>
<mo>+</mo>
<msub>
<mi>f</mi>
<mn>2</mn>
</msub>
<msub>
<msup>
<mi>a</mi>
<mo>′</mo>
</msup>
<mn>22</mn>
</msub>
<mo>)</mo>
</mrow>
<mi>v</mi>
<mi>cos</mi>
<mn>4</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>2</mn>
</msub>
<mo>]</mo>
<mo>+</mo>
</mrow>
</math>
<math>
<mrow>
<msub>
<mi>ϵ</mi>
<mn>2</mn>
</msub>
<mo>[</mo>
<msub>
<mi>a</mi>
<mn>11</mn>
</msub>
<mi>sin</mi>
<mn>2</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>1</mn>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mn>12</mn>
</msub>
<mi>cos</mi>
<mn>2</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>1</mn>
</msub>
<mo>]</mo>
<mo>·</mo>
<mo>[</mo>
<msub>
<msup>
<mi>a</mi>
<mo>′</mo>
</msup>
<mn>21</mn>
</msub>
<mi>cos</mi>
<mn>2</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>2</mn>
</msub>
<mo>-</mo>
<msub>
<msup>
<mi>a</mi>
<mo>′</mo>
</msup>
<mn>22</mn>
</msub>
<mi>sin</mi>
<mn>2</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>2</mn>
</msub>
<mo>]</mo>
<mo>+</mo>
</mrow>
</math>
<math>
<mrow>
<mo>[</mo>
<mrow>
<mo>(</mo>
<msub>
<mi>f</mi>
<mn>2</mn>
</msub>
<mi>cos</mi>
<mn>2</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>2</mn>
</msub>
<mo>+</mo>
<msub>
<mi>f</mi>
<mn>1</mn>
</msub>
<mi>sin</mi>
<mn>2</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<msub>
<msup>
<mi>a</mi>
<mo>′</mo>
</msup>
<mn>11</mn>
</msub>
<mi>cos</mi>
<mn>2</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>1</mn>
</msub>
<mo>-</mo>
<msub>
<msup>
<mi>a</mi>
<mo>′</mo>
</msup>
<mn>12</mn>
</msub>
<mi>sin</mi>
<mn>2</mn>
<mi>π</mi>
<msub>
<mi>φ</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<mo>]</mo>
<mo>}</mo>
<mo>.</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>24</mn>
<mo>)</mo>
</mrow>
</mrow>
</math>
the first four terms in equations (21) and (22) describe the mandatory effect of not modulating the baseline BMF. Is proportional to epsilon2 2Term (c) describes the mandatory influence of the BMF modulation part and is proportional to ε2The term (c) describes the EMBF oscillations and waves that are generated due to the interaction between the modulated and unmodulated portions of the RMF. It is clear that the amplitude and frequency modulation increases the magnitude of the EMBF fixed component by more than an order of magnitude, which increases the average rotational speed of the medium and adds four EMBF waves and two oscillations with different frequencies and initial phases in the azimuthal as well as radial directions, which additionally intensifies the medium agitation.
The above analysis fully considers the effect of current and magnetic field decay phenomena, the so-called skin effect, near the lateral surface of a conductive cylinder (liquid or solid), on the magnitude and spatial distribution of the EMBF generated by amplitude and frequency modulated currents. This makes it possible to select the optimum electromagnetic parameter ratio for a particular section, size and dielectric conductivity.
The evaluation of the efficiency of the proposed method is based on a method of calculating the angular velocity of a pseudo-solid core of rotating turbulence excited by RMF, which can be described by the following simple formula:
<math>
<mrow>
<mi>Ω</mi>
<mo>=</mo>
<mfrac>
<mi>Q</mi>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<msqrt>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<mn>4</mn>
<mi>Q</mi>
</mfrac>
</msqrt>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mo>,</mo>
</mrow>
</math>
wherein Q ═ Haa 2·δz/Reω·Co;Haa =Ba·RoV/eta is the effective value of the Hadamard number; reω=ωRo 2V is the Reynolds effect determined by the RMF rotational speed on the vessel wall containing the melt; deltaz=Zo/Ro(ii) a Co is an empirical constant that accounts for RMF modulation effects (for non-modulated RMFCo 0.0164, which is higher than modulated RMF); ba is the average effective value of the magnetic induction in the container; ro is the inner diameter of the vessel wall; η is the kinematic viscosity of the melt; ν is the kinematic viscosity of the melt; and Zo is the height of the liquid phase column.
Kinetic energy E of rotating flowkin=JΩ 22; wherein J is the moment of inertia of the rotating liquid; while the hydraulic efficiency is determined by the ratio of the power consumed for pressing and driving and maintaining the rotary motion:
ηhydr≈Ekin/Eel
it is clear that the consumption and power are higher in the case of modulating the BMF than in the case of not modulating the RMF.
The m-phase modulated thread spinning current system generates a magnetic field in the conducting medium that moves along a helix (i.e., rotates and simultaneously moves axially), which in turn induces a mirror current system that moves in the same direction. The interaction of the induced current and the magnetic field produces an EMBF that acts in the direction of movement of the magnetic field as well as in the perpendicular direction, where the magnetic field includes a fixed component and an unfixed component.
Under the action of a fixed EMBF component, a helical flow (in particular, rotating and moving axially) of the conductive liquid is generally generated, which has a turbulent structure as a rule. Waves and oscillations of different frequencies and directions are excited in the medium under the influence of the unfixed component, which turbulizes the flow structure to a greater extent. The energy of this turbulent component comes from the work that the unsteady forces act on to achieve on the flow and not from the mean flow energy. Thereby, the stirring depth of the liquid is significantly increased, which results in a rapid homogenization of the temperature and the impurity concentration.
When using an additional frequency and amplitude modulated current density field excited with km electrodes (where m is the number of phases and k is the number of electrodes per phase), an additional EMBF field component arises due to the interaction of the current density field and the magnetic field, which leads to a further enhancement of the forcing effect and extends the range of application of the method to media with ionic conductivity (e.g. electrolytes, salt and slag melts, etc.).
Fig. 18-20 show the spatial configuration of the simplest current system for exciting the helical, rotating and axially moving magnetic field, respectively, improved by the method of the present invention.
Fig. 21 shows the time dependence of the dimensionless EMBF excited by the modulated and unmodulated RMFs, respectively. It is clear that the peak value of the EMBF excited by the modulated RMF is about 10 times higher than without modulation at the indicated parameter values.
The following paragraphs reiterate the fundamental theories of the ultra-wave and metallurgical and related scientific associations disclosed herein.
The super-wave excited MHD technique is to have a uniquely modulated carrier wave acting as an excitation current to generate a rotating magnetic field that increases turbulence in the stirring liquid, thereby increasing the melting rate and mixing rate and improving the properties of the poured metal.
As indicated above, a super-wave may be understood as a carrier wave with amplitude, frequency and/or phase modulation. Oscillation modulation is the variation of an oscillation parameter over time according to a periodic law. The modulated fundamental wave (or oscillation) may be referred to as a carrier wave and its frequency may be referred to as a carrier frequency.
Mathematically, the mixed ultrasound display for liquid flow is very important. Fluctuations of the turbulence intensity that are sufficiently small when applied to metallurgical processes are very important for the thermal and chemical homogenization of the melt.
In practice the rotation of the liquid metal in a rotating magnetic field is always turbulent to some extent. Even weak rotation of the liquid melt improves their properties, since some vortex fluctuations can be found. However, simple rotation (fixed flow core angular velocity) produces classic Kolmogorov turbulence in a first order approximation (see, e.g., fig. 22). In this case, the turbulence energy depends on the size of the turbulent vortex, E ═ epsilon2/3r2/3Or E (omega) to omega in the frequency domain-5/3Where ε is the energy flux per mass over the frequency spectrum, ω is the frequency and E (ω) is the spectral energy density.
In the case of a simple rotation, the rotation,
E(ω)~E0(ω0)(ω0/ω)5/3, (28)
wherein E0(ω0) Is the energy injected into the system, which corresponds to the characteristic scalar value L0. Thus, in this case, in order to obtain the vortices for thermal and chemical homogenization, we must mark the value L in the system0Energy is introduced and after this energy is cascaded over the spectrum, we get vorticity at the following frequency ω:
E(ω)~E0(ω)(ω0/ω)5/3. If Δ ω is ω/ω0If the vorticity is large enough, the corresponding vorticity is small.
If, in addition to the mean rotation, more than ω occurs in the system0Frequency ofExternal fluctuations at rate ω, we can expect an increase in the number of vortices at this frequency. This situation is similar to the occurrence of Karman vortices when some frequency peaks appear in the spectrum that are multiples of the main vortices. We can estimate the eddy current occurring at a prescribed frequency ω as follows. Let E0~α1(F0/ω0)2For a frequency of ω0The turbulence of (2) is free of turbulence energy provided by flow equalization. If the system fluctuates due to external forces at frequency ω, their energy composition is:
E′(ω)~α2[F(ω)/ω]2. (29)
thus, at frequency ω, the relative eddy current magnitude is:
E′(ω)/E(ω)~(α2/α1)(F/F0)2(ω0/ω)1/3(30)
parameter alpha1And alpha2Characterizing the response of the medium to an applied force. If forces F and F0The same property, then1And alpha2The difference is not so great that their ratio is close to 1 (fig. 22). The size can be determined more accurately by experimentation.
When using a superwave modulated current, the calculation of the electromagnetic force excited by this frequency and amplitude modulated current indicates the formation of additional vortical forces in the liquid (see e.g. fig. 23). Except for uniform force F0According to omega0Outside the 50 Hz fluctuation amplitude, the appearance amplitude is F-7/8F0And the frequency is omega-2.3/2.5 omega0The pulsation of (2) fluctuates.
From (30) we conclude that the turbulence fluctuation at frequency w in such a system should increase as follows:
E′(ω)/E(ω)~(α2/α1)(7+8)2(2.3+2.5)-1/3~(36+48)(α2/α1)(31)
therefore, the effect of modulating the external force on the molten metal should be more densely homogenized than the effect of not modulating the force. Thus, to homogenize a turbulent medium, one can increase the average rotational speed by increasing inductor power (and Re) as in FIG. 22, increase the vorticity at lower rotational speeds with the use of ultrawaves as in FIG. 23, or both.
In the experiment, the ultra-waves increased the melt rate of the solid added to the liquid solution, increased the solidified metal density in the RMF and the ultra-waves behaved as expected from the above figures.
FIG. 24 is the result of an initial experiment of turbulence associated with the ultrasonic excitation of RMF. The ratio of the uniform angular velocity to the magnetic field angular velocity Ω/ω is plotted against Q, where Q is a representative thereof including Ha2(representing the ratio of electromagnetic force to viscous force) of the process set conditions. Q is also proportional to the square of the current in the stirring element coil. As the current in the coil increases (Ha increases), the angular velocity increases. The solid line represents the general theoretical relationship between angular velocity and the parameter Q. The data points above the solid line are for unmodulated RMF, while the points below the solid line are for ultra-wave modulated RMF.
The general curve shown in fig. 24 enables the selection of the necessary velocity regime (required reynolds number) at any combination of current amplitude and frequency.
The increased turbulence caused by the ultrasonic waves acts like a resistance on the stirring speed, thereby reducing the average value of the speed. The difference in velocity seen in the data of fig. 25 is consistent with the additional drag brought about by the increased turbulence caused by the ultrasonic waves during agitation. Thus, ultrasonics have the potential to increase mixing rates without the need for undesirably and expensive higher agitation speeds.
The effect of RMF by ultrasonic modulation was experimentally investigated on molten aluminum alloys.
The results of the melting rate test are shown in fig. 25. The results show that the melting rate can be increased regardless of the stirring speed. It is clear that the melting rate is increased by about 22% by the ultrasonic wave under otherwise the same conditions. These melting tests thus essentially verify the ability of the ultrasonic waves to generate turbulence and the effectiveness of the metallurgical process to utilize the ultrasonic waves to increase the mixing rate.
Aluminum alloy 201 was solidified under stirring conditions similar to the melting test. Except that the melt was able to solidify completely under the action of RMF. Examination of the solidified ingot showed that the ultrasonically excited RMF produced an ingot that was significantly denser than an ingot solidified with unmodulated RMF (see fig. 26). This density increase equates to the removal of 5.7 million micro-voids per cubic centimeter of poured metal. This suggests that a turbulent mixing effect is created that is mathematically predictive of the ultrasonic waves and that is beneficial for metal working.