MHD flow control for plasma technology applications

MHD Flow Control for Plasma Technology Applications G. Herdrich *,**),M. Auweter-Kurtz *,**),M. Fertig*), A. Nawaz*), D. Petkow *) *)Institut fur Raumfahrtsysteme (IRS), UniversiHit Stuttgart Stuttgart, D-70550, Germany **)steinbeis Transfer Centre Plasma and Space Technology (STC PRT) Stuttgart, D-70550, Germany Abstract MHD effects ansmg in plasma sources such as short-pulsed magnetoplasmadynamic generators and inductively heated plasma generators are analyzed with both algebraic models and measured data. Functional principles of the sources based on their MHD behavior are explained. Moreover, Stewart number is calculated for the systems and- based on this experience- the concept of a plasma probe to magnetically influence I control weakly ionized plasma flows is presented. Keywords: MHD (magnetohydrodynamic), Magnetoplasmadynamic Inductively Heated Plasma Source, Magnetic Probe Generator, 1. Introduction A variety of plasma sources has been developed at IRS for space applications (e.g. atmospheric entry simulation facilities and electrical thrusters) and plasma technology purposes. These sources differ in design and function depending on their application [ 1-4]. MHD effects can be used to improve the operational behavior of plasma generators, where magnetic forces can be used to rotate plasma arcs in order to prevent hot spots on the plasma generator's electrodes [ 1, 2], to protect plasma containments from thermal overload [4, 5] or to increase the total pressure and/or temperature ofthe plasma jet (magnetic acceleration of the plasma) either for space applications (e.g. the increase of thrust of an MPD propulsion system) [6] or for applications in plasma technology [3, 7, 8]. In addition, plasma magnetic systems are designed to control plasma free stream flows. Among these control purposes are plasma focusing e.g. using electromagnetic nozzles [9] and the interaction between charged particles and magnetic fields e.g. in order to increase the impinging velocities of these particles onto a substrate. Additionally, there is the potential to use magnetic pinch effects for the increase of local heat loads or to focus the plasma onto zones of defined geometry. An application for the latter purpose is that substrates are often to be treated only in specified areas such that magnetic pinch may supersede the need of protection measures (e.g. joints) for the remaining areas of the component. At IRS, short-pulsed coaxial magnetoplasmadynamic plasma accelerators capable of delivering power 2 densities up to 2 GW!cm onto material surfaces are under investigation for improving resistance against fatigue and for coating removaL In addition, a product family of inductively heated plasma sources initially developed for reentry simulation [4] is available, each of them capable of being operated up to 180 kW plate power at high efficiencies and specific enthalpies with different working gases. These sources are equipped with highly efficient water cooling systems and sophisticated gas supplies. The main fields of application for the inductively heated devices are coating and waste disposal [10]. For the source development and process control numerous diagnostic systems are in operation at IRS [11]. A first analysis of the influence of a magnetic field to plasma can be performed considering the Steward number St (sometimes also named N). This number is defined as ratio of magnetic force density to the gas dynamic momentum (static pressure neglected) (12]: avB 2 St=-,-,-. jL ｰｶｾ＠ Here, a is the electric conductivity of the plasma, v the plasma velocity, B the magnetic field strength, p the density of the plasma and L is a characteristic length, often related to an appropriate geometry parameter of the plasma system. Correspondingly, St gives an engineering type information on the influence of magnetic forces to the plasma, e.g. when the Lorentz force density is in the same order of 1 magnitude as the gas dynamic force (-7 O(St)=lO<) or one order less (-7 O(St)=l0. ). However, St often does not allow for the identification of the manner of interaction due to the complexity of the considered plasma sources and systems. Another dimensionless parameter to characterize the effect of a magnetic field applied to plasmas is the magnetic Reynolds number Rm· Consider f.lo as magnetic permeability. With the product f.lo<J as a measure to characterize the penetration of the plasma by a magnetic field a time 2 scale for the diffusion of magnetic field can be deduced by the product L f.1 0<J. The term Llv, however, is the time scale of turbulence provided that v is considered as root mean square of the fluctuating velocity (12] or at least the dynamic time scale ifv is considered as plasma flow velocity: f1 0 aLl - = u avL. R =' o L/v m Typically, values of Rm can be divided into two classes: Rm << 1 means that magnetic field and plasma flow do not affect each other while the larger values for Rm signify that there is a connection between magnetic field and plasma flow, i.e. that the condition must be calculated using models in which both magnetic field and flow are coupled. The combination of both equations yields St =R B2 / flo m pv2 = Rm j3 ' 2 2 where 13 is the ratio of the magnetic pressure B /(2f.lo) to the (gas) dynamic pressure pv /2, a parameter of which the reciprocal 1113 can be considered as virtually synonymic to St. The size 13 is preferably used within the field of plasma fusion technology (5]. Here, however, 13 is mostly used for static systems (Ptot instead of pv2/2). It becomes evident that large Rm may result in large St; small Rm, however, do not necessarily come along with small St (mind 13 !). 2. Inductively heated Plasma Generators (IPG) IPG3, IPG4 and IPG5 were developed enabling the generation of plasmas at plate power related efficiencies of more than 50 % achieving maximum plasma powers of more than Tube cooling system Tube 50 kW while different working gases such Water·coolec tube as oxygen, nitrogen, air, carbon dioxide or cOOling system ftange hydrogen can be applied [4]. They have been used at IRS mainly for atmospheric entry simulation. The application of these nano-powder coating, for devices production, chemical synthesis under plasma conditions, waste disposal proＧｾ＠ and hospital waste disposal is prescedures Optical Window Tube cooling Cal ently under investigation ( 10, 13]. system ftange Fig. 1 shows the plasma generator IPG3. Fi2. 1: IPG3 With RF-sources such as IPG3 the induction coil is closer to the plasma than it is with other designs reducing the electromagnetic field loss. ｾ＠ 2 An advanced water cooling system surrounds both the induction coil and the plasma tube. With this transparent tube cooling system, e.g., the position of the "plasma flame" within the tube can be observed with regard to different operating parameters such as pressure, gas, mass flow and anode power. The length of the coil is 1 = 0.12 m [4]. The plasma current amplitude and the Ohmic Heating depend on the electrical conductivity of the plasma and the resonant frequency of the electric circuit. The power system used in the investigation is a triode driven generator with variable frequencies as both the IPG coil and the resonant circuit capacitors can be changed. Both the seven capacitors, which have a capacity of 6 nF ± 20% each, and the induction coil are cooled using regular water [4]. For the characterization of the operational behavior, measurements with a cavity calorimeter were performed [4 ]. To support the development of the IPGs and to adapt them to the required working conditions, suitable measurement techniques enabling a characterization of the plasma and the sources were developed and qualified. Besides the calorimeter, coil current measurement systems were qualified and developed to characterize the electrodynamic behavior of the IPGs [14]. Plasma stabilization effects were observed when the tube cooling power decreased suddenly despite the simultaneous increase of the plasma power. Within this investigation an imaging spectrometer has been used to measure the radial intensity of the plasma within the IPG [ 15]. These investigations confirmed the existence of stabilization effects. Specifying the Stewart number for an IPG analyzing the ratio of the radially directed Lorentz force in the tube to the total pressure leads to [5] St = ; ｾ＠ (! = ; r, 05 wherein d is the diameter of the plasma tube and 8 is the skin depth (8 = 1/(nf.lo<Y£) · ), see also refs. 4, 5 and 15. This equation shows that the stronger the damping the greater the Stew art number. It follows from this equation, that stronger damping leads to higher Stewart number. Measurements of the plasma power depending on operational frequency f and the plate power of the facility were performed [4]. Using an electrodynamic model for the IPG in combination with models for the electrical conductivity cr and the mass specific enthalpy h enabled the statement of a boundary value problem for the skin depth 8. Correspondingly, values for d/8 = 3 ..4 were determined. The corresponding pressures in the tube were 14 hPa, the magnetic pressure Pm was 2 hPa calculated one-dimensionally using the results of the coil current measurements (-7 j3 :::: 7). This coarse estimation leads to St :::: 1. Therefore, the strength of the magnetic force density is in the order of magnitude as the gas dynamic momentum. This analysis confirms the existence ofMHD effects within IPG operation [5]. A theoretical analysis of the problem using the Maxwell equations allows for the statement of the wellknown Helrnholtz equations. Introducing an infinitely long solenoid resulting in an axial-symmetric situation in the IPG's tube motivates the introduction of a cylindric coordinate system. Using the corresponding Laplace operator delivers a set of differential equations of Bessel type which are the basis for the calculation of all plasma parameters such as the radial distributions of magnetic field H, electric field E and current density j [4, 5]. The induced plasma power P can be derived from the integral of /lcr over the volume. The resulting power has a maximum for d/8 :::: 3.6 proving that the power optimization for the above mentioned condition was succeeded. The corresponding power curves are presented in [4]. The one-dimensional formulation of momentum equation is dp dr . = JlolaH=. Both the current density j"' and the magnetic field Hz are functions of the radial position r in the tube. Integrating leads to Pm =JloHcoil 2 j,(!___) R ' I 3 where R = d/2, Hcoil is the external magnetic field of the coil and f 1(8/R) is a help function consisting of complex Bessel functions depending on 8/R. In order to quantify the theoretical results coil current measurements using the current sensor HOKA [14] were performed. In ref. [4] a corresponding plasma condition using oxygen at a mass flow rate of 3 gis, an operating frequency of 640kHz using a 5.5-tum coil and 4 capacitors, minimum pressure (40 Pa) in the plasma chamber and a plate voltage of 6.3 kV was characterized with respect to the IPG3 conditions and the plasma flow conditions (Mach number, Pitot pressure etc.). Within this investigation an effective coil current of 0.4 kA was measured for this condition. Fig. 2 shows the magnetic pressure depending on 8/R. Two facts can be derived from this Figure: • Both the maximum of the induced power reported in [4] and the maximum of the magnetic pressure in fig. 2 are identical. • The existence of a maximum shows that there is in principle the possibility to maximize plasma stabilization effects (MHD) over 8/R e.g. to reduce the thermal load to the plasma tube by a pinch effect, see also [4, 5]. For this condition d/8 z 3.6 (--4- 8/Rz 0.57) was determined in ref. [4], a value which conforms to the ,, 27 ﾷＯｾ＠ maximum of the induced power and which is ｾ＠ identical to the maximum of magnetic pressure in fig. 2 such that a value of 2.75 hPa is derived from = "this one-dimensional model. ; Ｍｾ＠ In addition, previously performed analysis using a 1X simplified model where d >>bled to ------ / ·-- 1$(; ""'-,"" Q. ｆＬ］ｾ＠ where Fr is the radially directed Lorentz force. This ., result can also be derived using a transitivity. With j iiRiexpressible by the coil current IcoiJ using a modified equation and H expressible by the coil transformator magnetic the of distribution Quantitative 2: Fig. force Fr can be expressed using Lorentz the current, 8/R on pressure dependin2: the Lorentz force must be Therefore, Icoi. the factor Icoi. The power, however, can be expressed using that the plasma observation the with proportional to the induced plasma power. This fact in combination power can be maximized with respect to d/8 led to the presumption that the Lorentz force could have a similar maximum, too. An analysis based on the results of the Bessel differential equations leads to C I Fr =ＭｊｲｦｬｯｈＬｾｵｺ＠ 04 , dfz (0) R , where l is the length of the coil and fl8/R) is a help function consisting of complex Bessel functions depending on 8/R. ---l The already mentioned value d/8:::::: 3.6 [4] is very close to the Lorentz force maximum as well, see -;. ｌＬｯＫＭ｟Ｎ［ＧｾＱ＠ fig. 3. Therefore, for this condition a Lorentz force ｾ＠ : Ｇｾ＠ of roughly 4.3 N is obtained. This value and thus ·"+-!Ｍｾ＠ the results in fig. 3 are in the same order of ＫＭｾ＠ magnitude as axial magnetic thrusts reported for .. l t - - - - - - - - r - - - - - - - 1 ﾷＮ［ＫＭＱｾｬ＠ self-field MPD-thrusters [16]. Additionally, a other The maximum can be seen at 8/R : : : 0.5. maximum at 8/R --4- 0 is of an academic nature Fig. 3: Quantitative distribution of the Lorentz and is not reached in reality within the context of force depending on 8/R, Icoil.cff = 400 A partially ionized plasmas. Moreover, Fr is linear in R for constant attenuation factors 8/R. ＺｾＱ＠ ］ＭＡＺｲ［ｾＢＧＬ＠ ' . .:1 4 "" 3. Short Pulsed Plasma Accelerator Activities A high power short pulsed plasma accelerator system is being technical for developed applications [8]. This activity for non space application is focused Anode on the design, realization and experimental investigation of a compact and efficient pulsed selffield coaxial plasma accelerator the demonstration and early for Nozzle Accelerator of Detail 5: Fig. Fig. 4: Accelerator Assembly commercial evaluation of plasma impulse peening and plasma impulse de-coating methods as well as other industrial processes [8]. The 2 design phase resulted in a plasma gun capable of delivering an incident power density of up to 2 GW/cm in less than 1 )lS on a target surface. The plasma gun is currently in the process of be ing assembled. The overall system as seen in fig. 4 consists of a capacitor bank holding 22 capacitors of 1 )lF chargeable to 40 kV, the accelerator nozzle unit and the vacuum chamber with a diameter of 0.9 m and a length of 2.6 m, see fig . 4 . The plasma accelerator nozzle as shown in fig . 5 has an overall length of 255 mm and consists of two coaxial stainless steel electrodes. The central electrode (cathode) has an outer diameter of 20 mm, the inner diameter of the outer electrode (anode) is 70 mm. The gas inlets near the head of the hollow anode require a fast acting valve currently under construction. Before breakdown, the density is in the Anode order of 10·5 kg/m 3 [8]. 22 General Atomics 31158 i(t) i(t) capacitors are arranged parallel within the circuit Cathode eo and are placed at equal distances from the accelerator as seen in fig. 4. The capacitors are charged through a high voltage power supply, ＮＱ＠ ｉ ＼ｾ ﾷｾ Ｇ ｟Ｉ ＾＠ ｾ providing up to 40 kV. A more detailed description La of appropriate peening and de-coating processes Fig. 6: Electrical Circuit assumed for Plas ma Dynamics using pulsed plasma accelerator systems is given in [8]. In principle, a gas fed pulsed plasma accelerator consists oftwo electrodes, a gas inlet connected to a valve and a capacitor bank. After the capacitor bank is charged up to its initial voltage, the fast electromagnetic gas valve opens and a short pulse of working gas is released into the gap between the two electrodes. Breakdown occurs at z = 0 (least inductance, see fig. 6) after the gas density reaches its critical value according to Paschen's law. A washerlike planar current sheet of ionized gas is propagated in axial direction due to Lorentz force . The snowplow model as found in [17] describes this discharge process. The current flow within the circuit produces an azimuthal B-field between the electrodes. This magnetic field interacts with the current flowing through the plasma resulting in an axial Lorentz force . According to the model all the gas between the electrodes is swept up and compressed by the traversing plasma sheet. Due to the skin effect, the current conducting layer is very thin. The circuit is assumed to be an RLC-circuit as shown in fig. 6. The capacitor C 0 discharges causing a current i(t) to flow through the circuit components of resistance Ro and inductivity L 0 as well as across the plasma sheet which has a changing inductivity Lp(t) over time due to its movement along the electrodes. The following two equations describe the snow plow model [ 17]: =· _Q+R i+L .:!..!: _ d (( L0 + L p) i) =O 0 0 ' dt dt c dp dt ］ＡＮ｟ dt ＨｾｭＩ ］ｆ＠ L (t ) = t_ d (LP) dt . dt dz 2 5 0 The first equation describes the electric circuit model and was derived according to Kirchhoff' s Mesh Law. The current as well as the inductivity of the plasma and the charge Q of the capacitor depend on time. The second equation contains Newton's second law and is the dynamic model. Here m is the time dependent mass of the plasma sheet and FL is the Lorentz force. The magnetic field B(r) between the two electrodes can be derived from Ampere's law. Using cylindrical coordinates a point P(r0,<p0) between the electrodes is considered. Every infinitesimally small wire in the electrode located at an angle <p carries the currentj*==i/(2rrra) causes a magnetic field in P according to f.l·}* B=-2n:r' ' where r' is the distance from the wire in the electrode to the point P considered. By integrating the contribution of all infinitesimally small wires along the circumference of cathode as well as anode, the overall magnetic field at point P is found. The term cos(8) accounts for the fact that only the angular component of the magnetic field has an effect on the acceleration. B = Bcathode + Banode Bcarhode == ｊＧｾＺＬ＠ ·cos(B)ds ］ｉ｛ｾＺＬＪﾷ＠ eo{ arcsin(;:, · sin(qJ- qJ0 )) JlijdqJ Banodc ］ｉ｛ｾＺﾷ＠ co{!l- ｡ｲ｣ｳｩｮＨＺｾ＠ · sin(qJ- qJ0 )) )l radqJ Fig. 7 shows the distribution of the magnetic field inside the accelerator nozzle over the radius r0 according to the equation above after numerical integration assuming a lower limit for the expected current of 180 kA [8] through the electrodes. This results in a magnetic field of -2 Tesla at r 0 ==50 mm. In order to approximate the current density j(r) inside the plasma, the thickness 8 of the plasma sheet is "i: ·······,,·,,..._____ needed. However, since no values for 8 could be obtained, "-.... J the order of ma!!Ilitude is < 1 mm and is assumed to be ｾ＠ . . I 0.1 mm resulting ｾｯ＠ a current density of 1.2 · 106 Alcm2 . The . same thickness 8 is assumed in order to approximate the 30 25 35 20 density inside the plasma before leaving the electrodes. ｒ｡､ＡｵｾｴＮｊｩｭ＠ Assuming that the complete mass is compressed into the Fig. 7: Magnetic Field Distribution 3 plasma sheet yields a density of 0.24 kg/m . The exhaust velocity of the plasma sheet was approximated in [8] to be in the order of 100 km/s. The reference length Lis the diameter da==0.07 m of the anode. This leads to the Steward number: Magnet1c F1eld U1stntutwr, between Electrodes 4,,ＭｾＮ＠ j ovB 2 jB St == -,-,- == -,-.- "" 0.67 . pv"jL pv" /L This means that the Lorentz force density is in the same order of magnitude than the total pressure of the plasma. 4. Magnetic Probe A concept for a magnetic probe to experimentally study the influence of magnetic fields to weakly ionized plasmas in the IRS plasma wind tunnels has been developed for a program of the European Space Agency (ESA) in cooperation with the German Aeropace Research Center in Braunschweig, Gertman (DLR). The primary purpose of this concept is the investigation of potential in-flight experiments aiming for the reduction of thermal loads to the thermal protection system of a vehicle during the re-entry into the earth's atmosphere. However, it is evident that such investigations combined with validated numerical investigations are of great importance to other technical applications such as in the field of plasma technology (see section 1). 6 Shock Plasma Diamete£ lower Than 100 mm Figure 9: Scheme of the magnetic probe in the plasma flow ｐｾ ＢｬＮＶＵﾷＱＰ Ｔ ｫｧ Ｏｭ The axis of the coil will be aligned with the axis of the plasma flow as depicted in Fig. 9 [15]. Pressure and heat flux will be measured in the probe's stagnation point. The magnetic flux density wi ll be measured with a Teslameter. In order to determine composition and temperature, the IRS optical measurement techniques will be used [11] . In the program, a typical peak heating condition during re-entry is characterized by a velocity of ｶ ｾ Ｂ＠ 6.5 km/s at Ｓ＠ complying with a total 10' enthalpy of ha "" 21.1 MJ/kg and a total pressure 10' 10' of about Pa"" 6.3 kPa. In Fig. 10 the approximate 10' dependence between magnetic field strength, 10 5 plasma enthalpy of air in equilibrium at p = 10 1 Pa and magnetic forces is shown. Obviously, for 115 10"' - 10, a significant influencing of a weakly ionised 10 ) 1T plasma with ha"" 20 MJ/kg a magnetic field 10' 2T 3T 10 ' strength of about 1 T is necessary. Due to the 4T 10'' resistance of copper, a rough approximation of a 10 " coil with a sufficiently high current leads to 10"' - - - - - - - - 10 20 30 40 0 losses of about 40 kW, which does not permit the hI MJ/kg use of a copper coil for stationary operation. Figure 10: Stuart Number versus enthalpy for air at Therefore, the development of a cryogenically p = 10 5 Pain equilibrium depending on magnetic field cooled coil made of a superconducting material strength is foreseen within the program. ---f 1 50 5. Conclusions Potential applications for magnetically controlled plasmas in both fields space technology as well as in plasma technology have been identified. An analysis of existing plasma generator systems, high power inductively heated plasma generator and short-pulsed plasma accelerator, was performed which confirmed the appearance of MHD effects essentially for the functionality of both plasma generator systems. Here, the authors emphazise that additional investigations in Refs. 4-6, 8 and 15 proved this analysis e.g. by the investigation of magnetic pinch effects related to the operation of the inductively heated plasma generator system. Finally, a concept of a magnetic plasma probe, developed in cooperation with DLR Braunschweig, Germany, was presented. This probe will deliver essential information on the influence of magnetic fields weakly ionized plasmas. 6. Acknowledgement The authors thank the research students D. Kammerlocher and S. Krauss for their support. 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