Final Report FLUID MECHANICS OF MAGNETICALLY BALANCED ARCS IN CROSS FLOWS S.W. Bowen ORA Project 07912 Supported by National Aeronautics and Space Administration Grant No. NGR 23-005-128 Washington, D. C. Administered through OFFICE OF RESEARCH ADMINISTRATION The University of Michigan Ann Arbor July 1968

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SUMMARY OF EFFORT NASA Grant NGR 24-005-128 has been concerned with the properties of magnetically balanced arcs in a supersonic flow of air. In the following summary, several findings of interest are briefly discussed. For a further discussion of these points, the references listed in Appendix A should be consulted. The magnetically balanced arc behaves somewhat like a solid body, impervious with respect to the external flow. This behavior was experimentally verified by the fact that small magnesium tracer particles introduced into the arc near the upstream anode root were carried along within the arc column for a substantial fraction of the arc length, at velocities on the order of 10 m/sec. The free stream velocity was about 600 m/sec. The significant similarity parameters for the magnetically balanced arc are: 1. The Lorentz convection parameter P1 BI d U1 c 2 where B and I are the magnetic field and arc current, P1, dl and ul are a reference density arc, dimension and velocity given by u1 = a1 EB d S/l, al is a reference electrical conductivity and E the electrical field strength. 2. The power loading PL = EI1/41

where 01 is a reference heat flux potential =f/kdT and k the thermal conductivity. 3. The Prandtl number Pr l hi/=1 and 4. The Eckert number K1 = u /h where hi is a reference enthalpy. A combination of the above parameters, the joule heating parameter, can be formed KH =PL/Prl icT KJH is the ratio of joule heating to energy transfer by convection and is useful in characterizing when Lc is "large" or "small". L plays a dominant role in determining the arc behavior. One find that PL correlates with Lc for both subsonic and supersonic flows. For large L

while for lower L one must correlate (E - E )I/Prl 1 vs L. Numerical studies performed on a digital computer indicate a sharp ridge in the interior temperature distribution is developed together with an interior doublet flow pattern. The temperature ridge is pushed forward in the Lorentz direction with increasing values of the magnetic field. The doublet flow pattern does not appear to strongly depend on external boundary conditions. Some qualitative experimental confirmation for this internal arc structure was obtained by comparing the side on transverse luminosity profile, obtained by numerically integrating the visible air radiation volume emission coefficient along the line of sight through the arc, with the experimentally measured profiles. Although the relative intensity distributions are similar, they are not exactly the same and the experimental radiances are 3 orders of magnitude greater than theoretically calculated. The reason for this difference is not understoodo The reason for the arc slant is not understood. It does not appear to be related to the Hall effect. Although usually the anode root is upstream, this behavior can be reversed using blunt rather than cone-cylinder electrodes. It seems to be related to the flow field and shock wave pattern between the electrodes. The slant angle is usually quite close to the Mach angle. It is interesting that even subsonic balanced arcs on rail electrodes show a

slant*. One may conjecture that the arc slant may be related to the stability of the arc. Such an analysis is far beyond that presently possible however. Appendix A contains a list of all publications generated on this NASA Grant. Appendix B is an abstract of the Ph. D. thesis of L. M. Nicolai which was satisfactorily accepted by the Graduate School and has been submitted to NASA for publication as a NASA Contractor report. *Winograd, Y. Y. and Klein, J. F., "Electric Arc Stabilization in Crossed Convective and Magnetic Fields, " AIAA Paper 68-709, AIAA Fluid and Plasma Dynamics Conference, June 1968.

APPENDIX A Listof:Publications from NASA Grant NGR 23-005-128 Kuethe, A. M., Harvey, R. L., Nicolai, L.M., "Model of an Electric Arc Balanced Magnetically in a Gas Flow, " AIAA Paper 67-96 presented at Fifth AIAA Aerospace Science Meeting, Jan. 23-26, 1967. Kuethe, A.M.,, Harvey, R. L., Nicolai, L.M., "Model of an Electric Arc Balanced Magnetically in a Gas Flow, " First Annual Report, ORA Project 07912, Apr. 1967, 07912-1-P. Kuethe, A. M., "Fluid Mechanics of Magnetically Balanced Arcs in Cross Flows, " Progress Report, ORA Project 07912, Sept. 1967, 07912-3-P. Bowen, S. W., "Fluid Mechanics of Magnetically Balanced Arcs in Cross Flows, " Progress Report, ORA Project 07912, Mar. 1968, 07912-4-P. Kuethe, A. M., "Fluid Mechanical Structure of Balanced Arcs," Invited Lecture, Proceedings Midwest Conference on Mechanics, Colorado State University (extended abstract, in Press). Harvey, R. L., "An Experimental and Theoretical Investigation of Magnetically Balanced Arcs, " Ph. D. Thesis, University of Michigan, 1968. Nicolai, L. M., "An Experimental and Theoretical Analysis of the Convected Balanced Arc, " Ph. D. Thesis, University of Michigan, 1968.

APPENDIX B An Experimental and Theoretical Analysis of the Convected Balanced Arc* The purpose of this investigation was to examine the behavior of a Do C. electric arc in a cross-flow and transverse magnetic field. The experimental part of the investigation was carried out on high current arcs (175 to 500 amperes) balanced by a magnetic field B in a supersonic airstream at Mach numbers M of 2. 5, 3. 0, and 3. 5. The arc slanted in the airstream with the anode spot upstream of the cathode. The slant angle was close to the free stream Mach angle and increased slightly with increasing current. The velocity normal to the arc varied approximately as u00O I. The measured electric field E was nearly constant for a given M A reference station 1/3 the distance from the anode to the cathode was selected for all the measurements. The streamwise dS and transverse d dimensions were measured from photographs with dT about 50% larger than dS. Both dimensions increased with current according to d ~- Io The value of B at the reference station was nearly constant for a given Mo. The normal force coefficient CD based upon dT was nearly constant at 1. 75 for all three Mach numbers. *Ph. D. Abstract by Leland Malcolm Nicolai.

Microdensitometer scans of the arc photographs showed the peak temperature well forward of the arc axis. Results from the numerical solution of the governing equations showed the same feature. The measured radiance distribution was three orders of magnitude larger than the calculated distribution. The measured and calculated radiance distributions had similar shapes, however, suggesting similar kinetic temperature distributions. The theoretical analysis was based upon a continuum fluid and the experimental observation that the convected balanced arc is impervious to the free stream. The physical model chosen for the arc column consists of 1) an arc core, 2) an external flow and 3) an interaction region. The model assumes that energy transfer by radiation and mass transfer is small compared with El. A characteristic velocity for the arc core is u1 = aIT E B dso Based upon u1, a reference temperature T1 and dimension d1 the significant similarity parameters for the arc core are Lc = P1 BI d/ul2, PL = EI1/OI Pr = gl hl/~1 and K1 = u /hl. Here the quantities A1, hi, I1, P1 and al are the viscosity, static enthalpy, heat flux potential, density and electrical conductivity respectively, evaluated at T1. Since the arc is balanced with CD nearly constant, A/ic p u d1/g ~ As Lc becomes large (i. e. large uch) the energy equation simplifies to the joule heating and convection terms. At large Lc the coefficient of the joule heating term KJH = EI/$1 Prl' becomes constant and we must have EI/A1 Pr ~ L-. The characteristic relation for large L and constant pressure is E~U 2/3/ I1/3 E "u /

The experimental results from Roman (ARL Report 66-0191) and UM (the present investigation) were used to test the theoretical model. For large Lc the theory simplies the energy equation considerably and predicts EI/1 L7 C which is in close agreement with UM data. Roman's data, however, displays an EI/k1 ~ Lc behavior and is in the low Lc region (i. e. low ufh) where the simplified energy equation is not valid. If the data from Roman and UM is expressed as log (E - E )I/Prl m7 versus log Lc, Roman's data collapses about a curve having a slope of. 0 and the UM data collapses about a curve having a slope near 1/2. A continuous curve drawn through the two sets of data appears to describe the macroscopic behavior of the convected balanced arc from low Lc to large Lc c c

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