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NSWC TR 88-146
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- N4 GRAPHITE HEATING ELEMENT THERMAL AND
STRUCTURAL PERFORMANCE IN THE NSWCHYPERVELOCITY WIND TUNNEL 9 - A FINITEELEMENT ANALYSIS
BY MICHAEL A METZGER
STRATEGIC SYSTEMS DEPARTMENT
JUNE 1988 T, 1.
SEP 0 5 i989•'
Approved for public release; distribution is unlimited.
irel•l ontains coler"]pi.V.: All ..-TIC r-cpro-¶irt-Ir.,' s4- L2 wiU b z oa aad
NAVAL SURFACE WARFARE CENTERki Dahlgren, Virginia 22448-5000 * Silver Spring, Maryland 20903-5000
89 9 01139
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NSWC TR 88-146
6a. NAME OF PERFORMING ORGANIZATION 66 OFFICE SYMBOL 7a. *NAME OF MONITORING ORGANIZATION(If applicable)
Naval Surface Warfare Center K23
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10901 New Hampshire AvenueSilver Spring, MD 20903-5000
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PROGRAM PROJECT TASK WORK UNITELEMENT NO. NO. NO ACCESSION NO
11 TITLE (Include Security Classification)
Graphite Heating Element Thermal and Structural Performance in the NSWC Hypervelocity
Wind Tunnel 9J--A Finite Element Analysis
12 PERSONAL AUTHOR(S) Metzger, Michael A.
13a TYPE OF REPORT 13b, TIME COVERED 14. DATE OF Rg(RTJ (Year, Month, Day) 15 PAGE COUNTFinal FROM O___OTI_ TO ___ June 78
16. SUPPLEMENTARY NOTATION
17 COSATI CODES 18 SUBJECT TERMS (Continue on reverse if necessary and identify by block number)
FIELD GROUP SUB-GROUP
13 0120 11 SEE REVERSE
19 ABSTRACT (Continue on reverse if necessary and identify by block number)
A general finite element based method for investigating the electrical, thermal, and
themostructural performance of electrically powered heating devices is presented. The
method is used to investigate the performance of a graphite heater configuration-ttilized>.' ,-
in the NSWC Hypervelocity Wind Tunnel Facility (No. 9) for heating nitrogen gas to tempera-
tures up to 31000 F prior to a tunnel run to prevent condensation of the gas durinp tunnel
operation. The graphite heaters presently have a limited and erratic service life--ja
newly installed heater may fail after only 1 or as many as 100 or more tunnel run cycles.
Electrical, thermal, and thermostructural performance data are presented for two graphite
heater configurations. Thethermostructural model is shown to correctly predict brittle
fracture at fillet locations in the heater body where, in fact, most fractures are knownto occur. Two methods for reducing fillet stresses are proposed which, if implemented,
could substantially increase the useful service life of the graphite heaters.
20 DISTRIBUTION /AVAILABILITY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATIONC3] UNCLASSIFIED/UNLIMITED [XI SAME AS RPT [__ DTIC USERS UNCLASSI FI ED
22a NAME OF RESPONSIBLE INDIVIDUAL 22b TELEPHONE (include Area Code) 22c. OFFICE SYMBOL
Michael A. Metzger 202/394-2063 K23
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All other editions are obsolete U.S. GO",,-,-n" P iultiuiaofice 1988407-04*
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18. Cont.
Graphite Heating elements Brittle fractureBrittle Failure' Failure T'heory FractureMaximum Normal Stress Hypersonic Wind TunnelThermal-electric analogy Electrical Finite elementHypervelocity Crack- NitrogenRefractory Probability ThermostructuralFatigue Heat transfer Stress-Strain Voltage TemperatureThermal Stress/strain Heat flux Resistance-Ri4etingJoule Heating Convection ABAQUSPATRAN Principal stress CurrentCurrent Density Radiation ConductivityResistivity Free Convection Tensile strengthThermal Expansion Service lifeStrain-to-failure
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NSWC TR 88-146
FOREWORD
This report documents an investigation of the electrical,thermal, and thermostructural performance of graphite heatingelements used in the Naval Surface Warfare Center (NSWC)Hypervelocity Wind Tunnel No. 9. This study is part of a largerand ongoing effort by the Aerodynamic Facilities Branch(Code K23) to reduce or eliminate the problem of frequent andcostly failures of the graphite heaters. The analysis hereinfocuses on the nitrogen preheating period of the tunnel run cycleduring which most heater failures are known to occur.
A general finite element-based method for investigating theperformance of electrically powered heating elements ispresented. The technique is applied to the Tunnel No. 9 graphiteheater, and it is shown to correctly predict brittle fracture atfillet locations in the heater body where, in fact, most heaterfractures occur 4 Two methods for reducing fillet stresses areproposed which, if implemented, could substantially increase theuseful service life of the graphite heaters.
The author wishes to thank Dr. Robert Edwards and the K22Structural Mechanics Group members for their guidance concerningthis study. Also, thanks are extended to Margie Fung, Aero-Thermodynamics Group (Code K22), for providing the procedure forcalculating free-convection film coefficients, to Mr. RayTrohanowsky for developing the POWEF 7-tran subroutine. And,finally, thanks to the author's brai.ch head Dr. J. MichaelEtheridge for the many useful suggest .s for improving thistechnical report.
Accesion For Approved by:
NTIS GRA&I,DTIC TAB 03Unannounced 0 Co L. SCHMIDT, HeadJusht__ca__or ___ Strategic Systems Department
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A'I' iii/iv
NSWC TR 88-146
CONTENTS
Chapter Paae
1 INTRODUCTION . . . . . . . . . . . . . . . . . . . 1BACKGROUND . . . .................... 1
TUNNEL-9 OPERATION ............ .............. 1HEATER ELEMENT BREAKAGE PROBLEM ..... ........ 2
2 GENERAL HEATER ELEMENT PERFORMANCE ANALYSISPROCEDURE . . . . . . . . ............... 5
ANALYSIS PROCEDURE ............ ............... 5ELECTRIC RESISTANCE HEATING--STEP I ...... .... 6GRAPHITE ELEMENT HEATING--STEP 2 .... ....... 7GRAPHITE ELEMENT THERMAL STRESSES--STEP 3. 8
PRACTICUM ..................................... 8
3 PERFORMANCE ANALYSIS RESULTS FOR TUNNEL-9GRAPHITE HEATING ELEMENTS ............. 11
ANALYSIS RESULTS ..................... 11ELECTRICAL ANALYSIS RESULTS--STEP 1 ......... .. 11THERMAL ANALYSIS RESULTS--STEP 2 ....... 12THERMOSTRUCTURAL ANALYSIS RESULTS--STEP 3. . . 12
GRAPHITE HEATER ELEMENT FILLET STRESSES ....... .. 15FILLET STRESS BREAKDOWN ....... ............ .. 15STRESS REDUCTION METHODS ...... ........... 16
ASSUMPTIONS ............. .................. 17
4 CONCLUSIONS ............. ................... 18
REFERENCES ....................... 63
DISTRIBUTION . . . . . . . .............. (1)
A ANALYSIS SUPPORT PROGRAMS .... ............. A-1
B ABAQUS INPUT FILES . ............... B-1
C FREE CONVECTION HEAT TRANSFER FILM COEFFICIENTCALCULATION FOR MACH-14 END HEAT CONDITIONS. . . C-1
D TENSILE STRENGTH AND STRAIN-TO-FAILUREEXPERIMENTAL DATA FOR HEATER GRAPHITE ......... .. D-1
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NSWC TR 88-146
ILLUSTRATIONS
Fig~re Pacre
1 SCHEMATIC OF TUNNEL NO. 9 FACILITY............... 192 VERTICAL HEATER AND DIAPHRAGM SECTION . . . . . . .193 HEATER GAS CONDITIONS FOR A TYPICAL MACH-14
WIND TUNNEL RUN .o.... .. . . . . . . . . .. .. 204 COMPLETELY FAILED HEATER--TOP FILLET LOCATION . . . 215 COMPLETELY FAILED HEATER--BOTTOM FILLET LOCATION. . 216 TOP AND BOTTOM FILLET CRACK LOCATIONS IN THE
GRAPHITE HEATER .......... ................. 227 PARTIAL TOP FILLET CRACK ........... .............. 238 PARTIAL BOTTOM FILLET CRACKS ....... ............ .. 239 HEATER GRAPHITE ELECTRICAL RESISTIVITY
VERSUS TEMPERATURE . . . . . . ............ 2410 J HEATER DRAWING .A.I.N.................... .. 2511 K HEATER DRAWING . . . . . .. .. .. .. .. ...... 2612 MACH-10 HEATER BASE DRAWING. . ........... .2713 J HEATER FINITE ELEMENT MODEL ...... ........... 2814 K HEATER FINITE ELEMENT MODEL. . ........ . . 2815 FINITE ELEMENT MODEL USES HEATER SYMMETRY TO
REDUCE MODELSIZE.......... ........ ...... 2916 MACH-10 HEATER BASE FINITE ELEMENT MODEL. .. ........2917 VOLTAGE POTENTIALS IN THE J HEATER ................... 3018 CURRENT DENSITY CONTOURS IN THE J HEATER. .. ........3119 START HEAT TEMPERATURES IN J HEATER. ................ 3320 END HEAT TEMPERATURES IN THE J HEATER .... ....... 3321 END HEAT TEMPERATURES IN THE J HEATER. .............. 3522 START HEAT TEMPERATURES IN THE K HEATER ........ .. 35.23 START HEAT TEMPERATURES IN THE MACH-10 BASE . . .. 3724 AXIAL STRESS IN MACH-10 BASE. . . . . . . . . . .3725 HEATER ELEMENT/BASE CLAMPING ARRANGEMENT ......... .. 3926 DEFORMED SHAPE PLOTS--FLOATING BASE. ................ 4027 DEFORMED SHAPE PLOTS--CLAMPED BASE .. ................ 4128 AXIAL STRESS IN J HEATER .................. 4329 AXIAL STRESS IN K HEATER ................... 4330 MAXIMUM PRINCIPAL STRESS--J HEATER, START HEAT. . . 4531 MAXIMUM PRINCIPAL STRESS--J HEATER, END HEAT. . .. 4532 MAXIMUM PRINCIPAL STRESS--J HEATER, FREE BASE . . . 4733 MAXIMUM PRINCIPAL STRESS--K HEATER, START HEAT. . . 4734 MAXIMUM PRINCIPAL STRESS--MACH 10 BASE. ....... 4935 TEMPERATURES IN SQUARE AND ROUNDED CORNER
HEATER LEG ......... . . . .. . . 49
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NSWC TR 88-146
ILLUSTRATIONS (Cont.)
Fireae
36 TOTAL PRINCIPAL STRESS AND TEMPERATURE PROFILESEXTRAPOLATED TO HEATER SURFACE.TOP FILLET LOCATION . . . . . . . .... 51
37 TOTAL PRINCIPAL STRESS AND TEMPERATURE PROFILESEXTRAPOLATED TO HEATER SURFACE.BOTTOM FILLET LOCATION ... ............. 52
38 TOTAL PRINCIPAL ELASTIC STRAIN PROFILE EXTRAPOLATEDTO HEATER SURFACE. TOP FILLET LOCATION . . . .. 53
39 TOTAL PRINCIPAL ELASTIC STRAIN PROFILE EXTRAPOLATEDTO HEATER SURFACE. BOTTOM FILLET LOCATION . . .. 53
40 GRAPHITE HEATER SERVICE LIFE IN TUNNEL RUNS VS.CUMULATIVE FREQUENCY ......... ............... .. 54
41 BREAKDOWN OF THERMAL STRESS AT BOTTOM FILLET. . .. 5542 FINITE ELEMENT MODEL WITH SLOT EDGES ROUNDED TO
REDUCE FILLET STRESSES ........................... 5643 COOLING SLOTS FORMED IN HEATER LEGS BY SECTIONING
AT AA AND SEPARATING HALVES . ........... 5644 CONCEPT FOR HEATER ELEMENT WITH COOLING SLOTS . . . 57
TABLES
Table Pace
1 HEATER ELEMENT SERVICE LIFE HISTORY FOR 1985AND 1986 .................................. 58
2 SUMMARY OF HEATER ANALYSIS STEPS ..... .......... .. 593 HEAT TRANSFER INPUT DATA. . . . . ......... 604 PEAK THERMAL STRESS-STRAIN STATES IN GRAPHITE
HEATER* . . .. . . . . .. . . . . . . . . .. . . 615 PROBABILITY OF FAILURE FOR GRAPHITE HEATERS . . . . 61
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NSWC TR 88-146
CHAPTER 1
INTRODUCTION
The Naval Surface Warfare Center (NSWC) Hypervelocity WindTunnel No. 9 uses an electrically powered graphite heatingelement to preheat nitrogen working gas to temperatures up to3100 0 F. This prevents condensation of the gas which cools as itexpands through a nozzle to hypersonic speeds of Mach 10 orMach 14. The graphite heater elements have a limited and erraticservice life--a newly installed heater element may fail afteronly 1 or as many as 100 or more tunnel run cycles. Elementreplacement is costly (approximately $10,000 includinginstallation), and a half day or more may be required to replacea broken heater element which adversely impacts the tunnel testschedule. This report documents a general method forinvestigating the electrical, thermal, and thermostructuralperformance of electrically powered heating elements. It alsopresents the results of an investigation of the heatingcharacteristics of the Tunnel-9 graphite heater elements. Thisstudy was initiated to determine if thermal stresses induced inthe heater elements during the nitrogen preheating period couldbe the cause of the heater element failures.
BACKGROUND
Tunnel-9 Operation
The NSWC Tunnel-9 wind tunnel is a "blow-down" type tunnelwhich runs at Mach 10 or 14. High pressure vertical heater anddriver vessels (shown in Figure 1) are precharged with nitrogengas prior to a wind tunnel run while a vacuum sphere downstreamof the test section is evacuated. The fixed volume of gas in theheater vessel is preheated to the extreme temperature required.A tunnel run is initiated by bursting a set of metal diaphragmslocated just upstream of a 40-foot long nozzle which allows thehigh-pressure, high-temperature nitrogen (typically 20,000 psi at3100OF for Mach 14) to accelerate through the nozzle section andreach speeds of Mach 10 or 14 in the 5-foot diameter testsection. Relatively cool driver vessel gas pushes the hot gasout of the heater vessel under constant pressure to maintainconstant flow conditions in the test section during the tunnelrun. The tunnel run continues until all of the hot gas has beenexpended, a typical run lasting approximately from .25 second toas long 10 seconds.
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The heater vessel (shown in Figure 2) is lined with arefractory insulation liner which safely contains the nitrogengas during the preheating process. The liner encloses thegraphite heater element which heats the nitrogen precharge to thespecified final temperature of 1500OF (for Mach 10) or 3100OF(for Mach 14). This heating process is depicted in Figure 3.During the heating period, which lasts about 15 minutes, a 60 Hz,single phase ac current of 5500-6500 rms amps is passed throughthe hairpin-shaped graphite heater element which reaches atemperature of 4000-5000°F as a result of resistance heating.The nitrogen gas, which is essentially transparent to radiation,is heated primarily by convection and conduction off the hotgraphite element and hot liner walls. Since the volume ofnitrogen in the heater vessel is fixed, both its temperature andpressure rise during the constant volume heating process untilthe final desired pressure and temperature are reached. At thispoint the tunnel flow is started by rupturing the metal sealingdiaphragms.
Heater Element Breakage Problem
Service life histories for heater elements used during FY1985 and 1986 are shown in Table 1. A heater element istypically operated until it fails "catastrophically," usually byfracturing completely through one of the heating legs as shownin Figures 4 and 5. The timing and mode of failure are fairlyconsistent. The element usually fails completely at some pointduring the nitrogen heating period. The fracture is always abrittle-type fracture typically located at either a top fillet orbottom fillet (as shown in Figure 6) with the crack surfacesoriented approximately perpendicular to the longitudinal axis ofthe heater element.
Interestingly, it is now fairly well documented that aheater may develop partial cracks at the top or bottom fillets(as shown in Figures 7 and 8) which, at least for a time, willnot adversely affect the heater operation. However, eventuallythe element fails completely and must be replaced. Althoughcomplete element failure occurs during the heating period, it isnot clear if a partial crack is initiated at this or some othertime.
Other work has been done to try to improve heater elementlife. Results of an investigation of thermal stresses, inducedby quenching of the heater as the cool driver gas fills theheater vessel during a tunnel run, did not correlate well withTunnel-9 experience. In another study, graphite material samplestaken from both long-lived and short-lived failed heater elementswere tested in an attempt to correlate service life with certain,easily obtained, non-destructive test measurements which couldthen be used as a quality control criterion for screening outunacceptable graphite material billets; however, no definitecorrelations were found. 1
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The present study is concerned with determining if thermalstresses induced in the heater elements during the nitrogenpreheating period could be the cause of heater element failures.
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NSWC TR 88-146
CHAPTER 2
GENERAL HEATER ELEMENT PERFORMANCE ANALYSIS PROCEDURE
ANALYSIS PROCEDURE
The heater analysis procedure can be broken down into threebasic steps:
Step 1: Solve the Electrical Problem--Get volumetricresistance heating in the graphite heatergenerated by a (5500 amp) current flow through theheater.
Step 2: Solve the Theral_ • oble--Use internal heatingfrom Step 1 to "heat up" the graphite element andobtain graphite temperatures.
Step 3: Solve the Structural Problem
"o Use temperatures from Step 2 to obtain thermalstress and strain in heater due to thermalexpansion. Determine maximum principal stressand strain in the heater.
"o Subtract the hydrostatic stress orstrain (generated by the high-pressure nitrogengas surrounding the heater) from the peakprincipal stress or strain to obtain the netmaximum principal stress or strain.
"o Compare net maximum principal stress or strainwith graphite strength to determine the.probability of failure.
The entire three-step procedure above was implemented usingthe ABAQUS 2 Finite Element Analysis software (version 4-5) inconjunction with the PATRAN 3 pre- and post-processing code. Theimplementation of each of the three steps is described in moredetail below.
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NSWC TR 88-146
Electric Rcistance Heatina--SteD .
Implementation of Step 1, that is, obtaining the volumetricresistance heating (also known as joule heating) due to theelectric current passing through the graphite heater element,required a novel application of the well documentedthermal/electric (T/E) analogy principal. 4 The T/E analogy hasbeen widely used to solve analogous engineering problems in thefields of heat conduction, fluid dynamics, and solid mechanics.Phenomena which are governed by the Laplace equation, such asboth electrical and heat conduction, yield mathematicallyidentical solutions; the solution of a particular electricalconduction problem is also applicable to the corresponding oranalogous heat conduction problem and vice versa. Analogousmathematical terms for the T/E analogy are given below:
THERMAL ELECTRICAL
Heat, Q Charge, QTemperature, T Voltage, VHeat Flux Vector, q Current Density Vector, jThermal Conductivity, k Electrical Conductivity,s
The typical approach to applying the T/E analogy has been toobtain a solution to a particular heat conduction problem usingan analogous electrical conduction model (e.g., electrolytictanks or conductive sheet models). In the present analysis,however, the opposite approach has been taken; that is, theelectrical conduction in the heater is obtained by solving theanalogous heat conduction problem using a geometrically similarfinite element heat conduction model.
The ABAQUS thermal conduction capability can be utilized toeasily solve for current flow in an arbitrarily shaped conductorsubjected to some prescribed voltage. Since ABAQUS does not"know" that it is solving an analogous electrical conductionproblem, it will state the results as "temperatures" and "heat-flux," etc. However if consistent analogous electrical terms areinput, the "temperature" and "heat-flux" results from ABAQUS willactually be voltage and current-density, respectively. For thisanalysis, the units used for the input quantities were inches,volts and, for electrical conductivity, 1/ohm-in which produceunits of volts and amps/sq in for the voltage and current-density output quantities,respectively. ABAQUS will calculatethe components and also the magnitude of the current-densityvector, J, at each gauss point in the finite element model. Thevolumetric resistance heating at each gauss point can then beobtained by Equation (1):
q - Iij 2p ()
where: q - volumetric heat flux (watts/cu in)Iii - current density magnitude (amps/sq in)p - electrical resistivity (ohm-in)
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NSWC TR 88-146
This last step of calculating the heat flux at each gausspoint is done by running a short Fortran program I2RFIL (listedin Appendix A). This program simply reads the current densityvalues from the ABAQUS results (FIL) file and generates a file ofvolumetric heat flux at each gauss point using Equation (1).This file of heat flux values is then used to heat-up thegraphite element (Step 2 in the analysis procedure) to obtain thetemperature in the heater.
Limitations of T/E Method. There are two principallimitations in the T/E method described above. First, theelectrical conductivity must remain constant with temperature.Although ABAQUS will handle temperature dependent thermalconductivity, this capability cannot presently be utilized fortemperature dependent electrical conductivity since the actualtemperatures are not known in Step 1. They are computed later onduring Step 2 in the analysis procedure. As Figure 9 shows, theelectrical resistivity (the resistivity is simply the inverse ofconductivity) of the graphite material is strongly temperaturedependent up to about 1400 0 F, then remains fairly constant attemperatures above this. It was found that the heater elementlegs run at temperatures above this, except for the initial heat-up period, which lasts about a minute, so that for most of the15-20 minute nitrogen heating period the electrical conductivitycan be taken to be uniform and constant.
This method is also in a strict sense limited to dcelectrical power. Recall that the Tunnel-9 heater elements arepowered by a 60 Hz, ac power source. An ac current-produces aso-called "skin effect" which causes a concentration of thecurrent density at the outer surface of a conductor rather thanbeing uniformly distributed through the cross section as in dccurrent flow. This effect is proportional to the ac frequencyand size of the conductor and is inversely proportional toresistivity. It was determined that, in regard to the volumetricheating, this effect would be secondary for the graphite heaterelements so that the dc current flow analogy should adequatelymodel the heating characteristics.
Graohite Element Heatina--SteD 2
Since both Steps 1 and 2 in this analysis procedure use aheat conduclinn finite element model, the basic model used inStep 1 car, : used in Step 2 with changes in the boundarycondition- 1 reflect the new nature of the problem. ABAQUS iscapable oi solving very general transient and steady-state heattransfer pro'*l',s involving internal heat generation, radiation,and convyctio:, with temperature dependent properties.
Recall from Figure 3 that once power to the heater is turnedon at the start of the heating period, the graphite element heatsup in about 1 minute. During this time the temperature of the
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NSWC TR 88-146
nitrogen gas in the heater vessel does not increase appreciably.For analysis purposes this initial heating transient must beviewed as a nonsteady-state phenomenon. After about 1 minute,the heater element temperature reaches a nearly steady-statelevel and, thereafter, both the heater and nitrogen gastemperatures rise slowly for the remaining 15-20 minutes ofheating time. For analysis purposes this relatively slow heatingprocess can be treated as a quasi-steady state process so thatthe heater temperature can be assumed to be a function solely ofthe surrounding gas/liner-wall temperature. The problem ofobtaining the temperature distribution in the heater at any pointduring the quasi-steady heating reduces to simply fixing thegas/wall temperature and solving for the steady-state heatertemperature distribution. Since performing a transient analysisis in general much more costly, it was decided to limit thepresent study to investigating the heater temperatures andstresses at selected points in time within this quasi-steadyheating period. The two points selected for study were at thestart and end of the quasi-steady heating period and which aredesignated as "START HEAT" and "END HEAT" in Figure 3.Additionally, the gas and liner-wall temperatures were assumed tobe identical permitting the use of one sink temperature for bothradiation and convection boundary conditions.
Obtaining the temperature distribution in the graphiteheater at the START or END HEAT is a matter of specifying theproper sink temperature in ABAQUS, as well as specifyingradiation and convection heat transfer coefficients, and thenallowing ABAQUS to solve for the steady-state temperatures in theheater due to the resistance heating provided by Step 1. Sincethe resistance heating in the heater is non-uniform, the ABAQUSsubroutine option DFLUX is used with the subroutine given inAppendix A to read the heatin7 flux values from the filegenerated in Step 1. ABAQUS calculates the temperatures in theheater which are then used to evaluate thermal performance of theheater and to obtain thermal stresses in the heater.
Graphite Element Thermal Stresses--Step 3
Once again the same basic finite element model from Steps 1and 2 can be used in Step 3 if the element type designator ischanged to the corresponding solid structural element. ABAQUSwill then use the temperatures obtained from Step 2 to computethe thermal stresses and strains in the graphite heater element.A suitable failure criteria can then be applied to the stress orstrain results to determine probability of failure or assessmargins of safety of the heater design.
PRACTICUM
In practice, implementation of this three-step analysisprocedure involves additional work, primarily in Step 1, to
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NSWC TR 88-146
ensure that correct results are obtained. Table 2 summarizes thesemi-automated steps for the entire procedure as implemented on aVAX computer system. In Step 1 the user specifies a heatervoltage and ABAQUS solves for current flow. The current checkingprogram CURRENT (Appendix A) will verify that the net currentflow through the heater is correct. If it is not, then theapplied voltage may be adjusted. Once the correct net current isobtained, the program I2RFIL (Appendix A) is run which createsthe resistance heating file (FOR032.DAT file) from the ABAQUSresults file. Once the heating file is generated, it should bechecked by running the POWER program (Appendix A) whichcalculates the total heater power that will be generated by theheating file. The total power calculated by POWER should bewithin a few percent of the specified heater voltage multipliedby the total heater current computed by CURRENT (i.e., the totalresistance-heating power should equal applied heater volts timestotal amps). Some discrepancy can be expected since thealgorithm used in POWER to compute finite element volumes is notexact for quadratic elements with curved edges.
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CHAPTER 3
PERFORMANCE ANALYSIS RESULTS FOR TUNNEL-9 GRAPHITEHEATING ELEMENTS
ANALYSIS RESULTS
The two most current graphite heater element configurations,hereafter referred to as the J-type and K-type heaters, are shownin Figure 10 and 11. The drawing for the Mach 10 heater base isshown in Figure 12. The K heater has superceded the J heater,the differences being in the flared top and the side slots. Inthe K design, the slight flare-out of the outer diameter at thetop end was lengthened, and the slot was also lengthened in orderto "beef-up" the top fillet region where the earlier J-typeheaters tended to break. This change appears to have reducedtop fillet breaks but, unfortunately, the K heaters continued tofracture at the bottom fillet. Both the J and K heaters wereanalyzed with the basic finite element models shown in Figure -13and 14. Both are 1/4-symmetry models utilizing the two planes ofsymmetry in the heater to reduce model size as shown in Figure15. The J model is a full-length model, whereas only the topportion of the K design was analyzed. Extensive studies showedthat such top models would give the same stress results as thefull model when out-of-plane motion of the cross section at thecutoff is prevented. Quadratic finite elements were used in boththe thermal models and the stress models (20-node hexes and 15-node wedges, ABAQUS DC3D20- and C3D20-type elements,respectively). The Mach 10 graphite heater base, which holds theheater element, was also analyzed separately using the 1/4-symmetry model shown in Figure 16. Only the bottom portion ofthe heater element, up to the bottom fillet region, is includedin the base model. The results of the base analysis will not bediscussed extensively in this report--these results are presentedfor reference.
Electrical Analysis Results--Step 1
Results for voltage and current density distributions in theJ-type heater are shown in Figure 17 and 18, respectively. Thecurrent density plot can be viewed as a topographical map withpeaks showing regions of high current densities, such as at boththe top and bottom fillets, and valleys indicating areas ofrelatively low current densities. The ABAQUS material andboundary conditions are given in Appendix B for the J heaterelectrical model.
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Thermal Analysis Results--SteR 2
Thermal Model Setup. In all cases convection heat transferwas allowed on the inner diameter (I.D.) and outer diameter(O.D.) "wetted" surfaces of the heater element as well as on therounded end of the crown and edges of the side slots. The O.D.and I.D. of the threaded-base portion of the J heater was fixedat 300 0 F. Radiation heat transfer was allowed on the wettedO.D., slot edges, and the rounded end of the crown. No radiationwas allowed on the wetted I.D. since the inside surfaces of theheater element legs face each other so that the net radiation toeach surface is taken to be zero as a first approximation. Table3 lists the film coefficients and radiation boundary conditionsused. ABAQUS input data for the J thermal model are given inAppendix B, and Appendix C shows the method used to compute thefree convection film coefficient.
Thermal Results. Figures 19-23 show temperature results forthe three models analyzed. Figures 19 and 20 show temperaturesin the J heater for a standard 613 kW power case (5481.8 A @ 112V) for both START HEAT and END HEAT periods. The peaktemperatures in the graphite are 3620°F at START HEAT and 4858°Fat END HEAT, and they occur at the "hotspot" apparent on the I.D.surface near the top fillet. Cross-sectional temperatureprofiles at the top and bottom fillets for the END HEAT case(Figure 21) reveal internal hotspots at both fillet locationscorresponding approximately to the locations where the highcurrent densities occur. Also readily observed in these plots isthe hot core along the inside center of the heater element legwhich is undoubtedly due to the lack of radiation cooling on theI.D. of the heater leg. An END-HEAT case was run at 913 kW (6680A) which resulted in an increase of peak temperature to 5622 0 F.No experimental data were available at this time to correlatewith these temperature results.
Figure 22 shows the temperature results for the K heaterwhich was run only at the START HEAT condition. The graphitebase model results are shown in Figure 23. The base resultsshown in Figures 23 and 24 are for a slightly higher heater powerof 653 kW.
Thermostructural Analysis Results--Step 3
Although the heater element is clamped to the graphite basewith set screws (as shown in Figure 25) both clamped and freeheater element leg end-fixity conditions were analyzed to studythe effects of end- fixity on stresses. ABAQUS input data forthe clamped-base J model are given in Appendix B. Figure 26 and27 give highly exaggerated deformation plots showing both theclamped- and free-end results. The fact that the heater elementleg deflects inward at the free end is probably due to the
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NSWC TR 88-146
relatively cool edges of the heater element leg, which do notgrow by thermal expansion as much as the hotter center portion,and tend to pull or warp the center toward the edges.
Since it is known in advance that the heater elements failby brittle fracture at the top and bottom fillets and that thefracture plane is approximately perpendicular to the heaterelement longitudinal axis, one might expect to find high axialtensile stresses at these fillet locations if, indeed, thethermal heating stresses are the cause of heater failures. Theplots of axial stress in Figure 28 in fact show peak tensilestresses of 6896 and 7046 psi occurring in the J heater at thetop and bottom fillets, respectively, for START HEAT. The axialstress distributions in the K heater and the heater base areshown in Figures 29 and 24. An assessment of heater elementfailures, based on these stress results, is given in thefollowing two sections.
Failure Analysis--Stress Based. For brittle-type fracturesin an isotropic material the so-called "maximum normal stress"failure theory can be used as the failqre criterion. 5. This theorystates that tensile fracture will occur when the maximum tensileprincipal stress exceeds the tensile ultimate strength of thematerial. The (algebraically) maximum principal stress plots forthe J and K heater and the heater base are shown in Figures 30-34 (Figure 35 is discussed on page 16). Peak tensile principalstresses at START HEAT of 7000 psi* occur at the fillets in the Jheater in Figure 30, but the K heater in Figure 33 shows arelatively low stress at the fillet and a relatively low peakstress at the center of the leg of 4124 psi. Table 4 lists thestate of thermal stress and strain at each gauss point in the topand bottom fillets where the highest principal stress occurs. Asshown in Table 4 by the "axial tilt" angles of 6-19 degrees,these principal stresses act approximately in the axial directionas expected.
High axial principal stresses also occur at the threadedbase of the heater element where it necks down to the thinnerwall, and they are especially noticeable for the END HEAT cases(both clamped and free) in Figures 31 and 32. Failures in thisbase region are fairly rare, however, indicating that perhapsthere is some give at the base/heater interface which limitsthese stresses.
The principal stress profile in the graphite near thesurface of the fillets can be seen in Figures 36 and 37. Thesefigures show profiles of temperature and the total principal
wThe axial fillet stresses in Figure 28 are "nodal averaged"
results whereas the principal stresses in Figure 30 were manualextrapolations to the fillet surfaces of more accurate gausspoint data. The use of two different extrapolation methodsaccounts for the predicted bottom fillet axial stress beinghigher than the principal stress.
13
NSWC TR 88-146
stress (the total principal stress is equal to the thermal stressminus the 750 psi compressive stress due to the hydrostaticpressure of the nitrogen gas which surrounds the heater). Thestress reaches the maximum level at the fillet surface where boththe temperature and the strength of the graphite are lowest. Thestrength of graphite, unlike most common engineering materials,actually increases substantially with increasing temperature upto about 5000 0 F. In both Figure 36 and 37, the stress at or nearthe fillet surface exceeds the indicated 4100 ksi tensilestrength of the graphite indicating that a fracture is likely tooccur in the fillets. This result correlates very well with thefailures observed in the Tunnel-9 heater elements.
Failure Analysis--Strain Based. Table 4 lists the strainsat the critical locations in the top and bottom fillets. Boththe total strains and elastic strains are shown. The elasticstrain (or "strain due to stress") is equal to the total strainminus the thermal strain component, a4T, at the point inquestion. This elastic strain value can be compared toconventional strain-to-failure data to assess probability offailure. Test data for strain-to-failure, taken from actualheater element graphite material, is shown in Appendix D. Thedata are for axial and circumferential directions at an elevatedtemperature of 20000 F, and they are plotted as strain versusprobability-of-failure (POF). A POF of 60 percent, for example,means that 60 percent of the test samples failed at the indicatedstrain level. Profiles of total principal elastic strain in thetop and-bottom fillets are shown in Figures 38 and 39. As in thestress case, the maximum strain occurs at the fillet surface.The estimated maximum principal strains indicated in Figures 38and 39 were obtained by increasing the axial strain by theprincipal to axial stress ratio at the point in question and thensubtracting the hydrostatic strain* as shown here:
principal strain = axial strain (rincipal stress)- hydro. strain\ axial stress /
= .00319 (5815/5471) - .000326
- .00306 in/in (@ Top Fillet, GAUSS POINT 7)
The maximum principal elastic strains at START HEAT are.00375 and .00388 in/in in the top and bottom fillets,respectively, as shown in Figures 38 and 39. These strain levelscorrespond to a POF of 65 percent and 75 percent, respectively,which says 65 to 75 percent of the heater elements should failrelatively quickly, and that the remainder should have relativelylong service lives. The actual heater element service livesshown earlier in Table 1 can be plotted statistically as service
* The hydrostatic strain, Eh, due to the 750 psi gas pressure iscomputed using: Eh - (1-2v)P/E where Eh=hydrostaticstrain, v-poisson ratio, P-pressure, E= Young's modulus.
14
NSWC TR 88-146
versus percentage of heater elements which will fail by this life(cumulative frequency) as Figure 40 shows. Interestingly, thedata show that up to about 70 percent of the heater elements hadaverage (20 cycles) or shorter service lives, and about 20percent had relatively long service lives of 50 or more cycles.This result agrees well with the strain based failure rateprediction, and this is somewhat fortuitous considering the smallstatistical population used and other factors. This result showsthat, for a linear stress analysis such as this one, the strainbased failure criterion yields more realistic results than thestress based one which, in all cases, predicts a 100 percentfailure rate based on the data in Appendix D. This is due to thefact that graphite material exhibits a strain-softening stress-strain relation which, if ignored, will cause the thermalstresses to be over-predicted.
Table 5 summarizes the stress and strain failure analysisresults. Note that even the strain failure rate is 100 percentfor the high power (913 kW) case in Table 5 owing to thesubstantial increase in fillet stress with increased heaterpower. It has been found that, in fact, heater element failuresoccur more frequently when the heater elements are run at higherpower levels.
GRAPHITE HEATER ELEMENT FILLET STRESSES
During the course of this investigation various studies wereperformed to:
1. Explain why high axial tensile stresses occur at the topand bottom fillets.
2. Investigate methods to reduce high stresses in thegraphite heater elements, thereby providing a means toextend the useful service life of a heater element.
Fillet Stress Breakdown
Parametric studies were performed to breakdown the bottomfillet stress into component parts. Figure 41 presents theresults of these studies. Five main effects are identified herein order of importance:
1. Differential Radiation Effect (42 percent)2. Edge Cooling Effect (31 percent)3. Thickness Cooling Effect (17 percent)4. Beam Bending Effect (6 percent)5. Fillet Hotspot Effect (4 percent)
15
NSWC TR 88-146
Each effect is described below briefly.
Differential Radiation Effect. The O.D. of the heater tuberadiates freely to the heater vessel liner whereas the I.D. ismore or less enclosed; hence, there is a decreasing temperaturegradient from the I.D. to the O.D., tending to induce axialtension at the O.D. and axial compression at the I.D.
Edge Coolina Effect. The edges of the heater element legsare more efficiently cooled than the center portion because ofexposure to the cool nitrogen gas on three surfaces instead ofjust two. Hence the edges tend to stay at a lower temperaturethan the center and, due to less thermal expansion, are"stretched" axially by the hotter center and develop axialtensile stress.
Thickness Cooling Effect. Internal volumetric heating in athin slab with cooling on the slab surfaces produces a parabolictemperature gradient. The core of the slab tends to expand morethan the outer material creating a compressive core and tensileskin.
Beam Bending Effect. The gross thermal expansion of theheater element sets up "beam bending"-type stresses in the heaterelement legs when the base is clamped. The 6 percent figureindicated for this effect may be conservative since it is basedon a case where the heater was uniformly heated to 4000OF whichdoes not induce the more severe gross warping evident inFigure 26.
HotsDot Effect. Additional thermal expansion of material atthe internal hot-spots located near the fillets tends to putadditional tensile stress in the fillets.
The first three effects perhaps explain why the axialthermal stresses in the heater element leg are tensile at theO.D., even more tensile at the edges, and compressive at thecenter core. The last two effects may explain in part why thetensile edge stresses tend to peak out at the top and bottomfillets.
Stress Reduction Methods
Regarding the edge cooling effect, it was noticed in thecourse of these studies that the temperature in a heater elementleg is lowest at the sharp corners on the edges of the leg (asshown in Figure 35). This cooler material cannot expand as muchas the core and, hence, the corners are stretched in tension asthe hot core expands. It was found that rounding off the sharpcorners, an shown in Figure 35 and 42, substantially reducedfillet stresses on the order of 20 to 30 percent.
16
NSWC TR 88-146
Another technique which may be useful for reducing filletand edge tensile stresses is to provide a "cooling slot" at thecenter of each heater element leg to help cool the hot core.Figure 43 shows how this could be done by "slicing" the legsthrough at section AA and rotating the halves outward. Aprototype design for such a heater element is shown in Figure 44where the cooling slot extends the full length of the hot portionof the heater element leg. It was found in one analysis of acooling slot design that the top and bottom fillet stressesdecreased by 25 percent and 35 percent, respectively, as comparedto the nonslotted heater element.
ASSUMPTIONS
Various assumptions were made in this analysis. Forexample, the use of one identical sink temperature for bothconvection and radiation heat transfer assumes the insulationliners run at the same temperature as the nitrogen gas. However,since nitrogen gas is essentially transparent to heaterradiation, the liner receives radiation directly from the heaterelement and probably runs hotter than the gas. (Preliminarycalculations indicate that the liner may run 800 0 F hotter.) Thiseffect would lead to a hotter element and, as some preliminaryanalyses have recently shown, somewhat lower thermal filletstresses in the heater element (perhaps 20 percent lower). Onthe other hand, although the fillet stresses may be lower, thetrue ultimate tensile strength of a given volume of graphite maybe significantly lower than the average strength used here. Thisis due to the actual strength of a brittle material (such asgraphite) being determined by the distribution of flaws in thematerial. 6 For this reason the tensile strength of graphite ishighly variable to such a point that the true strength of any onesample can vary significantly from the average strength data.The statistical tensile strength plots in Appendix D wereobtained from tensile tests on actual graphite samples which weremachined from failed heater element material, and they show thescatter typical for this graphite. The statistical strengthvariation shown in Appendix D holds only for the specific volumeof material associated with the tensile specimen gauge section(Vol - 0.066 cu in). In order to accurately assess failure in agraphite part such as a heater element, a sophisticated failureassessment must be carried out that accounts for the volume ofmaterial in the element which is subjected to high tensilestresses. A failure criterion with these features requires alarge body of statistical material data which is currently notavailable for the heater element. 7
17
NSWC TR 88-146
CHAPTER 4
CONCLUSIONS
This report documents a general finite element method forinvestigating the electrical, thermal, and thermostructuralperformance of electrically powered heating devices. The methodwas applied to a graphite heater element utilized in the NSWCHypervelocity Tunnel No. 9 to pre-heat nitrogen working gas totemperatures of 3100 0 F. Electric current density and temperaturedistributions at the start and end of the nitrogen preheatingperiod are presented. Thermal stresses in the graphite heaterelement are presented which predict that crack initiation of thetype actually exhibited in the heater elements is likely to occurat the top or bottom fillet of the J-type heater due to hightensile thermal stresses which occur in these regions. Thelikelihood of a crack starting is greater near the beginning ofthe heating period. Also, it is greater with lower Reynold'sNumber tunnel conditions since the relatively low hydrostaticpressure of nitrogen gas at these conditions does not relieve thetensile fillet stresses enough to prevent fracture. The resultscorrectly predict that crack initiation is more likely at higherheater powers due to an increase in fillet thermal stresses withincreased power. The stress models also correctly predict thatthe K-type heater will tend to fail at the bottom fillet becausethe geometry of the K heater at the top fillet effectively limitsthe axial tensile stress in the top fillet to relatively lowlevels.
Two methods for reducing fillet stress levels are presented.First, the technique of rounding the edges of the heater elementlegs is shown to reduce fillet stresses by perhaps 20 to 30percent. Second, by providing a central cooling slot in eachheater element leg, the fillet stresses were reduced by 25 to 35percent.
The results presented here suggest that the fillet stressesgenerated during the nitrogen heating period are a primary causeof heater element fracture. The exact mechanism for initialfracture may be tensile fracture or fatigue. If high tensilefillet stresses during heating are in fact causing the heaterelement failures, then the two methods presented for reducingfillet and edge stresses, if implemented, may significantlyincrease the survivability of the Tunnel-9 graphite heaterelement.
18
NSWC TR 88-146
GASOLATER OIZONTVALVE
TAST DRIERL VIESSELS
FIGUREO 1.4 CEAI FTNNLN.9FC~T
(VRIGUE2CERAALEAE)N DAHAM ETO
DIFSRS(ONETDT
NSWC TR 88-146
/
-j LU 0 -L C
0 ~0~ C cL
zzWLU 0 U
0d
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uii
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20
NSWC TR 88-146
0
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0. U
0
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u-i
21.
NSWC TR 88-146
TOP
FILLETOP CRACK LOCATIONAND ORIENTATION
S~ BOTTOM
BOTTOM CRACK LOCATION
FIGURE 6. TOP AND BOTTOM FILLET CRACK LOCATIONS IN THE GRAPHITE HEATER
22
NSWC TR 88-146
FIGURE 7. PARTIAL TOP FILLET CRACK
FIGURE 8. PARTIAL BOTTOM FILLET CRACKS
23
NSWC TR 88-146
2500
92000
0
150
I-
? 500
42
NSWC TR 88-146
S-Z
lt
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112 ~t1U.
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-NSWC TR 88-146
a 'a
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NSWC TR 88-146
7.
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I x -T
Inc-
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27
NSWC TR 88-146
FIGURE 13. J HEATER FINITE ELEMENT MODEL
"- ":Z" .
FIGURE 14. K HEATER FINITE ELEMENT MODEL
28
NSWC TR 88-146
FULL MODEL 1/2 SYMMETRY MODEL 1/4 SYMMETRY MODEL
FIGURE 15. FINITE ELEMENT MODEL USES HEATER SYMMETRY TO REDUCE MODELSIZE
--•' •.,•:•V:,,•: ..,i -" - .
MACH-10 HEATER BASE + REVJ/K GRAPHITE HEATER1/4 SYMMETRY MODEL
FIGURE 16. MACH-10 HEATER BASE FINITE ELEMENT MODEL
29
NSWC TR 88-146
LA LA LA LA LA LA In Lr In
<1,
L~J
ZlI-
w <wcy. -U
a ZU=
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KNI><~ N30
NSWC TR 88-146
TOP BOTTOM
FIGURE 18. CURRENT DENSITY CONTOURS IN THE J HEATER
31/32
NSWC TR 88-146
4 - -c
4CC4
4 TEMPEPi4TiJPE F 4 C1
.
mri-14 STAPT HEAT3TEA[,', STATEN2 '5IN•TEmP-3ees
-END HEAT'ONTOUP LE' PLSUSED,
'619 KW
2121.
i1 120,.
'304.
- . .600.S2a96.
FIGURE 19. START HEAT TEMPERATURES IN THE J HEATER
4554.UTEMPEPATURE , F 42SO.M-14 END HEAT
N2 TEMP-*310OF 3946.
5481 AMPS3641
gIIII KWI1•I•3337.
3033.
2-29.
2425.
2121.
z
FIGURE 20. END HEAT TEMPERATURES IN THE J HEATER
33/34
NSWC TR 88-146
TErMPEPATUPE FPICH-14 ENDE HEAT 4 '4
STEACDl STATE 4680.
N".2 SINK TEMP- 3100F54SI1 AMPS 4576.
ELEM 197-103 ELEM 1241-252 4472.4368.
4264.
4160 ."J
4056.
3952.
3348.
3744.
3640.
3536.
3432.
3328.
3224.
FIGURE 21. END HEAT TEMPERATURES IN THE J HEATER
TEMPERATURE, FMACH-14 START HEAT, REV-K 3173.
GRAPHITE 5500 AMPS 3682.
2832.
2661.
2491.
2320.
2150.
1979.
• 1889.
1468.
1298.
1127.
957.
786.
616.
FIGURE 22. START HEAT TEMPERATURES IN THE K HEATER
35/36
NSWC TR 88-146
TEMPEFIITUPE F 3399.PE' J ' ,iPiPHITE HEiTEP * f-1CH-16 BASE56%S2 A'p5 ,63 t 3206.N2 STNt TEl SOO F 3014.I 2821.
2629.
2436.
2244.
2851.
1859.
1666.
1474.
1281.
1889.
896.
784.
511.
FIGURE 23. START HEAT TEMPERATURE IN THE MACH-10 BASE
ZZ-STRESS (PSI) seoo8.
5652 AMP•S (653 KW, 4see.
CLAMPED BASE 4888.REV JýK GRAPHITE HEATEP + MACH-10 BW
3588.3888.
2588.
1586.
1886.
586.
8.
-1888.
-2088.
-3888.
-408e.
FIGURE 24. AXIAL STRESS IN MACH-10 BASE
37/38
NSWC TR 88-146
3.5" ;
I
FIGURE 25. HEATER ELEMENT/BASE CLAMPING ARRANGEMENT
39
NSWC TR 88-146
I-LU
LA.
CL
NN..
\N LU
USU
go LU
L" LU
ULA
LL v(0Z
0
U. I
40
NSWC TR 88-146
14U
0 L
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LU
a-
LU
LALL
LLU
CD\
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054
QXW>
41/42
NSWC TR 88-146
6500.
5850.12.6896.
5288.
ZZ STRESS (PSI)M-14 START HEAT 4558.
CLAM'PED BASE54SI AMPS , 1121)88 ~N12 SINlK-30OF k3250.GRAPHITE
2608. 1- -
1950.
1388.
658.
0.INN~ER SURFACE OUTER
SURACE -600.4. 704r
-1288.
Z -1808.
y X -2488.
-3888.
FIGURE 28. AXIAL STRESS IN J HEATER
U~~ E T 3688.
3288.
2888.
2488.
1288.
8.
-1888
-2888.1
-2588.
FIGURE 29. AXIAL STRESS IN K HEATER
43/44
NSWC TR 88-146
7000. -
7888. 6388.rAX PRINCIPAL S1ESS (PSI)REU-J GRAPHITE S600.
START HEAT 4906.CLAMPED BASE(613.9 KU) 4208.
5481 AIlP•3588.
2888.
2188.
1488.
788.
8.
7 ?888 -288.
Z -688.
x -888.
FIGURE 30. MAXIMUM PRINCIPAL STRESS -- J HEATER. START HEAT
S~6388.j
MA~X PRINCIPALREU-J GRPIT • 5688.END HEAT .:CLAM'PEO BASE 4988(613.9 KU) •.•
"• ~28e.•
2188.
1488.
788.
• 8.
-288.
-488.Z -688.
-1888.
FIGURE 31. MAXIMUM PRINCIPAL STRESS - J HEATER, END HEAT
4 5/46
NSWC TR 88-146
7000.
6300.MA~X PRINCIPAL SVESS (PSI) S688.FLOATING BASEEND HEAT 4988.RE'J-J GRAPHITE(613.9 KW) 4288.
350e.
2880.
2180.
1488.
-488.
x -see.
S-1888.
FIGURE 32. MAXIMUM PRINCIPAL STRESS - J HEATER, FREE BASE
3688.
3288.
2888.
2488.
1688s.
1288.
80.8
-240.
-488.
FIGURE 33. MAXIMUM PRINCIPAL STRESS - K HEATER, START HEAT
47/48
NSWC TR 88-146
t`IA:*: PPIMCIPAL STRESS (SI) 3000.
MACH-10 HEATER BASE - 70
2460.
2100.
1500.
1200. _
600.
300.
0.
-40.0
-80.0
Z -120.* • -166.
-260.
FIGURE 34. MAXIMUM PRINCIPAL STRESS - MACH-10 BASE
TEMPERATU1tt , f
318S. 33
3121.
3056. 192992. 3W.
2928. 1614.
2863. am.
2799. 2919.
2734. em.2670. 2166.
26M6. em3.
2S41. 27,
24??. e649.
T-9 GRAPHITE HEATER 2412. ro9?.BOTTOM FILLET
1ACH-14 START HEAT 2348. e545.
ssee AMPS 2
H2 TEMP-300 2284.
2219. _ 440.
FIGURE 35. TEMPERATURE IN SQUARE AND ROUNDED CORNER HEATER LEG
49/50
NSWC TR 88-146
J HEATER, TOP FILLETHYDROSTATIC PRESSURE = 750 PSI613 KWATTS @ START HEATFINITE ELEMENT #263
8000-0 TOTAL PRINCIPAL STRESS (PSI)
A AVERAGE ULTIMATE TENSILE STRENGTH (PSI)
GRAPHITE TEMPERATURE (F)7000
6000'1
5000
4000
5.~O*~ -._.• *.__ __- _._--•--
3000
2000
1000
GAUSS GAUSS GAUSSPITPOINT POINT
7 3
.060 .310 .5550
-1000 DISTANCE FROM HEATER SURFACE (INCHES)
FIGURE 36. TOTAL PRINCIPAL STRESS AND TEMPERATURE PROFILES EXTRAPOLATED TOHEATER SURFACE. TOP FILLET LOCATION
51
NSWC TR 88-146
J HEATER, BOTTOM FILLETHYDROSTATIC PRESSURE - 750 PSI613 KWArTS @ START HEA T8000 FINITE ELEMENT #120
----TOTAL PRINCIPAL STRESS (psi)A AVERAGE ULTIMATE TENSILE STRENGTH (PSI)7000 GRAPHITE TEMPERATURE (F)
8000
5000
4000
2000
1000
-1000
POI AT E SUGCE B TT M FI LSS O AT O9R PROFILE EXG AU OL TEST
.052
.225
NSWC TR 88-146
J Heater, TOP FILLETHYDROSTATIC PRESSURE = 750 PSI
5 613 KWATTS @ START HEATFINITE ELEMENT #263
4 - TOTAL PRINCIPAL ELASTIC STRAIN
A AVERAGE STRAIN TO FAILURE OF GRAPHITE* _z
S3z
I -
o 2z4
S GAUSS GAUSS GAUSSSPOINT POINT POINT
7 5 3
0 1 1
.060 .310 .550
DISTANCE FROM FILLET SURFACE
FIGURE 38. TOTAL PRINCIPAL ELASTIC STRAIN PROFILE EXTRAPOLATED TO HEATER SURFACE,TOP FILLET LOCATION
J HEATER, BOTTOM FILLETHYDROSTATIC PRESSURE = 750 PSI618 KWATTS @ START HEATFINITE ELEMENT --120
4 TOTAL PRINCIPAL ELASTIC STRAIN
A AVERAGE STRAIN TO FAILURE OF GRAPHITE
zz-3z
2
1- 1 GAUSS GUSGAUSStoPIT POINT POINT
9
0 1
.050 .225 .400
-1 DISTANCE FROM FILLET SURFACE
.FIGURE 39. TOTAL PRINCIPAL ELASTIC STRAIN PROFILE EXTRAPOLATED TO HEATER SURFACE.BOTTOM FILLET LOCATION
53
NSWC TR 88-146
U.)
0 0LULi
U.
> -
0 U
0 < 7
LU
CL
LU Zo -r
I- ~L(S31OA3O 3:1 4 -W3
o54 -
NSWC TR 88-146
EFFECT AMOUNTSPSI %
* DIFFERENTIAL L
2917/42
RADIATION RA
*EDGE COOLING 2186/31
"qCOOL EDGEHOT CORE /
-- 'AT
0 THICKNESS COOLING 1169/ 17
0 BEAM BENDING 437 /6(CLAMPED BASE)
0 HOT SPOT @ 291/4FILLET
7000 / 000%
FIGURE 41. BREAKDOWN OF THERMAL STRESS AT BOTTOM FILLET
55
NSWC TR 88-146
CF2 284 ELEMS " , ••,
z~ z
Sy - -
FIGURE 42. FINITE ELEMENT MODEL WITH SLOT EDGES ROUNDED TO REDUCE FILLETSTRESSES
A .
AJFIGURE 43. COOLING SLOTS FORMED IN HEATER LEGS BY SECTIONING AT AA AND
SEPARATING HALVES
56
NSWC TR 88-146
4 i I0o IC
/I 0I-
-JCflH C,2Iii -�00
zI-
I-zLU
LU-JLU
LU
4I- LU
o I z-J
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C,U.
-I.
57
NSWC TR 88-146
TABLE 1. HEATER ELEMENT SERVICE LIFE HISTORY FOR 1985 AND 1986
ELEMENT LIFE(TUNNEL RUNS)
1985 FAILURES 1986 FAILURES
2 10 5 54 5 9
6 25 12 2 2 18
12 7 7 2 49 87
58 6 13
1/2 10 5
68 26 21
18 ELEMENTS. 294 RUNS 9 ELEMENTS, 228 RUNS
AVERAGE RUNS PER ELEMENT = 19.3AVERAGE ELEMENTS PER YEAR = 13.5
58
NSWC TR 88-146
2
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NSWC TR 88-146
LU
cc~z r
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NSWC TR 88-146
Co w 8 3(o 0 o 8
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I-61/62
NSWC TR 88-146
REFERENCES
1. Southern Research Institute, Evaluation and Comparison ofGraphite Heater Tube Materials Used in the HypervelocityWind Tunnel, SoRI-EAS-86-508-5787-I-F, Southern ResearchInstitute, Birmingham, AL, Jul 1986.
2. ABAOUS (Version 4-5), Hibbitt, Karlsson, and Sorensen, Inc.,Providence, RI, Jul 1985.
3. PATRAN, PDA Engineering, Santa Ana, CA, Dec 1985.
4. Schneider, P. J., Conduction Heat Transfer, Addison-WesleyPublishing Company, Inc., Reading Massachusetts, pp 338,1955.
5. Juvinall, R. C., Stress, Strain, and Strength, McGraw-HillBook Co., Inc., New York, NY, 1967.
6. Dieter, G. E., Mechanical Metallurgy, Second Edition,McGraw-Hill Book Co., Inc., NewYork, NY, 1976.
7. Buch, J. D., Crose, J. G., and Robinson, E. Y., FailureCriteria in Graphite Proaram, AFML-TR-77-16, Air ForceMaterials Laboratory, Wright Patterson Airforce Base, OH,Mar 1977.
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APPENDIX A
ANALYSES SUPPORT PROGRAMS
A-i
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PROGRAM CURRENT
C PROGRAM TO COMPUTE TOTAL CURRENT IN ABAQUSC HEATER MODEL BY SUMMING REACTION FLUXES FROMC ABAQUS THERMAL ANALYSIS RESULTS. USER MUST SUPPLYC NODES IN THE DATA STATEMENT WHICH DEFINE CROSS-C SECTION FOR WHICH TOTAL CURRENT IS DESIRED.C USER MUST UPDATE NODEN AND IMPLIED DO LIMIT BELOW.C BEFORE RUNNING ASSIGN THE XXX.FIL FILEC TO FORTRAN UNIT FOR0g8. ONLY NODES FOR WHICH TEMPERATURESC HAVE BEEN PRESCRIBED CAN BE SPECIFIED.
IMPLICIT REAL*8(A-H,O-Z)DOUBLE PRECISION ARRAYDIMENSION ARRAY(513), JRRAY(2,513) , NSET(500)EQUIVALENCE (ARRAY(1) , JRRAY(I,1))CALL INITF
NODEN=29RFLUX8=.0
CDATA (NSET(L),L=1,29) /1 189, 110, 111, 112, 113, 114,2 115, 116, 117, 118, 119, 128,3 382, 383, 384, 385,4 386, 387, 388, 389, 398, 391,5 392, 393, 394, 395, 396, 397, 398/
CK=IDO WHILE (K.LE.9?9999)
CALL DBFILE (0,ARPAY.,.JRCD)IF (JRCD.NE.0) GO TO 100KEY= JRRAY(1,2)IF (KEY.EQ.214) THEN
M=1DO WHILE (M.LE.NQDEN)
IF (NSET(M).EQ.JRRAY(1,3)) THENRFLUX=RFLUX+ARRAY(4)
END IFM=M+lEND DO
END IFK-K+1END DO
100 CURENT= RFLUX*2.0WRITE (6,2000) CURENT
2668 FORMAT(IX,24H TOTAL HEATER CURRENT = F10.3,1X,7HAMPERES)STOPEND
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NSWC TR 88-146
PROGRAM 12RFIL
C PROGRAM TO READ FLUXES AT MAT'L CALCULATIONC POINTS (=GAUSS PTS FOR DC3D2O) FROM ABAQUSC GENERATED XXX.FIL FILE AND CONVERT FLUXES TOC ELECTRICAL RESISTANCE (12R) HEATING VALUES. PROGRAMC WRITES HEATING VALUES TO FILE UNIT 032. BEFOREC RUNNING ASSIGN THE XXX.FIL FILE TO FORTRAN UNITC FOROG8. PROGRAM ASSUMES FLUXES ARE CURRENTC DENSITIES.
IMPLICIT REAL*S(A-H,O--Z)DOUBLE PRECISION ARRAYDIMENSION ARRAY(513), JRPAY(2,513)EQUIVALENCE (ARRAY(1) , JRRAY(1,1))CALL INITF
C***** SPECIFY MATERIAL ELECTRICAL CONDUCTI.ITY, SIGt.-C***** FOR BODY FLUX UNITS OF STU/SEC-CU.IN.C***** USE SIGMA UNITS OF (OHM-IN)**-IC
SI GMA=2832 .0
DO 100 K = 1 q 9999CALL DBFILECO',ARRAYJRCD)
IF(JRCD.NE.0) GO TO 118KEY=JRRAY(1 ,2)IF(KEY.EQ.I) GO TO 10IF(KEY.EQ.28) GO TO 20GO TO 108
10 CONTINUEJEL=JRRAY( 1 ,3)JPNT=JRRAY ( ,4:)GO TO 100
20 CONTINUERBFLUX=ARRAY( :3) *ARPAY ,3)/SI GMA
CC***** CONVERSION FOR BODY FLUX UNITS OF B.T.U./SEC-CU.IN.
RBFLUX=RBFLUX*8. 008948451
WRITE(32,120) JEL,JPNT,RBFLUX126 FORMAT(215,EIG.3)180 CONTINUE118 CONTINUE
ENDFILE 32STOPEND
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NSWC TR 88-146
SUBROUTINE DFLUX (FLUX,TEMP,KSTEP,KINC,TIME,NOEL,NPT,COORDS,JLTY'P-)IMPLICIT DOUBLE PRECISION (A-H,O-Z)DIMENSION COORDS(3), RBFLUX(1900,27)DATA KSET/8/
C***** FLUXES ARE READ FROMI FILE 32 AND LOADEDC***** INTO LOOK-UP TABLE RBFLUX ON FIRST CALL4C~***** OF THIS SUBROUTINE
IF (KSET.EQ.8) THENDO 29 1-1,30800
READ( 32,1808 ,END-30) NNOEL ,NNPT ,BFLLIXl99e FORMAT(215,E10.3)
RBFLUX(NNOEL ,NNPT)=BFLUX28 CONTINUE30 KSET-1
END IF
C***** DEFINE FLUX
FLUX=RSFLUX(NOEL ,tNPT)RETURNEND
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NSWC TR 88-146
PROGRAM POWER* TO RUN THIS PROGRAM YOU MUST:* (1) ASSIGN A XXX.FIL FILE TO A FORTRAN FOR088 FILE* (2) LINK/NOMAP/EXE:POWER POWER,VAXA$DUAI :CABAQUSJABQ5LIBi/LB
* THIS PROGRAM WILL COMPUTE:
* THE TOTAL POWER GENERATED IN THE MODEL, TOTAL VOLUME OF THE MODEL* AND IT WILL SHOW THE AVERAGE POWER GENERATED FROM EACH ELEMENT
* THE ELEMENTS MAKE UP ONE QUARTER OF THE MODEL, SO* THE TOTAL VOLUME AND TOTAL POWER IS MULTIPLIED BY 4 IN PROGPý.'M
IMPLICIT REAL*S(A-H,O-Z)DOUBLE PRECISION ARRAYDIMENSION ARRAY(513) ,JRRAY(2,513)
* YOU MAY WANT TO CHANGE THE VALUES DIMENSIONED IF YOU HAVE A* LARGER OR SMALLER MODEL
DIMENSION NODE(588.0), x(5s00), Y(50080), Z(5808)DIMENSION NELE(1880),NOD1(1080),NOD2( N1000)DNOL38,N0O4(eoc1lDIMENSION NOD5(1800), NOD,(10888), NOD7(1008), NODB( I000)DIMENSION AVE(1888), NELA(1800), VOL(1808)
EQUIVALENCE (ARRAY(1) , JRRAY(I ,4))CALL INITF
L=8N= 0DO 500 K = 1,97999
CALL DBFILE(0,ARRAY,JRCD)IF (JRCD.NE.I) GO..TO .600
KEY = JRRAY(1,2)
* KEY 1901 IS USED TO OBTAIN THE COORDINATES OF EACH NODE
IF(KEY.EQ.1981) THENN=N+ 1NODE(N) = JRRAY(1.3)X(N) = ARRAY(4)Y(N) = ARRAY(5)Z(N) = ARRAY(6)
* KEY 1980 IS USED TO OBTAIN THE NODE POINTS OF EACH ELEMENT
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NSWC TR 88-146
ELSE IF (KEY.EQ.198) THEN
L=L+ INELE(L) = JRRAY(1,3)NODI(L) = JRRAY(1,5)NOD2(L) = JRRAY(1,6)NOD3(L) = JRRAY(1,7)NOD4(L) = JRRAY(1,8)NOD5(L) = JRRAY(1,9)NOD6(L) = JRRAY(1,18)NOD7fL) - .JPRAY'I,11)N0(.8(L) = JPPA(( 12,
ELSET=2
END IF
508 CONTINUE608 TOTVOL = 8
00 980 I = 1,LLEVEL = 8DO 888 J = 1 ,N
IF(LEVEL.EQ.8) GO TO 850
* IF-THEN LOOP CHECKS AND GETS THE COORDINATES FOR THE 8 NODE POINTS* FOR EACH ELEMENT, THESE COORDINATES ARE LATER USED TO FIND VIOLUME
IF (NODE(J).EQ.NODI(I)) THENLEVEL=LEVEL+ 1PA =J
END IFIF (NODE(J).EG.NOD2(i)) THEN
LEVEL = LEVEL + IPS =J
END IFIF (NODE(J).EQ.NOD3-I)) THEN
LEVEL = LEVEL + IPC =J
END IFIF (NODE(J).ELT.NOD4(f)) THEN
LEVEL = LEVEL + IPD =J
END IFIF (NODE(J).EQ.NOD5(1)) THEN
LEVEL - LEVEL + IPE =J
END IFIF (NODE(J).EQ.NOD6(I)) THEN
LEVEL = LEVEL + IPF -J
END IFIF (NODE(J).EQ.NOD7(I)) THEN
LEVEL - LEVEL + IPG -J
END IFIF (NODE(J).EQ.NODS(l)) THEN
LEVEL = LEVEL + IPH -J
END IF8se CONTINUE
A-6
NSWC TR 88-146
*THE FOLLOWING CALCULATION WILL DETERMINE THE VOL OF EACH ELEMENT
858 AJI=-X PS) -XC PB) +XCPC) +XCPD) -X<PE) -XCPF) +X(PG) tYCPH'AJ4=-XC PA) -XC PB) -XC PC) -XC PD) +XC PE) +Xl(PF) +X( PG) +X( PH)AJ7=-XCPA)+X<(PB)+YCPC)-XCPD)-XCPE)+XCPF) +XPG)->$""PH.)
*AJ2=-YCPA)-Y'(PB)+Y(PC)+YCPD)-Y(PE)-Y(PF)+Y-'PG,)'+(,.'PH)AJ.5=-YC PA) -YC PB) -YC PC) -YC PD) +Y(PE) +YC PF) +Y( PG)+ r(PH')AJB=-Y(PA)+Y(PB)+YCPC)-Y(PD)-Y(PE)+YCPF)+YCPG)-'((PH)AJ3=--ZCPA)-Z(PB)+Z(PC)+Z(PD)-Z(PE)-ZCPF)+Z(PG)+Z(PH)AJ6=-ZCPA)-ZCPB)-ZCPC)-ZCPD)+ZC-PE)e-ZCPF).Z 'PG)+Z",PH)AJ9=-z(PA)+2CP8)+Z(PC),-Z(PD)-Z(PE)+z(PF)+:7(PG)-:7(PH"
VOLA=AJ1 *AJS*Aj9+Aj2*AJS*Aj7l+AJS*Aj4*AJS-AJSý*flJ5*&KReVOLB=-AJ2*AJ4*AJ9-AJ1 *Aj-6*AJSVOLCI) = 8.815-6258*CYOLA+VOLB)TOTVOL = TOTYOL +VOLCI)
900 CONTINLUETOTYOL = 4*TOTVOL
*THIS PART OF THE PROGRAM IS USED TO OBTAIN THE AVERAGE FLU',",* FOR EACH ELEMENT
SUM =
NUMB =IKB = 8DO 2008 KA = 1,99999
IFCNUMB.LE.27) THENREADC32, 15800,END=2108) NEL,NPNT,.FLUX
1500 FORMAT(2ZI5,E10.3)SUM =SUM +FLUXWNUMB =NUMB + 1
ELSEKB = KB + I
*THE AVERAGE FLUX IS MULTIRLIED BY 1054.5 TO CONVERT FROM* ~BTU/SEC TO WJATTS
AVECKS) =CSUM/27)*1054.5NELA(KB) = NELSUM =NUMB =I
END IF2888 CONTINUE
2108 TOTROW = B
*THIS PORTION OF THE PROGRAM IS USED TO WRITE OUT ALL THE PERTINENlT* INFORMATION TO FILE FO0R54.DAT* ALSO THE TOTAL POWER IS SUMMED UP BELOW
A-7
NSWC TR 88-146
WRITE(54 ,2156)2158 FORMAT(IH1,SX,33HTUNNEL-9 GRAPHITE HEATER ELEMENT /
WRITE(54 ,' 22013)2288 FORMAT( 1X,6X,S7HELECTRICAL RESISTANCE HEAT GENERATION,/.,.//'
I4R ITE( 54, z 250)2258 FORMAT( IX,7HELEtIENT,5X,6HYOLUM',E,7-X,SHAYE FLUX,7X, lOHAVE POWAER A
IARITE( 54,2388)2386 FORMAT(1X,18X,11H(CUBIC IN.),4X,IIH(WATT/INA3),S;X,Z1H(L4ATTS')./)
00 2758 tEL = I , LPOW = YOL(IEL) * AYE(IEL)WRITE(54,2508)NELE( tEL) ,YOL( IEL) ,AYE( tEL) ,POWJ
2588 FORMAT( I?,4X,3(E18 .3,5X))TOTPOIA = TOTPOLA + POW
27758 CONTINUE
TOTPOW = 4*TOTPOW
UJRITE( 54,21S0@)2888 FORMAT( 1X//./1X , 2'X, 1 IHTOTAL POWER, 1 2-X, 1 SHTOTAL VOLUME '
WRITEC 54,2988) TOTPOWJOTV.OL2988 FORMAT(E113.3,lxý,5HWATTS,7X,<,E1O.3,1X,9HCUBIC: IN.)3888 END FILE 54
ST OPEND
A-8
NSWC TR 88-146
APPENDIX B
ABAQUS INPUT FILES
ABAQUS THhRMAL/ ELECTRIC ANALOGUE INPUT FILEREV-.J HEATER653 KWATTS
*BOUNDARYINBASEIl,, 57. 743LIGA,11, ,10.0*MATERIAL*CONDUCTIVITY, TYPE=ISO** UNITS ARE (OHM-IN)**-I2032.0*RESTART,'WRRITE*STEP, LINEAR*HEAT TRANSFER, STEADY STATE*NODE PRINT2,,, ,2,2, ,2*EL FILE, TEMPS, HEAT FLUX, COORDS,LOADS*NODE FILE2, , , 2,2,*END STEP
B-1
NSWC TR 88-146
ABAQ08 THERMAL ANALYSIS INPUT FILEREV-J GRAPHITE HEATEREND HEAT
*MATERIAL*CONDUCTIVITY, TYPE=ISO** UNITS=BTU/IN-SEC-F9.745E-4, 76.87.731E-4, 568.85.763E-4, 1088.84.537E-4, 1503.83.773E-4, 2808.83.356E-4, 2580.63.055E-4, 3888.82.878E-4, 3506.62.685E-4, 4888.82.523E-4 4508.82.201E-4, 5000.8*RESTART,WRITE*STEP, CYCLE=1'3*HEAT TRANSFER, STEADY STATE, TEMTOL=18*RADIATE, ZERQ=-468.8** EMISSIvITY=.85, STEFAN-BOLTZMAN =
** 3.383E-15 BTU/SQ.IN.-SEC-F**4CUTOUT,R5,3108.8,2.87E-15CROWN,R4,3188 .,2.887E-15ODDOUT,R6,3188 .,2.887E-15*FILM** UNITS = STUi/SEC-SQ.IN.-FCUTOUT,F5, 318"0.0, 2.272E-84CROWN,F4, 3188.., 2.272E-84ODDOJT,F6, 3108.0., 2.272E-04EVENIN,F4, 3188.8, 2.272E-84*DFLUXALL,BFNU*EL PRINT, TEMPS, HEAT FLUX, COORDS,LOADS*NODE PRINT2,,,,2,2q,2*EL FILE, TEMPS, HEAT FLUX, COORDS,LOADS*NODE FILE2,,,,2,2,,2*END STEP
B-2
NSWC TR 88-146
ABAGUS STRESS ANALYSIS INPUT FILECLAMPED BASEREV-J GRAPHITE HEATER
*MATER I AL*ELASTIC, TYPE=ISOTROPIC1.31E+0 80.13, 78.0
1.34E+06, 0.13, 532.01.50E+00, 6.13, 1832.-01 .05E+0,A 8 .13, 2-732..01.73E+00, 0.13, 3632.01.6•?E+6, 8.1:3, 4532.01.62E+06, 0.13, 5432.0*EXPANSION, ZERO=78.0, TYPE=ISO** MEAN COEFF"S OF EXPANSION. REF STRESS-FREE TEMP=T70.0 F1.75E-06, 78.83.33E-06, 2508.03.,.0E-0 -6 5008.8*BOUNDARYXZERO,2, ,&3.OLIGA,2, .8.0INBASE, I ,8.0INBASE,3, ,8 .8OUTBAS,1 ,,'.0
OUTBAS,3, ,8.0*RESTART ,WRITE*STEP, LINEAR*STAT I C*TEMPERATURE, FILE=15, B'.TEPI'= INC=1I') ,ESTEP=I I INC=1)*NODE PRINT
*EL FILE, rEMF", .CCPE:.92
2,2, 1 ,2*NODE FILE
*END STEP
8-3/B-4
NSWC TR 88-146
APPENDIX C
FREE CONVECTION HEAT TRANSFER FILM COEFFICIENTCALCULATION FOR MACH-14 END HEAT CONDITIONS
Heater Gas Conditions: Gas = NitrogenPressure = 22,000 psi= 1496 atmTemp. = 3100OF (=3560°R = 1977 0 K)
First compute Grashof Number to determine whether laminar or
turbulent conditions apply:
Gr = g(Ts-Tg) BL 3 (p/u) 2
where:
Ts= Heater Surface Temperature- 5000OF (=5460°R =30330 K)T = Nitrogen Gas TemperatureB = Coefficient of Expansion = 1/Tg = 1/3560°Rg = gravity constant = 32 ft/sec/secL = vertical distance from Heater Element BaseP = Nitrogen Density @ Taveu = Viscosity of Nitrogen @ TaveTave = Average Film Temperature = (TgTs)i 2 2505°K = 4510°R
Compute density and viscosity of nitrogen gas:
pTave = b/cu ft (at 22,000 psi from nitrogen table)
U Tave= 6.111 x 10-5 lbm/sec-ft
Compute Grashof Number:
Gr (32 ft/sec2) (5460-3560) (4 ft) 3 ( 11 lb/cu ft3560°R (6.111 x 10-5 lbm/sec-ft)/
Gr= 3.686 E13
The following criteria apply:
Laminar Convection: Gr < 1.0 E+09Turbulent Convection: Gr 2 1.0 E+09
C-1
NSWC TR 88-146
It turns out that the flow is laminar for only an inch or so fromthe heater element base, so turbulent flow is assumed to existover the full length of the heater. The average film coefficient,h, can be gotten then from Figure 7-4, Reference C-1, forvertical cylinders.
h= .021 (k/L) (Gr*Pr) 0 "4
Where:
h = Average Film Coefficientk = Thermal Conductivity of gas at TaveL = Vertical height of Heater= 4 ftGr= Grashof NumberPr= Prandtl Number = cp*u/kCp= Specific Heat of gas at Tave
Compute conductivity and specific heat at average filmtemperature:
k (@4510 R) = 0.0975 BTU/hr-ft-R
cp = 0.305 BTU/lbm R
Then
Pr= (.305)(.22)/(0.0975) = 0.689
Evaluate Film Coefficient:
h = (.021) (0.0975) (.689 * 3.686 El3) 0 - 4 /4
h = 117.8 BTU/hr-sq ft-R
C-2
NSWC TR 88-146
REFERENCES
C-I. Kreith, F., Principles of Heat Transfer, InternationalTextbook Co., New York, NY, 1973.
C-3/C-4
NSWC TR 88-146
APPENDIX D
TENSILE STENGTH AND STRAIN-TO-FAILUREEXPERIMENTAL DATA FOR HEATER GRAPHITE
The Strength Data presented here was obtained fromReference D-1 and D-2. The data are for 2020-type graphitemanufactured by the Stackpole Corporation and YU60ST graphitemade by Ultracarbon Corporation.
D-1
NSWC TR 88-146
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D- 2
NSWC TR 88-146
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D-< 3
NSWC TR 88-146
REFERENCES
D-1. Southern Research Institute, Evaluation and Comparison ofGraphite Heater Tube Materials Used in the HvyervelocitvWind _Tnnel, SoRI-EAS-86-508-5787-I-F, Southern ResearchInstitute, Birmingham, AL, Jul 1986.
D-2. Southern Research Institute, Test and Evaluation ofCarbon-Carbon NosetiD Materials: Evaluation of FailedHeatiar Elements, SoRI-Eas-82-770-4179-8-I-F, SouthernResearch Institute, Birmingham, AL, Nov 1982.
D-4
NSWC TR 88-146
DISTRIBUTION
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