A + wt b L &, Tove L Jmiew y o R ¥ : : = '-l:. - P o e - & 5 (8 T -‘fiflh S oy A 3= o .“ e AEG RESEARCH AND DEVELOPMENT R CENTRAL REIFAECH LIBRARY DOCUMENT CULLECTION,. . EPORT ey EAELTAAT 3 {ob U: b Ll 07 3 IF ......... 3 i OAK RIDGE NATION i Systoms Al OPERATED BY UNION CARBIDE NUCLEAR COMPANY Lipalion, BORATORY- - 8 A ORNL.-.1976 J :\'\ ctors = Aircraft Nuclear, & & ; Propulsion Systems “s‘ ' 4 A ..'_,. v & & & STEADY-.STATE CONTROL CHARACTERISTICS OF CHEMICAL-NUCLEAR AIRCRAFT POWER FL@ a C. B. Thompson -, o‘\ vi/ W}i A L% q!-.';‘. Wy Rawser— 2 A Division of Union Carbide and Carbon Corporation \g/ 7 POST OFFICE BOX P - OAK RIDGE, TENNESSEE o i a y ¥ 4’"". / R ", | o ORNL 1976 C 85 = Reactors - Aircraft Nuclear Propulsion Systems Thsdoc met on i1stsof 44 p g s Copy? of 135 ¢ pies Ser A Contract No W 7405-eng 26 AIRCRAFT NUCLEAR PROPULSION PROJECT STEADY STATE CONTROL CHARACTERISTICS OF CHEMICAL NUCLEAR AIRCRAFT POWER PLANTS C B Thompson* DATE ISSUED FEB 29 1956 Minneapolis Honeywell Regulator Company Aeronautical Division OAK RIDGE NATIONAL LABORATORY Operated by UNION CARBIDE NUCLEAR COMPANY A Division of Union Carbide and Cerbon Corporation Post Ofi e Box P Ock Ridge Tenne ee AR | 3 4456 03LL0OO7? 3 o N WM — 711 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 ORNL 1976 C 85 - Reactors = Aircraft Nuclear ¥ Propulsion Systems QNTERNAL DISTRIBUTION 48 5 i C E Center 5, 3482 M King Biology Library f; _?jg;,-;“ D Cowen Health Physics Library . ;‘ D S Billington Central Research Library "(; ;’: J A Lane Reactor Experimental Englneerln ibrary -2.3; 8 M J Skinner Laboratory Records Department ";‘:"- %39 G E Boyd Laboratory Records ORNL R C _v:“"" ;,‘;:? 40 R R Dickison A M Weinberg rv t.,f 41 W T Furgerson L B Emlet (K 25) }"%jf 42 W B Cottrell J P Murray (Y 12) ¥ 425 43 R D Schultheiss J A Swartout ,“ : 44 R V Meghreblian E H Taylor 3 3 45 A P Fraas E D Shipley j{ 46 A J Miller W H Jordan 2 ,;.:E"'- 47 E P Epler S J Cromer ™. ¢ 48 E R Mann F C VonderLage % 49 C J Borkowski S C Lind , 50 J Eastman F L Culler 5'3;5, 51 E R Dytko A H Snell ,"" 52 S C Shuford A Hollaender £ % 53 C S Walker M T Kelley R 54 R G Affel G H Clewett & 55 M M Yarosh K Z Morgan & 3 56 A W Savolainen T A Lincoln s | 57 P M Reyling A S Householder % 58 G C Williams C S Harnll » W. 5960 ORNL — Y 12 Technical Library C E Winters ¥ "y Document Reference Section D W Cardwell t'; 4 ::':? ‘;5.;‘-.' . ¥ EXT NAL DISTRIBU ON 61 AF Plant presenfahve Balf ore 62 AF Plant Fepresentative Burbd 63 AF Plant@Representative Marief V- 64 AF Plan@Representative Santaonica 65 AF Plarif#Representative Sec:'r'rle 66 AF Ploft Representative Wood R% .*f 67 Awr Regfarch and Development Co '~; nd (RDGN) 68 Aur Refearch and Development Comfigand (RDZPA) 69 Air T@hnical Intelligence Center F" 70 Aur Ugkversity Library % 71 Asrcrdit Laboratory Design Branch ( _"?' 7274 ANP#°rojedt Office Fort Worth 'i 75 Argonne National Laborator ?“ 76 é Arrfd Forces Special Weapons Pr0|ect Sandla 77 78 83 84 85 86 87 88 89 90 91 92 93 94 96 97 99 100 101 104 105 106 107 108 109 110 111 112 113 114 115 117 118 121 122 123 124 125 126 128 129 134 135 Assistant Secrgtary of the Air Forgé R&D Atomic EnergfgCommission Wasjifngton Bureau of Aerdnautics Bureau of Aerqautics GeneraffRepresentative Chicago Operafgons Office g Chicago Patent¥sroup Chief of Naval Besearch # Convair GeneralfDynamigf Corporation Director of Labokatoriesf{WCL ) Director of Requitemengs (AFDRQ) Director of Resedgch ghd Development (AFDRD ANP) Directorate of Sysgenss Management (RDZ ISN) Directorate of Sys®ihs Management (RDZ 1SS) Equipment Laboratfky (WADC) General Electric @dpany (ANPD) Hartford Area Of Headquarters AY Fogke Special Weapons Center Lockland ;""J tficel Los Alamos Sgientific & aboratory Materials La@bratory Pifins Office (WADC) National Ad@ sory Com '“‘33 tee for Aeronautics Cleveland National Ad¥isory Commfgtee for Aeronautics Washington North Ameggican Aviation fnc (Aerophysics Division) Nuclear Revelopment Corgpration Patent BFanch Washingtor Powerj lant Laboratory (W&DC) Prattgfnd Whitney Aircraft Bvision (Fox Project) -_ -'- Corporation 4 Sch¥ol of Aviation Medicine USRF Project RAND University of California Radiatn Laboratory Livermore Wright Air Development Center (§COS! 3) Technical Information Extension Qak Ridge Division of Research and Development AEC ORO CONTENTS Summary Introduction Detailed Power Plant Descriptions — Component Characteristics Circulating Fuel Reactor G E X 61 Turbojet Engine Allison J 71 Turbojet Engine Steady State Power Plant Performance Characteristics — Nuclear Power Only Operation Control Rod Throttling Reactor Fuel Flow Throttling NaK Flow Throttling NaK Bypass Throttling Air Bypass Throttling More Complex Throttling Arrangements Static Stability Characteristics of @ Demand Sensitive Reactor—Turbojet Combination Coupling Between Engines in a Multiengine Installation Nuclear Power Source Control Requirements Manua! Operation at Flight Conditions Where Radiator Capacity Is Excessive Manual Operation at Radiator Design Flight Conditions Manual Operation at Flight Conditions Where Radiator Capacity |s Inadequate Automatic Control Requirements During Operation in the Power Range Appendix A — Radiator Design Procedure Appendix B — Steady State Performance Calculations Appendix C — Static Stability Caleculations 0 b W W N 10 10 11 12 12 15 20 21 21 22 22 23 27 29 36 STEADY STATE CONTROL CHARACTERISTICS OF CHEMICAL NUCLEAR AIRCRAFT POWER PLANTS C B Thompson SUMMARY It seems reasonable to believe that the simplest control system for the nuclear power source In a combination chemical nuclear aircraft power plant wtll result if nuclear power delivery during normal operational use can be throttled by variation of a single control quantity Studies to date of the steady state off design point performance charac teristics of two such power plants indicate that sattsfactory power control can be obtained by by passing NaK around the engine radiators alone f full range NaK bypass valves can be built and if the fuel temperature at the inlet of the reactor core can be allowed to rise as high as the design point mean fuel temperature If the fuel tempera ture at the inlet to the reactor core must be limited to some value less than the design point mean fuel temperature the control rod must also be moved as power delivery 1s varied Possibilities for throttling reactor power delivery by individual variation of reactor fuel flow control rod position NaK flow”and radiator air bypass percentage were also considered but each of these altemate schemes 1s unsatisfactory Study of the static stability charactenistics of a demand sensitive reactor turbojet load combination indicates that such a power plant should operate stably in the high power range erating conditions stability of such a power plant 1s questionable and appears to depend on the throttling scheme used In the example considered here the NaK bypass throttled power plant was stable at low power part load operating points while the air At part load op however the inherent static bypass throttled power plant was not stable The various engine loads are cross coupled through their common reactor power source If the power delivered to one engine 1s varied the power delivered to the other engines also changes When NaK bypass throttling 1s used and the con trol rod position is constant the magnitude of the coupling effect appears to be relatively small |f rod motion with total power level changes 1s re quired however cross coupling between engines will be more pronounced and may be large enough to make tedious the independent manual adjust ment of power delivery to each load Automatic control requirements for the nuclear heat source can be determined by considering how the flight engineer might perform typical power plant maneuvers without the help of automatic con trol equipment Study of the manual operations required indicates that the addition of automatic control equipment for the NaK bypasses 1s very desirable if not essential to limit movement of the valves 1n such a way as to maintain the retum line NaK temperatures between their upper and lower limits at all times Automatic control equip ment i1s also required for the rod 1f the fuel tem perature at the inlet of the reactor core must be held below the design point mean fuel temperature Such equipment might withdraw the rod to main tain the mean fuel temperature at as high a level as possible as limited by the requirements that both the core fuel inlet temperature and the core fuel outlet temperature be less than or equal to thetr maximum allowable values &XW, M . ! x INTRODUCTION Most of the control system thinking by the ORNL ANP grouphas quite naturally been directed toward the problems associated with controlling a circu lating fuel reactor which delivers power to a heat dump type of load This work 1s of major concern since a large part of the ANP effort at ORNL 1s now being devoted to the ART The control system for the ultimate reactor— turbojet engine power plant will obviously be dif ferent from the control system for the ART power plant because both a reactor control system and a properly mated set of chemical turbojet controls will be required The effectiveness of the ART In clearing up problems associated with controlling the large aircraft power plant depends largely on how well the inherent differences between the con trol requirements of the ART and those of large arrcraft power plants are understood The work described in this report was carried out to provide some of the information required for studying these differences The ultimate power plant will consist of one large reactor coupled to a number of turbojet engines (the number ranging from two to six de pending on the type of aircraft being propelled) The overall steady state performance charac teristics of such power plants when manually con trolled at part power off design operating condi tions must be thoroughly understood before con trol system requirements can be determined This report 1s concemed chiefly with the over all steady state manual control characteristics of the following two power plants L oad Powe Souce 60 Mw ART type reactor and chemical burners 60 Mw ART type reactor and chemical burners 2 GE X 61 turbojet engtne 4 Al sonJ 71 t rbojet eng nes These combinations were selected primanly be cause of the availability of performance data 1t1s not believed that they necessarily represent usable systems They are considered here merely as vehicles for studying control problems Detailed charactenistics of each of the com ponents of the above power plants are summarized in the next section Steady state part load per formance characteristics derived from these data are then discussed and the effects of potential throttling parameter variations are described The static stability of a demand sensitive reactor power source-—turbojet engine load combination 1s then considered and coupling effects between engines in a multiengine power plant are invest gated Finally the actions required of the power plant operator In carrying out typical power plant maneuvers without the help of automatic control equipment are outlined to show what types of equipment are needed The symbols employed in the calculations are defined below NOMENCLATURE A,, = frontal rea of rad tor fl'2 IR AHX = hezat ton fe urf ce ae | heat e changer ft AR = heat t nsfer surf e area n radiate ff2 C = spec fc heatof r Bt /Ib °F Cg = spec fc he t of ulat ng fuel Btu/Ib °F Cy = spec fic heat of NaK cool nt Bt /b °F FN = eng ne net thr st output |b g = grav tational constant M = fl ght M ch n mbe N = eng ne otor peed rpm P = powe Mw P = powe del ve ed pe engne b lan ed load % Mw PN = power del vered to Nth eng ne Mw PT = total eactor powe Mw P = total pe sue at nlet of exh t no le T6 2 Ib/ ft P0 = ambient tatic pre ve Ib/ §12 Pl = power delivered to engine No 1 Mw P - = Prandtl numbe of fuel R = gas constant for air ft/°R T = mean reactor fuel temperat e °F FC = fuel temperature at inlet of rea tor core °F T Ty = fuel tempe ature at outlet of e ctor ore °F T NC = NaK temperat re at nlet of heat exchange o F 2 % %*flz v fiw_i-% T‘m NaK tempe ature at outlet of d tor °F TNH = N K tempe atu e at outlet of heat exchanger ( nlet of radiater) °F TT3 = total temperature t omp e sor o tlet °F TT4 = total temperatue at let of turbine °F TT6 = total temper ture at iniet of exhaust nozzle °F Up = over all heat transfe ocefficient of r d ator Bt /hr ft2 OF UHX = over all heat tr nsfer coefficient fuel to NaK heat exchanger Btu/hr f2 OF Va = aft velo 1ty fps 4 =€ng ne ar flow Ib/ sec waD = direct a1 flow r te through adiater pe engine 1b/ se W.gp = bypass o1 flow rote per eng ne Ib/sec WF =re to fuel flow rate b/ sec N = tot | NaK flow rate Ib/ sec Wangp = NaK bypass flow te per eng ne Ib/sec = f Mux = heat exchanger effect veness Np =r diator effectiveness fr = s ostyoff el Ib/ft se By = v scosity of NaK b/ ft se P = average density of a1 In Pr = density of fuel 1b/ fta py = density of NaK b/ 2 = drect N K flow rate th o gh adiate pe ND engine lb/se WNe = NaK flow rate pe engi e b/ e X = fr ct on of tot | re ctor power del ve ed to each engine y = specific heatr toforar APR = adi tor p essure d op Ib/ ft2 AT = log mean tempe ature d ffe ence for the heat m exch nger ATa = air temperature difference (TTA - TTS) ATF = fuel tempe t e dffeence (T, - TFC) ATN = NaK temperature diffe ence (T, - Ty ) adiator b/ f'r3 DETAILED POWER PLANT DESCRIPTIONS — COMPONENT CHARACTERISTICS Detailed performance characteristics of each power plant component must be known before the over all composite behavior of a power plant can be calculated Each of the components of the two power plants under consideration 1s described in this section CIRCULATING FUEL REACTOR An early version of the 60-Mw ART circulating fuel reactor 1s used here as a basis for control studies Design values for several important re actor and heat exchanger quantities and fuel and NaK physical properties used are tabulated below Design power Mw 60 Core fuel outlet temperature °F 1600 Mean core fuel temperature °F 1450 Core fuel inlet temperature °F 1300 Fuel flow rate Ib/sec 702 Temperature coefficient of reactivity -55x 102 (Ak/E)/F Heat exchanger NaK nlet tempe a ture °F Heat exchanger NaK outlet tempera ture °F Total NaK flow rate |b/sec Total heat exchanger heat transfer area ft2 Over all heat transfer coefficient at des gn po nt Btu/hr ft2 °F Fuel Reynolds number n heat ex- changer at design po nt Heatexchanger effect veness at des gn point NaK Reynolds number 1n heat ex changer at design point Detailed heat exchanger parameters Bundles Tubes per bundle Diameter of tubes 1n Spacing between tubes mils Tube length ft 1100 1500 569 1388 1023 3180 08 125 000 24 132 30 6 67 Equivalent diameter (fuel) 1n 0 1328 per bundle Free flow area (fuel) In 2 per 3852 bundle Fuel and NaK physical properties (from ART design meeting Jan 7 1955) Cp Btu/Ib°F 0 27 CN Btu/ib °F 025 fp (at 1450°F) Ib/ft sec 379 x 103 gy Ib/ft sec 011x 10-3 Pry (at 1450°F) 2 475 Y 200 Py Ib/ft> 46 The heat exchanger design described above was obtained from M M Yarosh This design was prepared some time before detailed heat transfer tests were run and before final heat exchanger designs were completed Heat transfer coefficient estimates fuel property estimates and the design power rating have all been changed since the design described in the above table was made Hence the heat exchanger used here 1s not the same as the heat exchanger currently planned for the ART However the external performance char actenistics of the design considered here and the current design do not appear to be different enough to change any of the general conclusions drawn from this work The variation of the over all heat transfer coef ficient of the reactor heat exchanger with changes in fuel flow rate NaK flow rate and mean reactor fuel temperature must be known if the part load steady state performance characternistics of the power plant are to be calculated The vanation of this coefficient with changes in fuel flow rate has been estimated for a mean reactor fuel temperature of 1450°F and a midrange NaK flow rate (320 Ib/sec) by use of a procedure suggested by Yarosh The result 1s plotted in Fig 1 Average temperature changes and NaK flow rate changes also affect the over all heat transfer coefficient but these effects are thought to be relatively small for NaK flow rate and average temperature varia tions 1n the normal safe operating range 15 D Goodlette et al Second Summary Report — Nuclear Powered Seaplane Feasibility Study ER 6621 (Oct 27 1954) w 1200 1100 1000 w o o 800 700 600 500 400 300 200 100 o 0 100 200 300 400 500 600 700 800 REACTOR FUEL FLOW W (ib/ ) OVERALL HEAT TRANSFER COEFFICIENT Uy (Bt /h it Fig 1 Variation of the Over All Heat Transfer Coefficient of the Main Heat Exchanger with Reactor Fuel Flow 320 Ib/sec 1450°F NaK flow Mean temperature G EX 61 TURBOJET ENGINE The G E X 61 turbojet engine 1s described briefly below ! Static thrust output per engine at sea level 23 600 (SL) maximum nterburning b Static thrust output per eng ne at sea level 33000 maxtmum interburning and afterburning Ib Static thrust output per eng ne at sea level 6 780 w th 30 Mw power 1nput |b Max mum allowable powe nput pe eng ne 103 5 SL tatc mitay Mw Max mum turb ne nlet temperatu e °F 1800 Rated a rflow per engine SL static |b/sec 325 Design pressure ratio 8 451 Part load engine performance data that describe the variation of the turbojet load imposed on the reactor at off design operating conditions are re quired for over all power plant steady state per formance determination The curves of Figs 2 through 5 show how pertinent off design steady state X-61 engine parameters vary with net thrust output at various altitudes and flight speeds for power inputs less than 30 Mw These curves were calculated from the corrected quantity data of Goodlette ! Net thrust output and required power input were calculated from (n P=W,Co(Tyy—Tyy) RS Bh OW 3 & 55 50 15000 ft MACH 0 92— SL MACH 0 3 A 45 — / = a0 / /’ - / / ,,’ 5 35 g ] L = / - -7 = //,/ W30 gy o z g /%’/,/ /< o 25 P ’.If// / E // _” - L~ \ 3 15000 {1 MACH O 45— ,7—:/ ~SL STATIC - pr & 20 el \/”:// - - 15 ] — //<\ —35 000 ft MACH O 92 - "K [ 10 Pt [ ~ 35 000 ft MACH O 75 5 ) 0 1 2 3 4 5 6 7 8 9 NET THRUST OUTPUT £ (lb 10) Fig 2 Variation of Steady State Power Input Required with Net Thrust Output for the G E X 61 Engimne Exhaust nozzle open © ol 1800 ORN L D 69 1700 1600 1500 S 35 000 ft MACH 0O 75\7/ 1400 e //4\35 000 f1 MACH 032 1300 / | // 15 Q00 ft MACH 0 92 P 1200 / % sL Mw—/ 1100 o~ // // S b | < SL STATIC 300 / // // 800 A X /,/ 15 000 ft MACH O 45 700 / 0 { 2 3 4 NET THRUST QUTPUT £, (Ib X 10%) N \ 1000 STEADY STATE TURBINE INLET TEMPERATURE ( F) 600 o o ~ ®© Qo Fig 3 Vanation of the Steady-State Turbine Inlet Temperature with Net Thrust Output for the G E X 61 Engine Exhaust nozzle open » R o — 300 260 ] ) 220 ] 0 oo ¥ wals o — 5 0 03 / / ¢ a5 180 S et ° 2" 00 140 — ‘/ 092// L # Mho 25 0005 facn © 100 000t /y ENGINE AIR FLOW ' [(Ib/ \ ; o 60 0 1 2 3 4 NET THRUST QUTPUT F~ {lb 10} wn [¢] =~ o 0 Fig 4 Vanahon of the Steady State Engine Air Flow with Net Thrust Output for the G E X 61 Engine Exhaust nozzle open . - 850 o WG9 2 800 750 TC0 650 SL MACH 03\ 600 15 000 ft MACH O 92\ 550 35000 ft MACH 0 92\ )/ __j’ COMPRESSOR OUTLET TEMPERATURE ( F) 500 e ] | e 450 A// =1 35000 ft MACH O 75 / | 400 \ - — SL STATIC 350 /// N | / \45 000 ft MACH O 45 300 — 250 0 1 2 3 4 5 6 7 8 9 NET THRUST OUTPUT (Ib 103) Fig 5 VYanation of the Steady State Compressor Qutlet Temperature with Net Thrust Output for the G-E X 61 Engine Exhaust nozzle open 6 The value for C, was assumed to be constant at 0 26 E5RR No zle coe'?f‘s; ent Gross thrust for full nozzle expansion Ram drag K—Jfi r N A N 5 1 (2) FN = 0975 Wa\/TTé 2}/R/g()/—]) 1 -(—P——/—I;-)-m W Va/g T ° 0 The value for y was assumed to be constant at 135 A hypothetical radiator was designed for the X 61 engine by use of the procedure and basic data outlined in Appendix A which were obtained from R D Schultheiss This radiator was de- signed to transfer 30 Mw of nuclear power to the engine load imposed during cruise at 35000 ft Comparison of the total thrust available from two X 61 engines operating at 30 Mw power input at 35000 ft with the total thrust required by a repre sentative seaplane airframe shows that such an aircraft might be expected to cruise at about Mach 0 87 o TABLE 1 Flight conditions Radiator and X 61 engine match point and de sign data are shown in Table 1 The varniation of the over all heat transfer coefficient of this radia tor with changes in airflow per unit frontal area s shown in Fig 6 The over all heat transfer coef ficient also varies with changes in the NaK flow rate and the mean temperature of the radiater but these effects are thought to be small in the normal operating region The engine performance curves discussed pre viously (Figs 2 through 5) were worked out for a normal combustion chamber pressure loss between RADIATOR AND ENGINE MATCH POINT VALUES 35000 ft Mach 0 87 nuclear power only G E X-61 Engine Allison J 71 Eng ne Net thrust output [b per engine Number of engines Nuclear power 1nput required Mw per engine NaK temperatures °F NaK flow ate b/ ec pe eng ne Compressor outlet temperature °F Eng ne a flow lb/ ec Turbine inlet temperature °F Engine speed ¥ of rated Exhaust noz le area Radiator heattransfer area ft2 Over all heat transfer coefficient Btu/hr ft2 °F Radiator frontal area 12 Radiator depth In Rough estimate of radiator pressure drop 7 of compressor discharge pressure 5500 2750 2 4 30 15 1500 to 1100 1500 to 1100 2845 142 2 487 454 132 4 657 1311 1286 926 932 Open 87 77 closed 9018 4883 315 26 8 16 12 19 4 14 66 18 the compressor and turbine Strictly speaking the increase in pressure loss resulting from the add: tion of a radiator causes all the equilibnum operat ing charactenstics of the engine (Figs 2 through 5) to shift Recalculation of the new steady state operating characteristics 1s a major job however which requires engine component performance maps which are not available The effects of radigtor pressure drop on steady state engine performance are therefore neglected in the calculations that follow This should not cause serious errors 1n final conclusions because the radiator pressure drop in this case appears to be relatively small The overall trends being sought should still manifest themselves ALLISON J 71 TURBOJET ENGINE OVERALL HEAT TRANSFER COEFFICIENT ¢, (Bt /h f12 F} 4 6 10 12 14 16 18 20 22 24 26 ° 2 ° » The J 71 power plant was considered in addition AIRFLOW PER SQUARE FCOT FRONTAL AREA W /A'M.,[(lb/ }/ft ] to the X 61 power plant described in the preced ing section because the available X 61 perform Fig 6 Vanation of the Over All Heat Transfer ance data are not conststent in the low power Coefficient of Radiator with Changes in Air Flow operating region the compressor power required per Unit Frontal Area does not agree with the turbine power available at ¢ 1300 1200 TURBINE INLET 7 / \ Mp 100 \% // 1000 \\ L~ 900 / B . p\R‘:\"o\N 28 — ~ 800 e 140 24 — 2 700 - 120 7 < L~ — > ~ . £ / / ; 220 |— 600 100 o = / - = w L o / / z 216 — 500 e 80 § o P = RE & pOWER /1 TEMPERMU & 5 porarte /SSOP‘ OUTLE « 212 [~ 400 &" COMPRE 60 « - g ';’ 8 M— 300 fw—— s 40 w Q / a 4 — 200 20 ot 100 0 3000 3500 4000 4500 5000 5500 6000 6500 ENGINE SPEED ( pm} Fig 7 Steady State Performance Characteristics of the Allison J 71 Turbojet Engine ot Sea Level (SL) Static conditions exhaust nozzle open equiltbrium points Preliminary estimated per formance data on an early version of the Allison J 71 engine were used so that reactor turbojet behavior in the low power operating range could be studied The J71 engine 1s roughly half the size of the X-61 engine Its full power SL static pressure ratio 1s about 8 5 to 1 Pertinent performance characternistics of th:s engine at SL static conditions are plotted in Fig 7 Radiator and engine match point values and design data are summarized in Table 1 The basic procedure and data used in designing this radiator are outlined in Appendix A The variation of the over all heat transfer coefficient of the J 71 engine radiator with changes in airflow per unit frontal area 1s shown in Fig 6 STEADY STATE POWER PLANT PERFORMANCE CHARACTERISTICS - NUCLEAR POWER ONLY OPERATION The steady state performance characteristics of the two power plants under consideration during operation on nuclear power only can be calculated by combining the component charactenstics sum marized in the preceding secton Figure 8 1s a schematic didgram showing the parts of the power plants under consideration and the nomenclature used Of particular interest 1s the behavior of such power plants when throttling in each of the five ways listed below 1s attempted Contral Rod Throttling Variable Constont at rated values Mean reactor fuel temperature Reactor fuel flow and NakK flows Air ond NoK bypasses Closed Reactar Fuel Flow Throtthing Vartable Constant at rated values Reactor fuel flow Mean reactor fuel temperature and NaK flow rates A r and NaK bypa se Clo ed NaK Flow Th ottling VYariable Constant at rated values NaK flow rates Mean reactor fuel temperature and reactor fuel flow rote Aw and NaK bypasses Closed NaK Bypass Throtthing Yariable Constont at rated values NaK bypass percentage Mean reactor fuel temperature reactor fuel flow rate and NoK flow rates Air bypasses Closed Ar Bypass Throttling Variable Constant at rated values Air bypass percentage Mean reactor fuel temperature reactor fuel flow rate and NaK flow rates NaK bypasses Closed The behavior of the hypothetical reactor-X 61 power plant when throttled in each of these ways 1s described in the following paragraphs CONTROL ROD THROTTLING The behavior of the reactor-X 61 power plant when throttling by control rod motion 1s attempted at a typtcal off design flight condition 1s shown in Fig 9 A sample calculation illustrating the procedure used to determine these curves is In cluded in Appendix B At this flight condition the radiators have more heat transfer surface area than 1s required for transferring 30 Mw to each engine |f the power transferred to each engine s to be limited to the maximum allowable value of 30 Mw one or more of the potential control quanti ties generally must be reduced with decreasing altitude Figure 9 shows that the mean reactor fuel tem perature must be reduced to about 1260°F 1f power delivery 1s to be limited to 30 Mw during flight at 15000 ft and Mach 0 45 Under these cond: tions the reactor NaK inlet temperature drops to about 900°F Operation of the system at such a low NaK temperature at the inlet of the main heat exchanger 1s unsafe because of the possibility of focal cold spot formation and fuel freezing The situation becomes more unsafe 1f an attempt s Myy HEAT EXCHANGER EFFECTIVENESS mi\l K PUMP Tre COLD FUEL TEMPERATURE | we COLD N K TEMPERATURE P POWER DELIVERED TO OTHER ENGINE _—m A TOTAL 7 pot FUEL Tuw HOT N K POWER TEMPERATURE TEMPERATURE o Wye TOTAL N K FLOW un K BYPASS VALVE RATE PER ENGINE TF AVERAGE FUEL TEMPERATURE = T, RADIATOR EFFECTIVENESS 4, N K BYPASS g FLOW RATE P POWER DELIVERED TO FIRST ENGINE o DwG 9 S T COMPRESSOR DISCHARGE TEMPERATURE AIR BYPASS VALVE Wyp DIRECT N K FLOW RATE THROUGH RADIATOR w AIR FLOW RATE " THROUGH BYPASS W AIR FLOW THROUGH RADIATOR (N W TOTAL AIR FLOW RATE 7 TURBINE INLET TEMPERATURE Fig 8 Partial Schematic Diagram of Reactor Turbojet Power Plant made to reduce power delivery to each engine be low 30 Mw When the rod i1s inserted far enough to throttle power delivery to only 25 Mw for ex ample the core fuel inlet temperatire 1tself drops to below 1000°F From the curves of Fig 9 it 1s apparent that the thrust output of the power plant cannot be throttled safely by moving only the reactor control rod Control rod throttling 1s also unsuitable f independent variations in power delivery to each of the engines are to be made since motion of the control rod affects all engines in the same way REACTOR FUEL FLOW THROTTLING The behavior of the power plant when 1t is throttled by reactor fuel flow variation with all other quantities at their design point values s shown 1in Fig 10 At the 15000 ft Mach 0 45 flight condition reactor fuel flow must be reduced to roughly 60% of its rated value to himit power delivery to each engine to 30 Mw When this is done the fuel temperature at the outlet of the 10 reactor rises to 1700°F and the NaK temperature at the inlet of the reactor falls to 900°F Operation at these temperatures 1s unsafe if not impossible Further reduction in fuel flow does reduce the power delivered to each engine and reduces the engine thrust outputs but as the fuel flow 1s reduced the fuel outlet temperature continues to rise and the fuel and NaK inlet temperatures con tinue to fall Thus reactor fuel flow alone 1s very unsuitable as a primary power control parameter Virtually all the critical steady state temperature variations which result when such a scheme s used are unsafe and independent adjustment of power delivery to each load 1s not possible NaK FLOW THROTTLING The behavior of the power plant when it is throttled by NaK flow variation alone 1s shown in Fig 11 The NaK flow must be reduced to 42% of its rated value to limit power delivery to each engine to 30 Mw at the 15 000 ft Mach 0 45 flight ON DWG 8 © 1500 ~ R = 3 X 1400 ; W P PER ENGINE /7 2 0l / W 20 1300 /, , 6000 o / ul g / ) A / W FH 74 Yool 1200 A4 5000 5 @ v & / Z ol noo - 4000 o / a2 1000 / TEMPERATURE ( F) 900 800 / 1000 700 600 800 200 1000 1100 1200 {300 AVERAGE FUEL TEMPERATURE 7. ( F} Fig 9 Steady State Performance of Reactor and Two G E X 61 Engines Altitude 15000 ft Mach 0 45 reactor power delivery throttled by moving the control rod condition Such a NaK flow reduction with all other quantities at thewr rated values causes the NaK temperature at the inlet of the reactor to drop to around 640°F which is far below the 1050°F safe lower limit Further reduction in NaK flow does reduce power delivery but 1t causes the return line NaK temperature to drop still lower Thus NaK flow alone 1s not a suitable power control quantity because the NaK temperature at the inlet of the reactor drops rapidly to dangerously low values as the flow rate 1s reduced Some means of protection against return line NaK under cooling must be added if power delivery 1s to be throttled safely by NaK flow rate reduction NaK BYPASS THROTTLING When the reactor—X 61 power plant 1s throttled by bypassing NaK around the radiators the thrust output of each engine and the reactor power de livered to each engine vary as shown in Figs 12 through 14 Fuel and NaK temperatures vary with power delivery as shown in Fig 15 O L R DWG9 7000 6000 |7 o ~ & 1600 5000 £ PER ENGINE 4000 n o T TEMPERATURE o B O o 3 8 8 o 3000 NET THRUST £, (ib} o [ 2000 POWER DELIVERED PER ENGINE 72 (M ) 1000 0 0 10 20 30 40 50 80 70 80 90 100 FUEL FLOW (¥ OF RATED) Fig 10 Steady State Performance of Reactor and Two GE X 61 Engines Altitude 15000 ft Mach 0 45 reactor power delivery throttled by varying the reactor fuel flow L] o G 1800 7000 TH 1600 - 6000 -t NH /fif 1400 5000 Jd/ 7 —_ I —_ = - / o =30 200 4000 = Q L W w g /(PER ENGINE e | g ’ z w20 & ooo 3000 £ o = z a p = [a] z w o & o 80C 2000 5 w o o ) e z 0 600 A 1000 & / we /| 400 0 0 20 40 60 80 100 N K FLOW (¥ OF RATED) Fig 11 Steady State Performance of Reactor and Two G E X 61 Engines Altitude 15000 ft Mach 0 45 reactor power delivery throttled by varying the NaK pump speeds 11 ORNLM 9149 N K FLOWING THROUGH BYPASS (7)) 100 90 80 70 60 50 40 30 20 10 0 SL STATIC 6 T 15 000 ft MA(|3H 045 ] SL' MACH 03 L—— ’.-—-—_______— A L= ’ / LT _z 35000 ft MACH 075 /! 7 / NET THRUST £, (Ib X 103) O 2 FH //L\as 000 ft MACH 092 ! 0 o 10 20 30 40 50 60 70 80 90 100 N K FLOWING THROUGH RADIATOR (¥ OF RATED) Fig 12 Net Thrust Output per Engine at Various Flight Conditions for Reactor and Two G E X 61 Engines Reactor power delivery throttled with radiator NaK bypasses Adequate throttling can be obtained through the use of NaK bypass valves alone if the fuel tem perature at the inlet of the reactor core can be allowed to rise as high as the design point mean fuel temperature Power delivery and thrust out put are relatively insensitive to changes in the NaK bypass percentage in the 50 to 0% bypass range Hence full range NaK bypass valves are required If power delivery 1s to be throttled in this manner AIR BYPASS THROTTLING The behavior of the hypothetical reactor-X 61 engine power plant when 1t s throttled by by 12 P L ORNL LR DWG 9150 15 000 fi MACH 0O 82 £ {5 00 ft MACH © 45 SL MACH 03\ {/ 35 000t MACH O 92 7 100 / / — ’ SL STATICL. //<~35 000ft MACH 075 80 J 7 70 Cy Wl ~ T THRUST OUTPUT (¥ OF MAXIMUM) 100 8O 60 40 20 0 N K FLOWING THROUGH BYPASS (/) Fig 13 Per Cent of Maximum Thrust Output At tainable with Nuclear Power Only vs Per Cent NoK Bypassed Around Radiator Reactor and two G E X 61 engines passing air around the engine radiators 1s shown in Figs 16through 18 Fuel and NaK temperatures vary with power delivery as shown in Fig 15 These curves show that power plant thrust out put can also be throttled safely through the use of air bypasses alone 1f the fuel temperature at the inlet of the core can be allowed to rise as high as the design point mean fuel temperature MORE COMPLEX THROTTLING ARRANGEMENTS It seems reasonable to believe that the simplest over all power plant control system will result when nuclear power delivery 1s throttled by varia tion of the fewest possible control quantities The steady state performance characteristics dis cussed In the preceding paragraphs indicate that power plant thrust output modulation through varia tion of a single control quantity — NaK bypass percentage or air byposs percentage — appears to be possible if the fuel temperature at the inlet of the reactor core can be allowed to rise as high as the design point mean fuel temperature o— N K FLLOWING THROUGH BYPASS (/) 6oqoo 90 B8O TO 60 S50 40 30 20 40 0O | 160 90 80 o & 50 6 = 40 —_ SL STaTIC Q "2 5 ¥ SL STATIC AND 35000 f1 MACH 092 o 5 MACH 03 | \\ = & 30 —— ’ — = & o 15000 ft // e T T - 15000 ft MACH 045 —L__ | Lt - = & MACH 0 92 —1 = a 4 o //;‘- /y( 35000 ft MACH 0 75 5 o / o Y 20 — = id 0 SL MACH 03 ~ o 74 2 o 15000 ft MACH 045 T3 o — 3 L | 10 Z & / / / 2 0 { 0O 10 20 30 40 50 60 70 8O 90 100 0O {0 20 30 40 N K FLOWING THROUGH RADIATCR (/) Fig 14 Variation of Reactor Power Delivered to Each Engine with Per Cent NaK Bypassed Around Radiator Reactor and two G E X 61 engines 1700 600 1500 1400 TEMPERATURE ( F) 1300 1200 1100 o ORNL LR DWG 9153 AIR FLOWING THROUGH BYPASS (7)) 70 60 50 40 30 20 10 ¢ \7 L, 092 | 15 000 ft MACH // 35 000 ft MACH 092 "~ 35 000 £t MACH O 75 50 60 70 80 AIR FLOWING THROUGH RADIATOR (7 ) POWER DELIVERED PER ENGINE £ (Mw) T 0 52 TEMPF—EE-‘.U/RE/—“/ TLET 7 FUE v -] / [ e 7N K OUTLET TEMPERATURE __ NH //_ :"--.._.___-- s \\ “-—__..______/:E REACTOR ,'NLET TEM \ PER“TURE --._____- \ - N \fr , v \Er » é‘.g,pe \’P“TU \’?E ‘-\ 4 g 12 16 20 24 28 32 90 Fig 16 Net Thrust Output per Engine power delivery throttled with air bypasses and two G E X 61 engines 100 Reactor Reactor Fig 15 Variations of Reactor Fuel and NaK Temperatures with Power Delivery per Engine Reactor and two G E X 61 engines throttied by NaK bypass or by air bypass 13 7 - ORNL LR DWG 9154 100 1 7 / SL MACH O 3———__| / / / 90 I I =z / SL STATIC——“/.é/ / /// 80 | | / / 3 15 000 ft / / 2 MACH O 92— / 2 70 # / = ' / / = A o 60 o 15 000 ft x~ MACH O 45— — // D Q. 5 40 /- o 35000 ft MACH O 92 ";,,) 30 / | | 1 | 2 Y | T ] & ~—~—35 000 ft MACH O 75 F 20 10 o 100 20 B8C 70 60 50 40 30 20 10 0 AIR FLOWING THROUGH BYPASS (7) Fig 17 Per Cent of Maximum Thrust Output At tainable with Nuclear Power Only vs Per Cent Air Bypassed Reactor and two G-E X 61 engines If the fuel tempesature at the inlet of the core mustbe limited to some value less than the design point mean fuel temperature the control rod must also be moved as power delivery 1s changed If the fuel temperature at the inlet of the reactor core is to be held at 1350°F or less in the reactor—X 61 power plant for example rod insertion is required when total power delivery 1s reduced to below 40 Mw As the development of the full scale aircraft power plant progresses 1t ts likely that many 14 ORNL LR DWG 9155 AIR FLOWING THROUGH BYPASS (7)) 100 90 80 70 60 50 40 30 20 10 o 50 15000 ft MACH O 45 l 15000 ft MACH 0 92 40 SL MACH 0 3 30 B r e it / SL STATIC —] / 20 / NN AN NN\ POWER DELIVERED PER ENGINE £ {Mw) \35 000 ft MACH O 92 35 000 ft MACH O 75 O 0 10 20 30 40 50 60 70 80 90 100 AIR FLOWING THROUGH RADIATOR (7 ) Fig 18 Vanation of Reactor Power Delivered to Each Engine with Per Cent Air Bypassed Reactor and two G E X 61 engines situations will arise in power plant design or operation which will make the use of more complex throttiing arrangements seem desirable Diffi culties 1n building full range NaK bypass valves for example may make the use of a more compl cated throttling arrangement imperative However the effect of increasing the complexity of the control system on the reliability of the over all power plant should be considered carefully before such changes are made o STATIC STABILITY CHARACTERISTICS OF A DEMAND SENSITIVE REACTOR-TURBOJET COMBINATION Stable operation of a reactor—turbojet engine combination 1s not assured by a large negative reactor temperature coefficient of reactivity Such a characteristic does undoubtedly simplify the con trol of the reactor but the demand characteristic of a turbojet load and the demand sensitivity char acteristic of a reactor having a large negative temperature coefficient of reactivity are not neces sarily compatible The turbojet load imposed on the nuclear heat source (airflow and radiator inlet temperature) varies 1n a complicated way with the power de livered to 1t Changes in power delivery to such a load cause the load characteristics themselves to change Changes in load charac teristics however can cause further changes in reactor power delivery because the large negative temperature coefficient of reactivity makes the reactor load sensitive |f it 1s possible for a sub sequent change in power delivery to reinforce an original power disturbance the reactor load com bination can walk or run away The possi bility for an instability of this type does not exist when the reactor 1s coupled to a heat dump type of load because the load characteristics are externally adjusted by blower speed and louver and bypass opening variation Changes in these external load adjustments do cause the reactor power level to change but changes in the reactor power level cannot in turn cause further changes in the load This 1s an important basic difference between the two load types The static stability of a demand sensitive reactor power source and a turbojet load can be studied from plots showing how the steady state power available from the radiator and the steady state power required to run the engine vary with engine speed when the reactor throttling quantities are constant Such plots obviously do not provide a complete picture of the stability of the over all 1 power plant but it does seem that an unstable intersection between a steady state nuclear power available curve and the steady state engine power required curve 1s a definite indication of trouble Steady state power required and power available curves for the reactor—J 71 system at SL static operating conditions are shown in Figs 19 and 20 for air and NaK bypass throttling (sample cal culations are included in Appendix C) All the potential reactor control quantities with the ex ception of the bypasses are constant at their rated values The awr and NaK bypasses are con stant along given power available curves at the values shown The intersections between the curves of power available at a constant air bypass setting and engine power requited are unstable i1n the low speed range The steady state power avatlable rises faster than the power required as the engine speed increases (air flow and compressor discharge temperature increase) Idle speed for the J 71 engine 1s around 3000 rem Net thrust output at this speed i1s down to about 3% of the rated SL static value Stable operation at speeds corresponding to less than maximum nuclear power input (5050 rpm 23% of rated SL static net thrust output) does not appear to be possible when the reactor—J 71 power plant 1s throttled by bypassing air around the radiators This apparent difficulty is a serious disadvantage of the air bypass throttling arrangement When the power plant 1s throttled with NaK bypasses the nuclear power available curves intersect the engine power required curve stably in the low speed region The power plant behaves differently in each case because of basic differences in the effect of each throttling quantity on radiator performance The power available from the reactor supplying a number of balanced loads s related to the various engine radiator and reactor parameter values by the following expression e_ W pCang + (1 = ny3)/myxWyC (Tg =~ Tr3) NeCN = 1/2XWCp v 15 ORNL LR DWG 9247 26 // /| 24 /'l / 0/ NKBYPA 22 //—_ 7 —{._. > / POWER AVAILABLE / 20 T ——— POWER REQUIRED // / . 18 > // 2 7/ 3 / £ w 16 e ——— 50/ N K BYPASS | O 7 = L w A - 14 - //, 60 / N K BYPASS — E:_, " » / ",/ - z /// - - / .—” © 7/ === -—:’————-—_'— /" 75 / NaK BYPASS - 8 6 4 2 3000 3500 4000 4500 5000 5500 6000 6500 ENGINE SPEED { pm) Fig 19 Steady State Power Delivered with NaK Bypass Percentage Constant Steady State Engine Power Required vs Engine Rotor Speed Reactor and four Allison J 71 engines at SL static conditions exhaust nozzle open fuel and NaK pump speeds constant at rated values When the fuel and NaK flows are constant at their rated values the last two denominator terms are small and tend to cancel The power delivered to each load then is approximately Destabil z ng Stab | ing term term — (4) Pe = WaDnR (TFuv - TTB) Ca The second term in the equation describes the stabilizing effect of the increase in compressor outlet temperature which results when engine speed Increases This effect alone would cause the power delivered at a constant mean reactor tem perature to decrease |f power delivery to an engine decreases with an increase in engine speed static stability at least will be assured because the power required increases with increasing speed 16 The first term 1n the power delivery expression describes the destabilizing effect of the increase i air flow which results when engine speed in If the NaK flow rate i1s constant the effectiveness of the radiator (p,) decreases as air flow increases but not so rapidly Hence the product (WaDqR) increases with increasing air flow This product for the hypothetical J 71 radi ator 1s plotted vs air flow for several constant NaK flow rates in Fig 21 creases The raptd increase in engine air flow with speed at low speeds causes W_.png to increase faster than (Tg,, - T.,) decreases Hence the power delivery curves rise with increasing speed at low speeds At higher speeds however the effect of the increase in radiator inlet temperature pre dominates (as the compressor outlet temperature moves closer to the mean fuel temperature) and 0% AR BYPASS 309 AIRBYPASS 45% AR BYPASS 60 AIR BYPASS POWER PER ENGINE (Mw) POWER AvalLABLE ———— POWER REQUIRED 3000 3500 4000 4500 5000 5500 6000 6500 ENGINE SPEED ( pm} Fig 20 Steady State Power Delivered with Air Bypass Percentage Constant Steady State Engine Power Required vs Engine Rotor Speed Reactor and four Allison J 71 engines at SL static conditions exhaust nozzle open fuel and NaK pump speeds constant at rated values ORNL—-LR DWG 9219 110 100 30 {00 97 NoK FLOW DIRECT O NaK BYPASS BO / // 70 —— 50 9% N K FLOW DIRECT 507 N K BYPASS T L LT \ A RADIATOR PERFORMANCE PARAMETER W, 7, s R 50 /’//_; — | 407 N K FLOW DIRECT _— 607 N K BYPASS ’ = 20 ///‘_ 25 7 NoK FLOW DIRECT 7 759 NoK BYPASS 20 10 0 0 10 20 30 40 50 60 7O 80 90 100 HO 120 430 140 450 160 170 RADIATOR AIRFLOW u;,a {(ib/ ) Fig 21 Radiator Performance Parameter for the Allison J 71 Engine 17 the W png product rises less rapidly These effects cause power delivery to reach a peak and begin to fall in the high speed range The increase in radiator inlet temperature with increasing speed thus causes the steady state power curves to inter sect stably in both cases at high engine speeds in spite of the destabilizing effect of increasing air flow with speed The relative flatness of the curves showing the variation of the power available with the NaK by pass percentage constant at low speeds can be explained from the W_,5. plot in Fig 19 and from Eq 4 the power delivered equation The differences in the performance characteristics of the air bypass and NaK bypass throttling arrange ments lie in the behavior of the W _,n. product as engine arr flow changes since the (T | - Trs) term varies with speed in the same way in both cases The power delivery curves rise most W, p curves are flattest of an engine air flow change on reactor power de livery 1s minimized when the variation of W, pn with changes in air flow 1s minimized slowly with increasing speed when the W.plg Vs The destabilizing effect R A study of Fig 19 leads to the conclusion that W, png varies least with changes in air flow when the air flow through the radiator 1s high and when the percentage of NaK flowing through the bypass 1s large Both these requirements are met best at part load points by the NaK bypass throttling arrangement The behavior of the NaK bypass throttled power plant at 35000 ft and Mach 087 1s shown in Fig 22 The very large amount of NaK bypassing required to throttle the engines at this flight con dition causes the nuclear power delivery curves ORNL LR DWG 9220 POWER DELIVERED —=——-— POWER REQUIRED 80 / N K BYPASS \‘_ - 1 POWER PER ENGINE (Mw) o 90 / N K BYPASS - 95 /o N K BYPASS 3000 3500 4000 4500 5000 ENGINE SPEED { pm) 5500 6000 6500 Fig 22, Steady-State Power Delivered with NaK Bypass Percentage Constant Steady State Engme Power Required vs Engine Rotor Speed Reactor and four Allison J 71 engines at 35000 ft Mach O 87 exhaust nozzle open fuel and NaK pump speeds constant at rated values 18 to be quite flat This bears out the conclusion drawn in the preceding paragraph heavy flow of NaK through the bypass results in flat power delivery curves All the nuclear power delivery variations con sidered so far have been worked out for constant fuel and NaK pump speeds [t might be desirable in the interests of simplicity to drive these pumps at engine speed This aggravates the static stability problem however since increasing the pump speeds with engine speed causes power delivery to rise faster with increasing engine speed than when the pump speeds are constant The behavior of the NaK bypass throttled power plant at SL static conditions when various com binations of pumps are engine driven 1s shown in Fig 23 (Pump flow rates were assumed to be proportional to pump speed ) Driving one or more pumps at speeds proportional to engine speed destroys most of the apparent natural static sta bility of the NaK bypass throttled power plant Thus from steady state considerations 1t seems that a turbojet—demand sensitive reactor combina tion should operate stably in the high power range At part load operating conditions however the stability of such a power plant appears to depend L ORNL LR DWG 9224 26 24 22 POWER AVAILABLE 20 POWER REQUIRED 18 12 POWER PER ENGINE {(Mw) o L % \ o /Q 6000 a"‘ == g 6 4 2 3000 3500 4000 4500 5000 5500 ENGINE SPEED (rpm) Fig 23 Steady State Power Delivered with 60% NaK Bypassed Steady State Engine Power Required vs Engine Rotor Speed (1) Pump speeds constant at rated values (2) NaK pump speeds constant fuel pumps engine-driven (3) fuel pump speeds constant NaK pumps engine driven (4) fuel and NaK pumps engine driven 19 on the throttling scheme used Relatively speaking use of a NaK bypass throttling arrangement seems from steady state considerations at least to result in more stable power plant operation than does use of an air bypass throttling arrangement In the example considered the NaK bypass throttled power plant was stable at normal part load operating points when the fuel and NaK pump speeds were constant while the air bypass throttled power plant was not Whether or not a NaK bypass throttled system will be stable in other power plant combinations 1s difficult to say A detailed check in each particular situation will no doubt be re quired If the *hucl®ar power source~turbojet engine load combination 1s not inherently stable or If the natural stability 1s not adequate the stability characteristics can be improved by adding the proper control equipment Static power plant stability in the cases considered here for example would be achieved if some sort of power level control system were added to the nuclear heat source to maintain nuclear power delivery to each engine constant at some preset adjustable value The power available from the reactor would then be independent of changes In engine speed or air flow and compressor outlet temperatures and the power available vs speed curves would be horizontal lines COUPLING BETWEEN ENGINES IN A MULTIENGINE INSTALLATION All the steady state performance characteristics considered so far have been worked out for balanced load operation where power delivery to each engine 15 the same |t 1s also interesting to consider the effects of coupling between engines when the power distribution to the various engines i1s not symmetrical assuming for the moment that the reactor design and load connection arrangement will allow unbalanced operation The various engine loads are not completely independent They are cross coupled through their common power source |f the power delivered to one engine s varied through manipulation of the NaK bypass of that engine the power delivered to the other engines also changes Power delivery to the other engines changes because variation in power de livery to one load causes the reactor outlet tem perature to change The power delivered to any given engine load 1s related to the reactor outlet temperature by (5) Py = (Tpy = Tra) x 1 IV pCang + (1 = Mx)/ M x¥neCn 092 The results which are plotted in Fig 24 show how the per cent of full nuclear power de livered to an engine load with a constant NaK by pass setting varies with power delivery to a second engine load In the event of complete failure of the second engine the power delivered OR L DWG 110 100 35 Q00 ft [0 80 70 60 50 40 30 POWER DELIVERED TO ENGINE NO { {¥ OF RATED) 20 0 10 20 30 40 50 60 7O BO 90 400 410 POWER DELIVERED TO ENGINE NO 2 (¥ OF RATED) Fig 24 Steady State Coupling Between Engines Reactor and two G E X 61 engines altitude 35 000 ft Mach 0 92 No 1 engine NaK bypass constant at 9 5% No 2 engine NoK bypass varied from 9 5 to 100% The magnitude of the cross coupling effect when the control rod posttion 1s constant has been de termined for the NaK bypass throttled reactor-X 61 engine power plant operating at 35 000 ft at Mach 20 to the first engine drops to 93% of its rated value If this lost power is to be regained the bypass on the first engine must be readjusted if possible or the control rod must be withdrawn slightly Cross coupling between engines can be eliminated by the addition of automatic control equipment When the control rod position 1s constant and NaK bypass throttling 1s used however the magnitude of the coupling effect does not appear to be great enough to justify much complication of the control system for i1ts elimination If rod motion with total power level changes 1s required cross coupling between engines will be more pronounced than in the example considered here and the coupling effects between engines may be so large that independent manual power delivery adjustments to each load will be tedious NUCLEAR POWER SOURCE CONTROL REQUIREMENTS Automatic control requirements for the nuclear heat source In a combination chemical nuclear aircraft power plant of the type discussed in the preceding sections can be determined by con sidering how the flight engineer might perform typical power plant maneuvers without the help of automatic control equipment altitudes flight speeds and ambient temperatures at which such o power plant might be operated can be grouped into three categories for purposes of discussion those flight conditions at which the radiators are (1) larger than they need be (2) yust large enough and (3) too small to transfer rated nuclear power to each engine If the radi ators are designed to transfer rated nuclear power to each engine at the nuclear cruise flight condition (Mach 09 at 35000 ft in the example considered here) excess radiator capacity 1s generally avail able during flight at altitudes below the nuclear cruise design altitude and the radiators will generally be too small to transfer rated nuclear power to each engine during operation at altitudes The numerous above the nuclear cruise design altitude Manual operation of the nuclear part of the reactor—X 61 power plant in each of these situ ations 1s described in the paragraphs which follow Throttling by means of radiator NaK bypass valves i1Is assumed and fuel and NaK flow rates are assumed to be constant at their rated values Startup and shutdown problems ground handling problems and sodium coolant temperature control problems are not considered MANUAL OPERATION AT FLIGHT CONDITIONS WHERE RADIATOR CAPACITY IS EXCESSIVE The radiators will generally be large enough to transfer more than rated nuclear power to each engine load at altitudes below the design nuclear cruise altitude Power plant maneuvers which might be performed in this operating range include engine startup operation on nuclear power only and operation on chemical plus nuclear power The engines will probably be started on chemical power only The higher turbine inlet temperatures obtainable with the chemical power sources should result in the lowest possible engine firing speeds and cranking powers The chemical power sources are also more maneuverable than the nuclear power source which probably will be advantageous during the critical starting and accelerating period Once the engines have been started nuclear power delivery can be imitiated by diverting NaK through the engine radiators It 1s assumed that the reactor has already been brought critical and ts known to be delivering power at some low level Care must be exercised in closing the NaK bypass valves to avoid transient undercooling of the NaK returning to the reactor Enough hot NaK must be allowed to flow through the bypass valves to ensure that the return line NaK temperatures will remain above their lower limits at all times Full closure of the NaK bypass valves is not permissible even during steady state operation at flight conditions where excess radiator capacity 1s available Rated nuclear power s delivered to each engine in the reactor—X 61 power plant during static operation at sea level, for example when only 45% of the total rated NaK flow passes through the radiators (Figs 12 through 15) If the NaK bypass valves ar= fully closed at such operating conditions exces. power demands will be set up and return line NaK undercooling and reactor fuel overheating will result Care must also be exercised in opening the NaK 21 bypass valves to reduce nuclear power delivery The return line NaK temperature should not be allowed to rise above the value at which isothermal idling of the reactor i1s desired when power de livery has been reduced virtually to zero Limiting the return line NaK temperature rise during load removal ensures that the load will be removed slowly enough to prevent reactor overheating If the reactor design 1s such that the fuel tem perature at the inlet of the reactor core must be limited to some value less than the design point mean fuel temperature control rod withdrawal s required as nuclear power delivery is increased Since the reactor fuel inlet temperature approaches the mean fuel temperature as power delivery is reduced the rod must be inserted to lower the mean fuel temperature during operation at low powers If the reactor fuel inlet temperature 1s to be maintained below the design point mean fuel temperature Subsequent rod withdrawal to raise the mean fuel temperature to the design point value cannot be initiated until some load has been reapplied [f operation on chemical plus nuclear power 1s desired engine fuel flows and exhaust nozzle areas must be controlled Control requirements for the turbojet section of the power plant during operation on chemical plus nuclear power will not be considered here For purposes of this discussion it 1s assumed that the automatic control equipment required 1s available Each time chemical power delivery to the engines I1s varied or the engine exhaust nozzle areas are changed the rate of nuclear heat delivery will also change The changes In compressor outlet temperatures and in air flow resulting from the changes in chemical fuel flows or nozzle areas upset previously established heat transfer balances in the radiators |f nuclear power delivery 1s to be held constant NaK bypasses must be readjusted each time the engine thrust outputs are changed during operation on chemical plus maximum nuclear power Continuous readjustment of the bypass valve positions 1s also required if nuclear power delivery I1s to be maintained constant as the aircraft alt tude and flight speed change since the engine air flows and compressor outlet temperatures are clso functions of the engine inlet total tempera ture total pressure and flight Mach number The demand sensitivity of the reactor makes continual 22 NaK bypass readjustment necessary if power de livery 1s to be held constant as the load charac teristics change Constant power delivery to a turbojet load is not necessarily desirable except when nuclear power only flight at the highest speed possible i1s to be maintained Operation In this manner will probably be required for a large percentage of the time during typical missions MANUAL OPERATION AT RADIATOR DESIGN FLIGHT CONDITIONS The manual control operations required in the execution of typical power plant maneuvers at flight conditions when the radiators are |ust large enough to transfer rated nuclear power to each engine are quite simtlar to those described in the preceding section except that full closure of the NaK bypass valves 1s now permissible during steady state operation Return line NaK under cooling and overheating must be guarded against during transients but the radiators are not large enough to cause undercooling during steady state operation at such flight conditions Full nuclear power delivery to each engine results when the bypasses are fully closed Rod control require ments are the same as those discussed in the preceding section Rod withdrawal or insertion during power level changes 1s required if the fuel temperature at the inlet of the reactor core must be held below the design point mean fuel tempera ture MANUAL OPERATION AT FLIGHT CONDITIONS WHERE RADIATOR CAPACITY IS INADEQUATE Radiator capacity will be inadequate at some flight conditions because the engine air flows and compressor outlet temperatures are such that the available heat transfer surface area 1s not sufficient to transfer rated nuclear power During dash for example only 71% of rated nuclear power can be delivered to each engine in the X 61 power plant even though the NaK bypasses are fully closed and the mean reactor fuel temperature s at its design point value This operating condition 1s described in Table 2 Since rated nuclear power 1s not being delivered the fuel temperature at the outlet of the reactor core 1s less than the T600°F upper limit Some increase 1n nuclear power delivery thus can be effected by further withdrawal of the control rod TABLE 2. DASH OPERATION (55 000 ft Mach 2 0) OF G E X 61 ENGINE Tg at Des gn Po nt Yalue TFH at Maximum Va]ue% TFGV °F Tey °F Tec °F NaK byp 7 Pump speeds Nuclea power delivered per engine Mw Chemical power delivered per eng ne Mw Total power del vered per engine Mw Chemical power reduct on effected by moving control rod 7 R 1450 1489 1557 1600 1343 1378 0 0 R ted Rated 214 223 40 9 400 623 623 22 to raise this temperature The operating con ditions described in the last column of Table 2 prevail after such action 15 taken Nuclear power delivery to each engine s increased to 74% of rated power and chemical fuel consumption s reduced by about 2 2% under these conditions If the fuel temperature at the inlet of the core must be limited to 1350°F however rod withdrawal to the extent shown in the last column of Table 2 1s not permissible and the potential advantages to be gained n raising the mean fuel temperature during operation at such a flight condition are not so great as those described in this column The discussion 1n the preceding paragraphs leads to the conclusion that some sort of automatic control equipment to raise the reactor mean fuel temperature to its maximum allowable value during operation at radiator hmited flight conditions 1s desirable but that equipment performing this function alone 1s not essential to power plant operation The potential advantages to be gained do not appear to be great enough to justify much complication of the control system unless such equipment 1s also needed for other reasons such as controlling rod withdrawal during power In creases AUTOMATIC CONTROL REQUIREMENTS DURING OPERATION IN THE POWER RANGE The foregoing discussion indicates that some sort of automatic control equipment Is required for the NaK bypasses Automatic control equip ment 1s also required for the control rod if the fuel temperature at the inlet of the reactor core must be held below the design point mean fuel temperature |f the reactor can be designed to operate 1sothermally at the design point mean fuel temperature however a reasonably conventional manual type rod control will probably suffice Movement of the NaK bypasses must be limited to maintain the return line NaK temperatures be tween their upper and lower himits at all times The lower limit for steady state operation i1s the temperature at which rated nuclear power 1s de livered to each engine The upper limit 1s the temperature at which steady state isothermal re actor 1dling 1s desired In simplest form the controls for the NaK bypass valves might be remote positioning servos with return line NaK temperature overrides and under rides to limit bypass valve openings to those values that will result in temperatures in the safe range Further studies of reactor and engine con trol integration may show that a more complex arrangement 1s needed If the reactor cannot be operated i1sothermally at the design point mean fuel temperature rod inser tion with power reduction 1s required to limit the core inlet fuel temperature rise Rod withdrawal with increasing power delivery 1s required either to restore the mean fuel temperature to its design point value or to raise the reactor fuel outlet temperature to its maximum value The discussion in the preceding section showed that a slight advantage would be gained during the dash if the 23 ve MEASURED CORE FUEL INLET TEMPERATURE THERMOCOUPLE THERMOCOUPLE SIGNAL AMPLIFIER B INSERT (NEGATIVE ERROR) AMPLIFIER (POSITIVE ERROR) RELAY WITHDRAW _I l | i {l; SERVO INSERT —_— SERVO { WITHDRAW A ROD DRIVE INTER OCKS AND PERMISSIVES } | INSERT MAXIMUM ALLOWABLE CORE FUEL CORE FUEL INLET INLET TEMPERATURE (4350 F) TEMPERATURE ERROR ¥ MAXIMUM ALLOWABLE CORE FUEL CORE FUEL OUTLET OUTLET TEMPERATURE (4600 F) TEMPERATURE ERROR + — MEASURED CORE FUEL QUTLET TEMPERATURE RELAY WITHDRAW AMPLIFIER (POSITIVE ERROR) | I (NEGATIVE ERROR) { I THERMOCOUPLE THERMOCQUPLE SIGNAL AMPLIFIER o Fig 25 Schematic Diagram of Rod Servo DWG ROD DRIVE rod were withdrawn to raise the fuel outlet tem perature to its maximum value rather than to raise the mean temperature to its design point valuve Hence one simple type of rod control for the reactor—X 61 power plant would be one which operates as follows 1 withdraws the rod if the reactor core fuel inlet temperature 1s less than 1345°F and the reactor core fuel outlet temperature i1s less than 1590°F 2 inserts the rod i1f the reactor core fuel inlet temperature exceeds 1355°F or the reactor core fuel outlet temperature exceeds 1600°F The basic form of such a control system is out ltned in Fig 25 Further study may show that additional stabilizing signals are required but this question will not be considered here The diagram 1s intended to be schematic only and does not necessartly represent the best way to do the |ob The fuel temperatures resulting from the use of such a control scheme are shown in Fig 26 Either the core fuel inlet temperature or the core fuel outlet temperature 1s held at i1ts upper limit at all times Operation with the fuel outlet tem perature at its maximum value 1s possible only when power delivery exceeds 83 4% of the rated valve The fuel inlet temperature limiting require ment does not allow the maximum fuel outlet temperature to be reached when power delivery 1s less than 83 4% of rated power ACKNOWLEDGMENTS The writer wishes to express appreciation for help received from A P Fraas M M Yarosh and L ORNL LR DWG 14493 1700 4600 - REACTOR FUEL OUTLET TEMPERATURE 7 H>/ 1500 = 0 / w 1400 < o D '_ < g 7 o REACTOR FUEL INLET = 1300 [~ EMPERATURE 7. — ] e ¢ 1200 1100 1000 0 20 40 60 80 100 TOTAL REACTOR POWER DELIVERY ( / OF RATED TOTAL POWER) Fig 26 Fuel Temperature Yariations Resulting from Use of Rod Servo R D Schultheiss of ORNL and from J Bendot of The Glenn L. Martin Company 25 B AR APPENDIX A RADIATOR DESIGN PRCCEDURE The basic radiator unit from which the engineradiators discussed in this report were composed, was designed by R D Schultheiss A sketch of this unit 1s shown This umit has 776 ft2 of heat transfer area and the vaniation of its over all heat transfer coefficient U, with changes in air flow per untt frontal area W /A, 1s as shown in Fig 6 The pro cedure followed in assembling a hypothetical radiator for the X 61 engine is outlined below 2 Fr 1 An engine radiator design point flight condition 1s chosen, and the engine load requirements at this flight condition are determined The 35000 ft Mach 087 nuclear power only cruise flight condition was chosen as the radiator engine design point for the reactor—X 61 power plant and the accompanying load re 6 quirements are shown below o - — = = TNC (1100°F) ¢e———rr~re—— TNH (1500°F) P_ = 30 Mw Wa = 13241b/ e TT3 (487°F) ——~r~r———> TT4 (1311°F) 2 The required value for the product U,A, (total heat transfer area—over all heat transfer coefficient) 1s then calculated as follows (1100 - 487) - (1500 - 1311) Log mean temperature difference = = 360°F In (1100 — 487)/(1500 - 1311) P, 28 425 RUR AT T 360 = 78 9 Btu/sec °F 3 The engine air flow per unit frontal area of the radiator Wa/A/R 1s calculated from W, which 1s known and A which 1s determined from the engine design In this case A, was arbitrarily chosen as 16 ##2 so W 132 4 T 2L 8 275 lb/sec ft2 Ap 16 4 A value for U, 1s read from the curve in Fig 6 with the use of W/A/R found In step 3 and the required heat transfer surface area A, 1s calculated Ug = 315 Btu/hr ft2 °F U,A R 78 9)(3600 a, R UBICEO _ 9415 42 U, 315 27 28 5 Next a number of the basic radiator units are stacked to provide the required frontal area Four units are needed in this example Since each basic unit contains 776 ft2 of heat transfer area the stacked array contains 3104 ft2 of heat transfer surface The array must therefore be lengthened to provide the required over all heat transfer surface Since a 6 67 in deep stacked unit contains 3104 f+2 and since 9018 ft2 1s required the depth must be increased to H -—90]8 667 =194 3104 0 00T A (N The pressure drop can be estimated by multiplying the calculations V of Schultheiss by the proper ratios Under the following operating conditions Wa = 579 Ib/sec ft2 p = 00434 radiator depth = 6 67 in R Schultheiss has calculated that the pressure drop of this type of radiator s AP, = 28 5n H,0 At other operating conditions the pressure drop 1s estimated to be wa/AfR 0 0434\ /radiator depth AP, = 285 579 P, 6 67 For the G E X 61 case AP, = 8216 H,O = 4268 Ib/ft2 At the design point (described in step 1) this pressure drop 1s (426 8/6470) = 6 6% of the com pressor discharge pressure The same procedure was used In assembling the hypothetical Allison J 71 radiators APPENDIX B STEADY STATE PERFORMANCE CALCULATIONS Control parameter values required to yield given engine thrust outputs during steady state operation at specified flight conditions can be determined by working backwards through the engine and reactor performance characteristics The engine [oad imposed on the reactor (as described by power compressor outlet temperature turbine inlet temperature and airflow) is first determined from Figs 2 through 5 When these load quantities are known and when values for all but one of the unknown potential throttling quantities are specified the value which the remaining unknown throttling quantity must have in order to meet the load conditions can then be calculated by use of one of the procedures outlined below For purposes of tilustration it 1s assumed In each case that the throttling quantity value required to deliver 4000 Ib of thrust output per engine during flight at 15 000 ft at a speed of Mach 0 45 1s to be determined Example 1 — Control Rod Throttling The engine load quantities resulting when 4000 Ib of thrust 1s delivered during flight at 15 000 ft and Mach 0 45 are (from Figs 2 through 5) T,y = 411°F W_ = 157 Ib/sec Tre = 931°F a P, = 22 5Mw = 21 300 Btu/sec Effectiveness values for both the heat exchanger and the engine radiators will be required for calculation of the unknown quantities Te , Tey Tpe Tyy Tne These effectiveness values depend on the fluid flow rates and the over all heat transfer coeffictents which are also functions of the flow rates - e(UHXAHX/WNCN)[(WNCN/WF CF)_I] TI = - 1 — (WyC\/WoChp) Uk Aux/ Wy Cy) Wy Cy/ W Cp)-1] (UgAp/W, C ) [(W,C /WyCy)-1] — e n = R 1 — (W,C,/WNCy) e(URAR/WaCa)[(Waca/WNCN)-I] Since the flow rates in the main heat exchanger are constant at design point values in this example the heat exchanger effectiveness 1s 0 8 as shown on page 3 The effectiveness of the radiator at this operating condition 1s found by substituting the foliowing values into the effec tiveness expression W, = 157 Ib/sec A = 9018 ft2 Ve 157 U, = 336 Btu/hr ft2 °F from = — = 98l and Fig 6 R T W, = 2843 Ib/sec C, =02 Cy = 025 This substitution shows that the radiator effectiveness 7, 1s 0768 Values for all the unknowns desired can now be determined from the following series of cal culations 29 NaK Temperature at Outlet of Heat Exchonger (Tyy) — By definition TT4 - TT3 Mg = TNH - TT3 or Tra = Tr3 931 - 411 Tyg = ———+ Ty =—————+ 411 = 1088°F e 0 768 NoK Temperature at Inlet of Heat Exchanger (Tye) - T T T T e g o 20 790°F Tnve = Tnuw = Tyn = Tne) = Typ - neCn - (284 3)(0 25) - Fuel Temperature at Outlet of Reactor Core (T ) = By definition TNH - TNC Tx = Tey = Tnc or T Tow 7 TNe MBI iexer FH = Y INc =g " = MHx 08 Fuel Temperature at Inlet of Reactor Core (Tre) - T T (T T.) =T e | 42 600 938°F FC — FH ~— FH ~ FCc/ — FH ~ WFCF - "—(7—02)(62_7)_ Twice the power delivered to one engine 1s used in the above expression since reactor power delivery to two engine loads has been assumed Thus 1f 4000 Ib of thrust 1s to be delivered by each engine during flight at 15000 ft and Mach 0 45 the control rod must be set to lower the mean fuel temperature to 1051°F f throttling Is to be by means of control rod motion alone Example 2 - Reactor Fuel Flow Throttling The engine load quantities at the 15 000 ft Mach 0 45 4000 1b thrust output flight condition were given in the preceding example The radiator effectiveness in this case 1s also the same as the effectiveness calculated in example 1 (ngp = 0768) since the air and NaK flow rates are the same It 1s assumed in this example that the control rod i1s adjusted to hold the mean fuel temperature at 1ts design point value Tp = 1450°F The unknown quantities to be calculated are We Ty T T and T, FC NH c The unknown NaK temperatures are the same as those calculated in example 1 since the load characteristics are the same and the radiator effectiveness 1s the same The fuel flow rate required to satisfy heat balances in the main heat exchanger can be calculated as outlined below The power transferred from the main heat exchanger is AT), Pr= WCplTpy - Tp ) = 2ch,< + Tye = Tp > THx 30 |f the power delivery to the two engines 1s the same P T 299 80 6 P, =——= 027V, + 790 — 1450 ) = W, - 1783 2 Ty x Tux Since P_ is known from the engine load requirements and 7, 1s a function of W (since the NaK flow rate 1s constant) the above expression might be solved directly for W_ However the complexity of the 5, to W relationship mokes solution by trial and error more attractive One procedure for solving this equation involves assuming a value for W calculating the associated value of Myx and calculating a value for P, The process 1s repeated unti| the calculoted power per engine Is equal to the required power per engine At the 15000 ft Mach 0 45 4000 Ib thrust output flight condition W, = 125 Ib/sec satisfies the power delivery requirement Fuel temperatures are then calculated from Pr 42 600 Tey - Tpe = = = 1257°F WoCp (125)(027) Tey = Tec 1257 . Toy = Th +—é—~:14so+ = 2079°F Tpy - TFC 1257 o Tpc = Tp ——— = 1450 - = 822°F Example 3 ~ NaK Flow Throttling The engine load quantities are again the same as those shown in example 1 since the aircraft flight condition and engine thrust outputs desired are the same In this example the fuel flow rate W, and the mean fuel temperature T are constant at their rated values (702 Ib/sec and 1450°F respectively) The unknown quantities to be calculated In this case are W, Tpy Tg( Tyy and Ty The reactor fuel temperatures are found easily from P - . T 42 600 _ 224°F rr = Tre T T ooz Tey -~ Tec 224 o Tenw = Tk +___2_——:]450+ - e Toy - Trc 224 . Tee = Tg -T2 7 1430 T2 1338°F The NaK flow rate needed for delivering the power required by each engine at the specified load conditions can be found by a trial and error process The right trial 1s outlined below A value for W 1s assumed and the resulting n, . 1s calculated If Wy 151554 1b/sec Tyx 'S 10 as calculated from the known fuel flow rate the over-all heat transfer coefficient and the assumed NaK flow rate The resulting NaK temperatures are then calculated From the definition of main heat exchanger effectiveness T - T P L 7 21 3% NC - = 1012°F FH 31 and T T (T T,.) =T e 1012 + 21 3% 1562°F - + - = Tyc + = e = NH NC NH NC W..Cn (155 4)(0 25) An alternate expression for the radiator effectiveness 1s o e(URAR/WaCa)[(ATN/ATa)-1] Mg = U,An/W C YL(AT /AT )1 | ary SRR Y CITAT /AT )] Substitution of the following quantities into this expression yields a value for radiator effective ness which exists when the NaK flow rate 1s 155 4 Ib/sec as was originally assumed W a 157 2 = — = 98] Up = 336 Btu/hr 12 °F (Fig 6) A 16 ATy 1092 2 10 UrAr (33 6)9018) - AT, 520 W,C, (157)(0 26)(3600) 1 - 22 063(2 10-1) g = = 0 450 1 - 210 62 063(2 10-1) The radiator effectiveness required to satisfy the load requirement 1s TT4 = TTB 520 0 45 '[]R = = = TNH - TT3 1562 - 411 If these two effectiveness calculations had not yielded the same result a different NaK flow rate would have been assumed and the calculations would have been repeated Example 4 — NaK Bypass Throttling The engine load quantities are again the same as those shown in example 1 and in this case the fuel flow rate total NaK flow rate main heat exchanger effectiveness and mean fuel tem perature are assumed to be constant at their rated values The unknown quantities to be calculated are WNBP] WND| Tey Tpe Tyw Tye and Tyhe Fuel Temperature at Qutlet of Reactor Core (TFH) - Tpy - Tec 224 + ————— = 1450 + T= 1562°F T = Tg > FH Fuel Temperature ot Inlet of Reactor Core (Teo) - TFH - TFC 224 To - =T - — - 1450 - 2 - o e = Tray > 5 — = 1338°F 32 NaK Temperature at Inlet of Heat Exchanger (T, ) ~ From the definition of heat exchanger effectiveness T - T Tne = Tpn = AT 1562 - fi = 1189°F Ty x 08 haK Temperature at Outlet of Heat Exchanger (T ) - Tng = Tne + Tnp = Tne) = Tye + - = 1189 + 210 W eCn (284 3)(0 25) T,y = 1189 + 299 = 1488°F NaK Temperature at Outlet of Radiator (7, . ) ~ Values for the following constants are first obtained Trs = Tra 931 - 411 0 453 nR = = = Tyy - T, 1488 - 411 Url (33 6)(9018) W.C_ (157)(0 26)(3600) = 2063 Substitution of these constants into the alternate radiator effectiveness expression given in example 3 yields 2 063 TNy ~Tye V(Tps-Tri)l-11 0483 = 2 Ty, -T AT =T =1} 1 - UTyy = Tye Ty = Trglle 063t TNy -Tye T -Trazl-1 Solving for (T, — Tye M Tpy = Trs) TNH TNC Try - = 190 T3 Thus Tye = Tayg - 190(Tp, - Tpy) = 1488 — 1 90(931 — 411) = 500°F at the outlet of the radiator Direct NaK Flow Rate per Engine Through Radiator Wyp) - Wyp = e 213% 859 Ib/ ND S T T T, )Cy | (1488 — 500)(025) " NoK Bypass Flow Rate per Engine (W ,,) — Wygp = Wne = Wyp = 2843 = 859 = 198 4 Ib/sec 33 34 or 198 4 00 = 69 8% 843 6 Example 5 « Air Bypass Throttling The engine load quantities are given in example 1 and the fuel flow rate NaK flow rate heat exchanger effectiveness and mean fuel temperature are assumed to be constant at ther rated values The unknowns to be calculated in this case are Wagp Yap Tey Tpe Tyy ond Ty~ The fuel and NaK temperatures are the same as those calculated in example 4 and are repeated here for reference T = 1562°F T = 1338°F T FH FC Ny = 1488°F Tye = 1189°F The remaining unknowns W.pand W_p, are calculated in the following way Direct Radiator Air Flow Rate per Engine (W,p) = The raaiator effectiveness 1s TT4 - TTS TNH = TTS Mg = Radiator power delivery i1s Pe = waCa(TT4 - TT3) Combination of these expressions yields Y . Pe . 21 300 75 8 DR = C (Tym - Tra) (026)(1488 — 411) The W png product 1s also given by 1 - e(URAR/WaDCa)[(WaDCa/WNCN)—I] = W waDnR aD 1o e o URAR Wap CAHapCo Wy C) 1] This expression might be solved for W_,, (inserting the known value of W, png product from above) since the NaK flow rate 1s constant and the over all heat transfer coefficient Up ts a function of W_,, The complexity of the right side of the above expressions makes direct solution difficult however The value of W,p resulting in a W_pn. product of 75 8 can be found graphi cally by plotting the right side of the above expression for W.png as a function of W_, Such a plot 1s shown in Fig B 1 This plot shows that the required W,.png value (75 8) results when ¥ p 's 83 Ib/sec a Bypass Air Flow Rate per Engme (W ;) - w =W, - W_p aBP 157 — 83 = 74 Ib/sec 74 % air bypass = x 100 = 47% 157 240 220 200 @ o 4160 140 120 100 80 60 RADIATOR PERFORMANCE PARAMETER Wa‘!?R 40 20 ORNL LR DWG 9224 / /, /,/ ] // 40 80 {20 160 200 240 280 320 360 RADIATOR AIRFLOW %D {ib/s ) Fig B 1 (Performance Parameter for X 61 Engine Radiator 400 35 36 e APPENDIX C STATIC STABILITY CALCULATIONS The steady state power delivered by the reactor is related to the engine load quantities in the following way ] (CH P = /W pCang + (1 = 03 )/ W e (TF v T'ra) voCn — 1/2XW_C,, Condition 1 ~ Variation of steady state power delivery with changes in engine speed when reactor control quantities are constant and throttling 1s by air bypass with pump speeds constant In this case the quantities listed below are constant at the values shown in the reactor—J 71 engine power plant MTyx = 08 X =025 Wye = 1422 Ib/sec We = 702 Ib/sec Cy = 025Bt/Ib°F Cp = 027 Bt/Ib °F €, = 026 Btu/Ib °F Tre, = 1450°F Substitution of these values into Eq C 1 yields 1 P, = (3846/W_,n.) — 0003517 (C 2) (1450 — T..) The W_,n, product 1s a function of the total engine air flow which is a function of speed (Fig 7) and the air bypass percentage The variation of W.png with W_. at rated NaK flow 1s shown in Fig 21 Steady state compressor outlet temperature variation with speed 1s shown in Fig 7 Substtution of values for W,png and T..; at each speed into Eq C 2 yields the power delivery curves of Fig 20 Condition 2 = Vanation of steady state power delivery with changes in engine speed when reactor control quantities are constant throttling 1s by NaK bypass and all pump speeds are constant Equation C2 applies in this case also The value for W_, is the same as that for W, (the total engine air flow) Variations of the W,png product with W_. at constant NaK bypass per centages are shown in Fig 21 The variations of T..5 and W_ with engine speed are shown in Fig 7 Substitution of these values into Eq C 2 yields the constant NaK bypass power delivery curves of Fig 19 Condition 3 ~ Variation of steady state power delivery with changes in engine speed when reactor control quantities are constant throttling 1s by NaK bypass and one or more pump speeds are proportioned to engine speed Equation C 1 applies to this case The vaiue for W.p is equal to that for W _ (the total engine air flow) the variation of W, 5, with radiator air flow 1s shown 1n Fig 21 variations of W, and T..3 with engine speed are shown in Fig 7 and heat exchanger effectiveness values are calcu lated from the fuel and NaK flow rates and the heat exchanger effectiveness equation given on page 29 In calculating the power delivery curves of Fig 23 it was furthermore assumed that the mean fuel temperature T._ _ was held constant at 1450°F at all times by rod motion 1f necessary and that the pump flows were proportional to the pump speeds Thus 702 F = %N 142 4 Ne = T5ean Substitution of these expressions into Eq C 1 yields the desired relationship between power delivery and engine speed which 1s plotted for various pump drive combinations in Fig 23 37