Investigation of Isothermal, Compressible Flow Across a Rotating Sealing Dam

NASA TN D-534k cpt.2, c.1

NASA TECHNICAL NOTE NASA TN D-5345

4 r/l 4 z LOAN COPY: RETURN TO AFWL (WLGL-2) KIRTLAND AFB, N MEX

INVESTIGATION OF ISOTHERMAL, COMPRESSIBLE FLOW ACROSS A ROTATING SEALING DAM

I1 - COMPUTER PROGRAM

by John Zuk, Patriciu J. Smith, and Lawrence P. Ludwig Lewis Resemch Center CZeveZund, Ohio

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. SEPTEMBER 1969 TECH LIBRARY KAFB, NM I111111 11111 Ill11 11111 Ill11 11l111111111111111 0132317

INVESTIGATION OF ISOTHERMAL, COMPRESSIBLE FLOW

ACROSS A ROTATING SEALING DAM

I1 - COMPUTER PROGRAM

By John Zuk, Patricia J. Smith, and Lawrence P. Ludwig

Lewis Research Center Cleveland, Ohio

NATIONAL AERONAUT ICs AND SPACE ADMlN I STRATI ON

For sale by the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151 - CFSTI price $3.00 ABSTRACT

A computer program is presented for the analysis of compressible fluid flow across a sealing dam, such as is used in a shaft seal. The mathematical model consists of two closely spaced parallel rings, one of which is rotating. The analysis is restricted to steady, laminar, subsonic, isothermal flow. The effect of rotation on mass flow, pressure distribution, and other physical parameters is determined. The computer program is written in FORTRAN IV. The input and output variables are in English units; printout of data in the International System of units is optional.

ii CONTENTS

Page SUMMARY ...... 1

INTRODUCTION ...... 1 COMPUTER ANALYSIS ...... 2 Sealing Dam Model ...... 2 Sealing Dam Analysis ...... 3 Description of Program ...... 6 Input Variables ...... 11 Program Variables ...... 12 Subroutines ...... 15 Flow Charts of Main Program ...... 17

APPENDIXES A-SYMBOLS ...... 20 B.PROGRAMLISTING ...... 22 C .SAMPLE PROBLEM ...... 33

t iii INVESTIGATION OF ISOTHERMAL, COMPRESSIBLE FLOW ACROSS A ROTATING SEALING DAM I1 - COMPUTER PROGRAM by John Zuk, Patricia J. Smith, and Lawrence P. Ludwig Lewis Research Center

SUMMARY

A computer program is presented for steady, laminar, subsonic, isothermal, compressible-fluid flow across a sealing dam of a radial shaft seal. Output variables include mass flow, volume flow, exit Mach number, rotational flow Reynolds number, pressure flow Reynolds number, Knudsen number, center of pressure, sealing dam force, pressure distribution, power loss, and approximate temperature rise of the gas leaking through the seal. The computer program is written in FORTRAN IV for the computer at Lewis Research Center, which is an IBM 709411/7044 or 7040 direct couple computer under IBSYS version 13 using ALTIO. All input, output, and calculations are in English units; printout of data in the International System of units is optional. The program flow charts are presented in detail and a sample problem is given.

INTRODUCTION

In a companion paper (ref. l), the analysis is given for the mass flow and pressure distribution for a parallel set of surfaces typical of that in the sealing dam of shaft face seals (ref. 2). The analysis is for steady, laminar, subsonic, isothermal, compressible- fluid flow with rotation of one of the sealing dam surfaces. Mass flow and pressure distribution with rotation are compared with the hydrostatic case. Reference 1 shows that rotation has significant effects when the speed is high or the radial pressure differential across the sealing dam is very small and the speed is moderate. When the sealing dam radius is much greater than the sealing dam width, which, in turn, is much greater than the film thickness, and the radial pressure flow is sufficiently large, a hydrostatic analysis is shown to be valid. Further, in the analysis presented in reference 1, the region of validity of the analysis is defined as follows: (1) The analysis is valid until the circumferential shear flow causes transition to turbulence. (2) The analysis is valid until the radial pressure flow approaches a Mach number of I/!!, where y is the ratio of specific heats or until the pressure flow becomes turbulent. The objective of this report is to present the computer program for the analysis given in reference 1. Input variables include the dimensions of the seal, pressure boundary conditions, and molecular weight and physical properties of the gas. For specified film thicknesses, which are used as parametric input, the output includes mass flow rate, pressure distribution, velocity distribution, Mach number, force, center of pressure, rotational flow Reynolds number, pressure flow Reynolds number, power loss, torque, and approximate temperature rise due to the viscous shearing. The computer program is written in Fortran IV for the computer at Lewis Research Center, which is an Il3M 7094II/7044 or 7040 direct couple computer under IBSYS version 13 using ALTIO. All input, calculations, and output are in English units; printout of data in the International System (SI) of units is optional.

COMPUTER ANALYSIS

Sealing Dam Model

A typical face seal is shown in figure 1. It consists of a nonrotating nosepiece held either in sliding contact against or in close proximity to a rotating seal seat; the dynamic leakage gap (sealing dam) between the nonrotating and rotating surfaces is exaggerated in

p2 p1> p2 Axial motion Spring i -

Figure L - Schematic of pressure balanced face seal.

2 the diagram. Since typical values of the sealing gap are less than 0.0010 inch (0.0025 cm), the gap is, in effect, a long narrow slot, and viscous forces are predomi- nant in leakage analysis. The model that approximates this sealing dam is shown in figure 2. It consists of two parallel, concentric circular rings, separated by a very narrow gap, with one moving at a constant speed. A pressure differential exists between

Inner I

L---- Figure 2. - Model of sealing dam.

the inner and outer diameter of the rings, and the fluid is stagnant in the inner and outer cavities that bound the sealing dam. The model formulation is based on the following restrictions : (1) Homogeneous, compressible, viscous, and Newtonian fluid (2) Steady and laminar flow with negligible inertia forces 2 (3) Bulk modulus, X = -3p (Symbols are defined in appendix A.) (4) Perfect gas fluid (5) Negligible entrance region effects (6) Isothermal fluid film (7) Entrance Mach number, close to zero

Sealing Dam Analysis

The governing flow equations for a compressible fluid with constant viscosity in vector notation are as follows (ref. 3): 3 Conservation of mass

Conservation of momentum (Navier -Stokes equation)

+ DV - -+ 4- P - = V'P - PVX(VXV) + (A + 2p)v(v . F) + F Dt

Equation of state for an isothermal process

In reference 1 the governing flow equations are applied to the sealing dam model, simplified, and solved by (1) Utilizing a cylindrical coordinate system (see fig. 2) (2) Simplifying the governing equations by using the restrictions listed for the sealing dam model (3) Applying the appropriate boundary conditions. The resulting equations are shown in table I in the form used in the computer program. The equations of table I are in the English system of units, and table I1 shows the conversions to SI units. The computer calculations are carried out in the English system of units, but the program contains provision for printout in SI units.

4 TABLE I. - FORM OF PERTINENT EQUATIONS FOUND IN COMPUTER PROGRAM

(IN SAME SEQUENCE AS EQUATIONS APPEAR IN PROGRAM)

~~ PlninUav2h(12 in. /ft) _- - Re2h Re(P) =(32.174 'bm-ft)' rR(T + 460) I lbf-sec2 61 ft-lbf- R = =, ft:lbf where @- = 1545.4 m Ibm OR (lb-mole) OR I Q = 13.063 M, scfm

If N=O AT = 0. OR then and if V = 0, C = 0, Btu/lbm OR P

= ZnN, rad/min

x =x1 + nAx, in. Re@) = po( Rz !? h ~~__ p)' (60 sec/min)(l44 in.'/ft2)

AX = Rz - 51- , in. (number of steps)

-, lb/niin

x + R1

'J 3R:f12

RinZ where K1 = - ~ where K1 = - - __ 561T 5 61T

5 TABLE II. - CONVERSION TO INTERNATIONAL UNITS

Quantity To convert Multiply by

From To

Length in. m 2. 54X10-L Mass Ibm kg 0.45359235 Time min sec 6C Force Ibf N 4.4482216 Torque lbf -ft m -N 1.355817s

Energy Btu J 1.05587X10' Power hP W 7.4569987X102 Density lbf -sec2/ft4 kg/m 5.15379X102 Viscosity lbf -se c/ft N-sec/m2 47.880258 Gas constant ft-lbf/lbm-OR J/kg-K 5.38095

Specific heat Btu/lbm -OR J/kg-K 4.1865783~10~ Temperature 3F K K = 5(F + 460)/9 Temperature difference 3F K K = 5F/9 Pressure ?si N/m2 6.8947572~10~ Velocity rPm rps 1/60 Ct/sec dsec 0. 3048 2 2 Area in. n 6. 4516X10-4 Mass flow rate !bni/min cg/sec 7.55987~10-~ Volume flow rate at jcfm n3/sec 4.7194744~10-~ standard conditions Heat flow rate 3tu/min N 17.59783

Also included are lists of the input variables and program variables along with their descriptions and English units, detailed descriptions of the subprograms, and a flow chart of the main program (fig. 3). (Listings of the programs are given in appendix B; the sample problem, with output options, appears in appendix C. )

Description of Program

RSEAL - Main Program. - The main program, RSEAL, performs the primary flow analysis. Subroutines are used for secondary operations such as numerical integrations and plotting data. Input to RSEAL is by punched cards in the following order: (1) Title card: alphanumeric identification of the data (format 12A6) (2) NJ card: number of film thicknesses to be analyzed in one running of the program (format 13) (3) Film thickness, hm, cards: 6 per card (format 6F12.0) (4) Data cards: seal dimensions, operating conditions, physical properties of gas and logical variables (read by NAMELIST/RINPT/) Data are read by NAMELIST to minimize the number of cards required to run a second case with the same title and hm cards. Input variables are set of zero initially.

6 Consequently, variables that are not changed during the reading of data will be calculated by the program. (See the list of input variables for the significance of each variable and any restrictions on them.) Output data are printed in English units in the following order of groups: (1) Program identification: compressible sealing dam with rotation and parallel surfaces (2) Data identification: printout of title card (3) Input data as it appears on RINPT cards (4) Calculated' constants: gas constant, reference density, speed of sound, length of seal, area of seal (5) Parameters that vary with hm: mass flow rate, volume flow rate at standard conditions, maximum Mach number, pressure flow Reynolds number, rotational flow Reynolds number, sealing dam force, center of pressure, dimensionless sealing dam force, dimensionless center of pressure, and Knudsen number. (Printout of dimensionless sealing dam force and center pressure may be skipped by setting RSKIP to TRUE. ) (6) Parameters associated with power dissipation: power, total shear heat, apparent temperature rise, and torque. (Printout of all data associated with power dissipation may be skipped by setting TSKIP to TRUE.) (7) Distribution of parameters across the sealing dam (one group for each hm): distance across seal, pressure, pressure ratio, average velocity, and Mach number. Printout of data in English units is followed by plots of various parameters. Plots appear in standard form with minimum X and minimum Y in the lower left-hand corner. Legends at the bottom of the plots give conversion factors for SI units. The plots are as follows: (1) Power versus hm for N f 0 (2) Pressure ratio versus distance across seal for first case for which the model is valid. Plot 2 may be suppressed by setting ASKIP to TRUE. Following the plots, the data are printed in SI units in the same order as for English units. This printout may be skipped entirely by setting NOUI to TRUE. RSEAL is divided roughly into eight sections. The first section reads data and calculates program constants (cards 41 to 56). Section two (cards 82 to 87) calculates the constants needed in the pressure equation. Section three (cards 93 to 105) tests input variables. If they are zero, new values for them are calculated. Since SPEED and CAPV both represent rotational velocity, they must be consistent. If SPEED is read as nonzero, CAPV is calculated from SPEED. If SPEED is read as zero, CAPV must be examined. In the case that CAPV is nonzero, SPEED is calculated from CAPV. If both SPEED and CAPV are zero, the system considered is static. 7 Section four (cards 111 to 139) is the first part of a loop which is done for each hm. This section calculates a starting value for X, mass flow rate, volume flow rate at standard pressure condition, pressure flow Reynolds number, rotational flow Reynolds number, maximum Mach number, and Knudsen number. If the maximum Mach number is greater than l/fi, this analysis is no longer valid, IHTAG(J) is set equal to 1 as a trigger, and no further calculations are made. If the model remains valid, the program calculates power, temperature rise due to power dissipation, total shear heat, sealing dam force, and center of pressure. The integrations in the force and center of pressure equations are done numerically by Simpson's Rule. Section five (cards 144 to 154) is the rest of the loop started in section three. Section five calculates pressure, pressure ratio, average velocity, and Mach number for several points across the sealing dam. Section six (cards 158 to 200) writes data in English units. Section seven (cards 204 to 233) plots the various parameters. And section eight (cards 237 to 295) writes data in SI units. Numerical constants in the program are for units conversion. Subprograms. - RSEAL uses eight subprograms whose listings appear in appendix B. These are SIMPS1, SIMPS2, PX, PXX, PRESS, ROT, EXPK, and ARRNG. RSEAL also uses two other subroutines that are not standard in IBSYS: SORTXY and PLOTXY. SORTXY sorts two numerical arrays. A statement such as CALL SORTXY (X, Y, N) results in the array X being rearranged such that X(l) 5 X(2) I. . . 5 X(N) with the Y array entries reordered to preserve the (X, Y) pairs. N is the number of elements inthe X and Y arrays. PLOTXY plots two numerical arrays. A statement such as CALL PLOTXY (X, Y, KODE, P) produces a printer plot of X versus Y with the minimum X and the minimum Y in the upper left corner of the page with X increasing down the page and Y increasing across the page. KODE tells which plotting options are to be used. For example, KODE = 6 gives a plot with most of the grid lines suppressed, with asterisks as the plotting character, and with the X and Y scales computed by the plotting routine. The array P contains information needed by the plotting routine such as the number of points to be plotted, the X and Y scales if the programmer computes them, and the frequency of grid lines in the X and Y directions. Special format statements are used to print plot titles and plot legends. A pair of statements such as

WRITE (6,l) 1 FORMAT (WPT, 10HPLOT TITLE) will print the title

I PLOT TITLE

above the plot. A pair of statements such as

WRITE (6,2) 2 FORMAT (BHPL, 11HPLOT LEGEND)

will print the legend

PLOT LEGEND

immediately below the plot. Listings of SORTXY AND PLOTXY along with details for their use can be found in reference 4 or can be obtained from the Instrument and Computing Division of the Lewis Research Center. SIMPSl is a function subprogram to perform a numerical integration by Simpson's Rule. The integrand is evaluated at interior points by the external function named in the calling vector. A statement such as F = SIMPSl (XO, XF, G, K) gives F as the definite integral

The integrand is evaluated at interior points by the function G named in the calling vector. The interval of integration XO to XF is not divided uniformly. More sub- divisions are made where values of the integrand are changing rapidly. If two successive evaluations of the integral on a particular subinterval differ by more than ~xIO-~X value of the integrand, the subinterval is divided into two subintervals and the integration is repeated. If the integration required more than 200 subintervals, the integer K is raised by 1 to indicate that the value of the integral is incorrect. SIMPS2 performs essentially the same operation as SIMPS1, but it permits carry- ing a constant parameter into the integration by means of the calling vector. A statement such as F = SIMPS2 (A, XO, XF, G, KK) gives F as the indefinite integral

6"G(A, x) dx

Use of SIMPS2 permits evaluating double integrals because the external function G can call SIMPSl to evaluate the inner integral. KK performs the same function as K, but KK is raised by 2 to indicate inaccuracies in the integration. Subprograms SIMPS1 and SIMPS2 are in general use at the Lewis Research Center.

9 PRESS is a function subprogram to evaluate the pressure at any distance from the inner radius of the seal. This distance appears in the calling vector. The pressure differential equation is solved analytically and the resulting formula is used in the program.

Pzexp -2 -P1 exp- E) . ~, P(x) = + P; exp (3)

where PX is an external function to evaluate the integrand in the integral

Similarly, PXX is an external function to evaluate the integrand in the integral

where Pmin is the smaller of P1 and Pa.

EXPK is a function subprogram to evaluate exp(Klx)/(@Ri) where x appears in the calling vector. ROT is an external function to evaluate the integrand in the integral

10 dx

ARRNG is a subroutine subprogram which arranges two arrays X and Y for plotting. The subroutine first eliminates cases for which the model does not remain valid. It then sorts the remaining data in order of ascending X. It then inverts both arrays and interchanges them. The data are now in the form of ordered pairs (Y(N), X(N)), (Y(N - l), X(N - l), . . . , (Y(l), X(1)) where Y(N) 2 Y(N - 1) 2 . . . 2 Y(1). Data arranged in this form permit plotting with Y as the independent variable in descending order. Consequently, the plots appear with the minimum X and minimum Y in the lower left corner.

Input Variables

The following table lists variables input to the program and their units. Arrays are given with their dimensions.

Variable Unit Description

TITLE (12) Data identification NJ Number of mean film thicknesses (NJ f 50) HMEAN(J) , -J=1, -NJ in. Mean film thicknesses L in. Width or mean circumference of sealing dam of flow SPEED rPm Rotational speed. Either SPEED or CAPV may be set. If both are set, calculate CAPV from SPEED CAPV ft/sec Surface speed. MOLWT lbm/(lb -mole) Molecular weight of the gas P1 psi Pressure at inner radius of seal P2 psi Pressure at outer radius of seal T OF Isothermal ref e rence temperature

11 Variable Unit Des cription

R1 in. . Inner radius of seal R2 in. Outer radius of seal RHOFKI lbf-sec /ft Reference density at inner radius of the seal. If RHORO is read as zero, program calculates RHORO. RHORF lbf-sec 24/ft Density at mean radius used in calculating the rotational Reynolds number. If RHORF is read as zero, the program calculates RHORF. MU lbf -sec/ft 2 Absolute viscosity of gas CP Btu/lbm -OR Specific heat of gas GAMMA Ratio of specific heats NGRID Number of steps across seal (ma = 20) ASKIP Logical variable. If ASKIP = TRUE, program skips calculation and printout of x, pressure, average velocity, Mach number, and pressure ratio. It also skips plotting of x versus pressure ratio. RSKIP Logical variable. If RSKIP = TRUE, program skips calculation and printout of dimensionless center of pressure and force. It also skips plotting of dimensionless F. TSKIP Logical variable. If TSKIP = TRUE, program skips calculation, printout, and plotting of power. NOUI Logical variable. If NOUI = TRUE, program makes no conversion to SI units.

Program Variables

The following table lists the variables used in the program in the approximate order of their appearance, any limitations on the variables, and their units. Variables marked with an asterisk are printed as output data.

PI 71 = 3.1415927 RUNIV ft-lbf/(lb -mole)'R Universal gas constant

12 Variable Unit Description

ZERO Input variables are set to 0. PREF psi Smaller of P1 and P2 in the COMMON block RR1 in. Value of R1 in the COMMON block MCUT l/fi = upper limit for which model is valid NN Number of grid points (1 5 NN 5 2 1) JMOD Integer number of pressure distributions that will fit on one page. RDIF in. Distance across seal = R2-R1 PDIF psi Total pressure drop across seal 2 AREA* in. Face surface area of seal R* lbf -ft/lbm -OR Gas constant 24 RHO1* lbf-sec /ft Density at inner radius of seal A* ft/sec Speed of sound RHOREF* lbf-sec 24/ft Calculated density at mean radius of seal OMEGA rad/min Rotational vel0 city 2 2 ECONST 1/in. -K1/2R2 (where K1 is defined in appendix A)

2 EA lbf /in. P 1exp3PT R2

AA lbf2/in. 2

S dx X + R1

DELX in. Distance between two successive grid points X(J, I)* in. Distance from inner radius of seal MDOT (J)* lbm/min Mass flow rate VAV ft/sec Average velocity at outer radius of seal MACHMX(J) * Maximum Mach number for given HMEAN REP(J)* Pressure flow Reynolds number

13 Variable Unit Des cription

RER(J) * Rotational flow Reynolds number Q (J) * scfm Volume flow rate at standard conditions KN(50)* Knudsen number IHTAG(J) Numerical flag MTAG(J) = 0 implies model remains valid MTAG(J) # 0 implies model is invalid POWER(J)* hP Power dissipated by viscous shearing DELTJ(J) * OF Apparent temperature rise due to power dissipation TORQUE(J) * lbf -ft Torque HTOTAL(J)* Btu/min Total shear heat of system F (J) * lbf Equivalent force XC(J)* in. Center of pressure K7 KK Numerical flags that indicate whether the numerical integrations in the calculation of F(J) and XC(J) are accurate P(J7 I>* psi Pressure at X(J7 I) Pl?AT(J, I)* Ratio of P to Pmin at X (J, I) UAVRG(J, I)* ft/sec Average velocity at X(J7 I) MACH(J, I)* Mach number at X(J, I) FBAR(J) * Dim ensionless force XCBAR(J) * Dimensionless center of pressure JJ Counter for valid cases. If JJ = 1 modulo JMOD, the printer will skip to a new page. XPT(50), YPT(50), Utility arrays used in sorting and plotting XPLOT(50), YPLOT(50) data PP(6 1) Array needed by plotting subroutine - see description of PLOTXY for details KODE Plotting code - see description of PLOTXY for details NP Number of points in a plot (1 5 NP 5 50) I X index J HMEAN index

14 Subroutines

Name Call Common Program Description vector block variables variables variables

PRESS - pressure function X Distance from inner radius of seal PRE F Reference pressure RR1 Inner radius of seal

EA R2 Pa2 exp K1- - P2 exp AA 1 2 R2

S X + R1

R1 Inner radius of seal

K Numerical flag indicates whether numerical integration is accurate Q p2 (4 ROT - integrand in integral R1 Inner radius of seal X Distance from inner radius of seal Y Radial distance = R1 + x

X+R1

PX - integrand in integral X Distance from inner radius of seal PREF Reference pressure A, B, Dummy variables to fill COMMON c, D block Y - Pmin

15 Name Call Common Program Des c ript ion vector block variables variables variables

PXX - integrand in integral X Distance from inner radius of seal PREF Reference pressure

A, B, Dummy variables to fill COMMON c, D block Y (p - Pmin)X EXPK - special exponential X Square of distance from center of function seal ECONST (K1/2)/R; w Distance from center of seal

ARRNG - arranges arrays in X Input array of independent variables proper order for plotting Y Input array of dependent variable XP Sorted and inverted array of new independent variable YP Sorted and inverted array of new dependent variable N Number of elements in input arrays I Number of elements in sorted arrays T Temporary storage for sorting

16 Do statements 2W to 400 for each J J = 1. NJ

I Set starting value 1 Ofl I 1 Calculate 1,vaV, 1 and Mach number I to zero

Read title card

Calculate Re(Pl. Re(R) 9, and Kn

Calculate power, AT, 7HShear, and torque

to SI units

I I calculation

Set starting value 13Test input variables x, P, PIPmin. Vav, and

(a) initial steps.

(b) Main calculation. Figure 3. - Flow chart of Main Program. R. L area. and V

for parameters that vary with film thickness

Skip Write column headings nondimensional- for dimensionless ization of F F and X, and X,

Mach number, ReiP), Re(R),

Skip Nondimensionalize ization of F F and Xc and write themout

Skip

power

for parameters associated with power

AT, and torque for J = 1, NJ

Write column headings

(cl Write routine. Figure 3. -Continued.

~~ ...... _. __ ...... is invalid, set HMEANIJ) = -HM€AN(J) I

speed zero

(Plot power against h,

1-No ( Plot PIP,^, again- I

For cases for which model is Invalid, reset HMEAN(J) = -HMEANIJ)

+NOto SI units @)

Yes

and print in same format as for English units

(d) Plot routine. Figure 3. - Concluded

Lewis Research Center, National Aeronautics and Space Administration, Cleveland, Ohio, June 24, 1969, 120-27-04-90 -22.

I APPENDIX A

SYMBQLS

22 A cr -sectional area, in. ; m Q net volume flow rate, scfm; 3 a speed of sound, ft/sec; m/sec std. m /see specific heat at constant pressure, R mean radius, (R1 + R2)/2, in.; m cP Btu/(lbm) (OR) ; J/(kg) (K) AR sealing dam length, R2 - R1, specific heat at constant volume, in.; m cV Btu/ (1bm) (OR) ; J/(kg) (K) Reynolds number in radial direc- Reh a a tion, PUh/p D/Dt material derivative, -at + u -ar va +w-a +-rad az Reynolds number in circumferential direction, pk2h/p F sealing dam force, lbf; N - @ gas constant, dm, F dimensionless force, ft -lbf/(lbm) (OR) ; J/(kg) (K) F/(P2 - pp2- R1)L + -63 universal gas constant, 1545.4 F body force vector ft-lbf/(lb -mole) (OR); h film thickness, nominal, in. ; m 8. 3143 J/(kg-mole)(K) 22 K1 -(3R2a /5@T) r radial direction coordinate L sealing dam width, in. ; m T temperature, OF; K - M Mach number T average temperature, 0 F, K M mass flow, lbm/min; kg/sec U pressure-flow reference velocity, AM change in mass flow ft/sec; m/sec m molecular weight of gas, U velocity in r-direction or lbm/(lb-mole); kg/kg-mole x-direction, ft/sec; m/sec N speed of rotation, rpm V reference shear flow velocity, ft/sec; m/sec n integer V velocity in @-direction,ft/sec; P static pressure, psi; N/m 2 m/sec AP pressure differential, psi ; 2 W velocity in y-direction, ft/sec; N/m m/sec smaller pressure of two pressure 'm in W reference velocity across film boundary conditions, psi; thickness, U(h/AR), ft/sec; N/m2 m/sec

20 center of pressure in radial or xC P density, (lbf)(sec2)/ft2; kg/m3 x-direction, in.; m s-2 angular rotational velocity, dimensionless center of pressure, rad/sec Xc/(R2 - la? R1) V Del operator, -- - J -a* k ard^i + r ae + az X coordinate in pressure gradient direction Subscripts :

Y coordinate across film thickness av average

Z shear flow coordinate in Cartesian h based on film thickness system m mean specific-heat ratio, C /Cv P r based on radius circumferential coordinate ref reference second viscosity coefficient or 0 reference coefficient of bulk viscosity 1 inner radius or inlet absolute or dynamic viscosity, (lbf) (se c)/f t2 ; (N) (se c) /m 2 outer radius or exit 2 U kinematic viscosity, ft /sec; m 2 /sec

21 II 11111111 I I 111 I I Ill II1111111111I 111111I II Ill II I ll111 I1 ll"lmmm~mlll I I I1 I1 11111-I I

APPENDIX B

PROGRAM LISTING

$IbFTL RSEAL DEBUG 1 P 1. 2 C COMP&tSSlBLE FLO~SEALINti DAM ANALYSIS WITH ROTATION) 3 r L 4 LOG1LAL ASKI P rRSK1P ,T SKIP 9 NOU I 5 KEAL MDOT,MULWT,MU,MACtl,MACHMX, HCUT (KNrL 6 DIMENSION XPLOT(50) ,YPLCT(50) ,XPT1531 rYPT(501 ,PP(6lJrLERO( 171 8 7 1 UI(30)tTITLE(lZ) 8 0 IMENbION F (501 ,XC(50) ,MDOT (50) ,XCBAR(50) ,FBAR(50 ), Q( 501, 9 1 POdtK( 50) ,HI (50) edTOTAL150) tD€LTJ(50),TORQUE1501 rHHEAN(5Olr LO 2 MAGHMX(501 ,KEP(50) tItlTAG(50) rKN(50) SKER(SO) 11 0IMENSlUN X( 50921 1 ,PI 50r21) rUAVRG(5O r*211, PRAT (50, 21) *MACH( 50, 21) 12 COMMON/ INTGRL/PKEf ,RRlt EA VAAI S 13 CGNMOiW ECON/ECUNST 14 EXTEKNAL PXtPXXtROT 15 NAMELIST/RINPT/L,SPtE0,CAPVtMOL~T rP1 rP2rT tRlc R21RHOR0, 16 1 HHUKI- 9 MUgLP,bAMMA,NGRIDt ASKI PtKSKIP rTSKIP,NOU I 17 OATA PI,U UNI V/3.141>92711545.4/ 18 EUUIVALENC~ (ZERU(l),MOLWT) , [ZER0(6), P1) t (ZERO(ll),L), 19 1 LZEKIJL2JrSPEED) 9 (LER0171, PZJt (ZERO(12)rTJr 20 2 LLtKU(3) ,&iOKO) r (ZERO(8)r Kl), tZER0113~rMU)r 21 3 (ZEKU(4) ,KHOKF) 9 (ZERO(9Jr R21, (ZERO(14)rCAPV)r 22 4 (ZkKU(5) iGAWMA) r (LEKO(10)tCPJ 23 DO 9lJ I=lr14 24 'iti LEKOiI) = 0. 25 c 26 C KEA.iJ ItJPUT DATAfLALCULATk PROGRAM CONSTANTS, AND WRITE INPUT 27 c CON0 1TI ONS 28 c 29 G GATA LARDb 30 C 1-1TLE - DATA IDENTIFICATION - 1 CARD (FORMAT 12A6) 31 C 32 c NJ - NUMtlEH OF FILM THICKNESSES (FORMAT 13) 33 C 34 C HMtAN - MkAN FILM THICKNESSES - 6 PER CARD (FORMAT 6F12.0) 35 C 36 c BkIluPT - SEAL DIMtNSIDNSs OPERATING CONDITIONS, PHYSICAL 37 c PKUPtRTlkS OF GAS 9 LOGICAL VARIABLES 38 C (KEN bY NAMELIST/RINPT/I 39 c 40 REAL, (593) TlTLE 41 KkAO (5,111 NJ 42 &EA0 (5rZJ (HM.kAN(J) rJ=LtNJI 43 lUil WKICt (6s 10) KEAU L5tKIIUPT) 2 PKEF = AMINL(P1,PZ) 46 kKL = Kl 47 MCUr = l./SQRT(bAMMA) 48 NN = IJGKID+l 49 JMdd = 59/(4+IUN) 50 AREA = PI*(&L**2-K1**2) 51 t( Dlf- =K 2-K 1 52 PClF=AdS( Pl-PZ) 53 c(= c(UM V/M~LWT 54 dhCJ1= P l/K/(I+460. J *4.4 75~636 55 A= aUKT(GAMMA*K*( T+460.)432.1 74) 56 dR1TE (bp54J TITLE 57 NU1 Tt(6 , 111 tJL tP1 ,I ,MU, MOLHT pGAMl4ArK2 tR1 ticKHOROt RHORFp NN 8 5a 1 SPEtU,CAtJV,LPrASKIPr KSKIPtTbKIP 59 IF LNC~UI) tic) ro 110 60

22 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 d3 84 85 86 87 88 89 90 C iEST ANPUT PARAMt TkRS AND UfrERMINt OPERATLNG CONDITONS 91 92 93 94 95 96 97 98 99 100 10 1 10 2 10 3 104 10 5 LO 6 LO 7 108 109 ,110 111 112 113 114 115 116 117 118 119 120

23 121 122 123 124 125 126 127 128 129 130 13 1 132 133 134 135 136 137 138 139 140 14 1 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 16 1 16 2 163 164 165 166 167 168 169 170 17 1 172 173 174 175 176 177 178 179 iao

24 18 1 18 2 It)3 184 185 186 187 188 189 190 19 1 192 193 194 19 5 196 197 198 199 200 20 1 20 2 20 3 204 205 20 6 20 7 208 209 2 10 211 212 213 214 215 2 16 217 218 2 19 220 22 1 222 223 224 22 5 226 227 228 229 230 23 1 232 233 L 234 C CCINVkKT 10 INTEkbJATIUNAL UNITS AND PRINT 235 236 237 238 239 240

25 24 1 24 2 24 3 244 24 5 246 247 24 249 250 25 1 252 253 254 255 256 257 258 259 260 26 1 26 2 26 3 264 26 5 266 267 26 8 26 9 270 271 272 273 274 275 2 76 277 278 279 280 281 282 283 284 28 5 286 287 288 289 290 29 1 29 2 2 93 294 295 296 L 29 7 1 FCIRMAT (13) 29 8 2 FUKNAT loFLL.4) 299 3 FORMAT (ALAD) 300

26 , .... , ,. ~

30 P 30 2 30 3 304 305 306 30 7 30 8 309 310 311 312 313 314 315 3 16 317 3 18 319 320 32 1 322, 32 3 324 325 326 32 7 328 329 330 33 1 332 333 334 335 336 337 338 339 340 34 1 34 2 343 344 3+5 346 34 7 348 349 350 351 352 35 3 354 355 356 357 35 6 359 360

I 36 1 36 2 363 364 36 5 366 36 7 368 369 370 371 372 3 73 374 375 376 377 378 3 79 380 38 1 38 2 38 3 384 385 386 387

38 8 389 390 34 1 39 2 39 3 394 39 5 396 39 7 39 8 399 400 40 I. 40 2 40 3 40 4 40 5 40 6

28 40 7 40 8 40 9 410 41 1 41 2 413 4114 415 4 16 41 7 41 8

419 420 421 422 42 3 424 42 5 42 6 42 7 428

429 430 43 1 432 43 3 434 43 5 436 437 438

439 440 44 1 442 443 444 44 5 446 44 7 4% 8

29 449 450 45 1 452 453 454 455 4 56 45 7 45 8 459 44 0 46 1 46 2 46 3 464 46 5 46 6 46 7 46 8 469 470 471 472 473 474 475 4 76 477 478 4 79 480 48 1 482 483 484 48 5 48 6 48 7 488 489 490 49 1 492 49 3 494 49 5 49 6 49 7 49 8 499 500 501

30 50 2 50 3 5 04 r 505 506 507 508 509 5 LO 511 512 5 13 5 14 5 15 5 16 517 518 5 19 5 20 52 1 522 523 524 52 5 526 527 528 529 530 531 532 533 534 535 536 537 53 8 539 540 541 542 543 544 545 546 547 548 549 550 551 552 55 3 554

31 555 556 557 55 8 559 560 56 1 56 2 56 3 564 565 566 56 7 56 8 56 9 570 571 5 72 573 574 575 576 577 5 78 579 580 58 1

32 APPENDIX C

SAMPLE PROBLEM

An example of the use of the computer program will now be given with the following conditions: Air at 45.0 psia is to be sealed from ambient air at 15.0 psia using a seal operating in the externally pressurized mode. The mean temperature is 100' F. The sealing dam outside diameter is 6.630 inches, inside diameter is 6.530 inches, and the design speed is 2795 rpm. It is desired to find a design mean film thickness which is large enough so that power dissipation and viscous heating temperature rise are sufficiently low , yet small enough so that the mass leakage is tolerable. From our experience, the best method is to try mean film thickness inputs of 0. 1 to 1.0 mil in increments of 0. 1 mil. The output desired is the mass and volume flow rates, sealing dam force due to the pressure drop, center of pressure, power loss, and approximate temperature rise due to shearing. A check on the validity of the analysis is made by examining the Mach number, Knudsen number, and rotational and pressure flow Reynolds numbers. Thus the program input will include

Speed of rotation, N, rpm 2796 Molecular weight of gas, m. lbm/(lb-mole) 28.9660 Pressure at inner radius or inlet, P1,psia 15.0 Pressure at outer radius or exit, P2, psia 45.0 2 Absolute or dynamic viscosity, p, lbf-sec/ft 3.06~10-~ Specific heat at constant pressure, Cp, Btu/lbm-'R 0.24 Mean film thickness (increase in increments 0.1 to 1.0 of 0. l), hm, mil Temperature, T, OF 100 Inner radius, R1, in. 3.265 Outer radius, R2, in. 3.315 Specific heat ratio, y 1.4 ~~

The data sheet for this sample problem is shown in table III. The sample output, with all possible output options are shown in both English and SI units. Note that the analysis is invalid for film thicknesses greater than 0. 5 mil (where the Mach number has exceeded l/n=0.845). The pressure and velocity distributions, torque, and plots of pressure and power versus mean film thickness are included for a more detailed ex- amination of this problem. This problem ran in approximately 0.1 minute on the Lewis computer.

33 Data for Sample.Problem SHEET-OF-

STATEMENTNUMBER 85 FORTRAN STATEMENT lDENTlFlCbTlON

$ 2 3 ~r 5 6 1 8 9 iD II 12\13 IC 15 I6 17 18'19 20 21 22 23 2LI25 26 27 28 29 3d 31 32 33 3lr 35 36 31 38 3V LO hi '11~36'15 '6 '7 '8 '9 50 51 52 53 S~/5556 51 58 59 60'6162 636' 65 66:61 68 69 10 11 12 13 IC 75 16 11 18 19 81 I , I""'1 """"" """'

A+-++-.~,& ' ' ~;AM:PLEI,PR.o.B~L~M_ . :~ : : , ' L_C-.-+* * + .-*cC_-:, , : , , , ~ :

-t44- '::::- ', ~ '' i,/--*+*- . , ~ :

A4* I , + , I A -4 L 3 CI i t . + , . t + & I * I _c_d + 1- -.-C?.+:: ', -:::!.':

-., * +. , , , * + +-, ,., * +..- +., ,~.I t . . I b t. * - L * *. I 3,* I. - * .*~++-- .++- e+ --I-

~- j I 2 3 L 5 ' 6 7 E 9 10 II 12 I3 14 15 16 I7 I8 19 20 21 22 23 21 25 26 21 2E 29 3[I 31 32 35 3lr 35 36 31 38 39 10 Irl LZ Ir3 '< G5 46 (rl LB L9 50 51 52 5s 5) 55 S6 51 58 59 LO 61 62 63 6' 65 66 61 68 69 10 11 72 13 1L 75 16 17 18 19 8

NASA-C-836 IREV 9-14-59) , O--72'1

P COMPRESalL3Lt bkALINC. UAM nllti UUTAJIUN ANU PARALLEL SUHFACES

SAMYLt PKULILtM

INPUI UATA -

PLvPbI A PltI'SIA TlOEG F VISCOSITY vL8-SECIFT2 MOLECULAR WEIGHT c PIcv 43.U0UL 15.000U 100. 0.38600E-06 28.9660 1.40000

R2, INLHE S K 1 ,INLtiE L t 1 NC Htb RHO ,L 8-S ECZ /F T4 R Ho ( RO T 1 L 8- SEC 2 /F T4 NO OF GRID POINTS 3.3150C 3.2b50U 0 0 0 11

NsKPM v, F T/bEL CPWI~TU/L~-OEGR SKIP A SKIP R SKIP T 2796.0C il 0.24000 F

tlm (NOI1 , LS-SEZL/F T4 &Hi) (11 v L8-SEC2/FT4 A(SWN0 SPEED), FT/SEC SPEEOsRPM 0.53jZlE-02 0.224 70 t-U2 1160.08 2796.00

GAS CU~bTANI,FT-Ld/L~(Ml-Ut~K L ,IiYLHES AREA, IN2 V ,F T/ SEC 53 .hLL 2u.b717 1.03358 80.2750

HtAN FILM MiUUTI U MACH KktP) RE(R1 KNUOSEN F xc XC F INLHES Lb/MIN SCFM i MAX) NUMBW LB INCHES BAR BAR 0.10UE-u2 \NALYSIS NOT VALID L.9 aoE- 03 \NALYSIS NOT VALID C. B00E- 03 \NALYSIS NOT VALID C -7OUE- 0 3 4NALYSIS NOT VALID C.603E-03 \NALYSlS NOT VALID C.500E-03 -0.242 -3.166 0.670 377.006 43.605 0.005 18.125 0.318E-01 0.635 0.585 C.450E-03 -0.176 -2.3Ud 0.543 274.638 39.244 0.006 ~8.125 0.318~-111 0.635 0.585 C.4CUt-03 -0.124 -1.021 0.429 193.027 34.884 0.007 18.125 0.318E-01 0.635 0.5 85 C. 350E- 03 -U. d30t-01 -1.086 0.328 129.313 30.523 0.008 0.635 0.585 C 300E- 0 3 -0 5 Lit-01 - 0.6 84 0.241 81.433 2 6.163 0.009 18.125 0.318E-01 0.635 0.585 C.250E-03 -0.302E-01 -3.396 0.167 47.126 21.802 0.011 18. 125 O.~LBE-OL 0.635 0.585 C.~C0€-03 -0.135t-Cl -U.243 0.1U7 24.128 17.442 0.013 ~8.125 0.318~-ai 0.635 0.585 c. i50t-uj -L).~~~L-oz-0. n55~-01 0.0bU 10.179 13.081 0.018 18-125 0.318E-01 0.635 0.585 C. h0E-03 -O.lY4E-G2 -U.253t-U1 0.OL7 3.016 8.721 0.026 18.125 0.318E-01 0.635 0.585

MtAN fILM,INCIiES PO WE K,H. P. SHEAK HEATvBTU/MIN 0ELiT)tDEG F TORQUE F T-L 8 a. iuuE-uZ \NALYSIS NOT VALID c. 90UE-43 \NALYSIS NOT VALIO C.800E-03 \NALYSIS NOT VALIO C.700t-33 \NALYSIS NOT VALID L.60UE-03 \NALYSIS NOT VALIO 6.5COE- 03 0.77908E-03 0.33048E-01 0.56909 0.9195 1E-02 c. 450~-a3 O.bb564E-03 0.36 720E-0 1 0.86739 0.1021 7E-01 C.400t-03 0. Y 13n5~-03 0.4131 IE-01 1.38Y39 0.11494E-01 C.350E-03 0.11 13OE -02 U .47 2 12E-0 1 2.37023 0.13136E-01 c. MOE-O~ 0.129385E-02 0.550dlE-01 4.39115 0.15 325E-0 1 C. 250k- 03 a. 15582~-02 0.66097E-01 9.10548 0.18390E-01 C.200E-03 0.19477E-02 0.8262 It-0 1 22.2302 0.22988E-01 C. 150E-03 0.25 96 9t-02 0.11016 70.2583 '0.30650E-01 G. lWE-U3 ~.~~YS~E-JL 0.16524 355.683 0.45976E-01 w cn w Q,

HtAN k1LM = u.5UJt-05 1NLrltb

x, lIULtlLS P/?(Mlhu) P,PbI ULUVu) ,kT/StC MACH NO 0 L. UJOUU L>.UUdU 71I .L5 1 0.66992 0.5Wt- L2 1 .r)4368 LO. l>52 57M.3&0 0.49857 11. luuk- C i I. 01546 24.2319 4M1.374 0.41469 0.15Jc- L 1 1 .a4730 L 7. 71 U4 42U .6b5 0.36264 C.2OuE- i L L .u 5294 5u. 7543 31 d .55Y D .32632 0.Z50k- CL 2.23945 33.5Yl 7 347.U50 0.29914 c. 3CruC- c 1 2.41133 j4.1700 522 .294 11.27782 0.32UE- CA L. 57151 58.212 I 302.218 0.26052 0.4011i-Cl L.722u7 4u. 6310 285 -502 0.24611 c .4 Jut- c 1 2. ~0431 4L.Yb 17 2il.305 0.23387 0.5 but- L A j.dclOU0 45. 0000 L59 .J52 0.22331

#tAN FILM U.45Ut-L3 INLHtS

X, INLHt S P/P (MI&) PtPSI IJ(AV) ,FT/SEC MACH NO 0 1 .UUUOO 15.00UO 629.497 0.54263 0.5Uut- CL 1-345bM 2U. 1552 4b8.488 0.40384 O.1UUt-C 1 1.0154b 24.2319 3M9.610 0.33590 0.15Ot- Cl L.d4?30 27. il04 34u .755 0 - 29313 0. LOUT- c L L .u3294 30.1940 300.033 0.264 32 0. L 5UE- C 1 2.23945 33.59L 7 281.095 0.24231 0.3uot- Ll 2.4113, 36.1700 261.058 0.22504 d.350t-C 1 2.57151 3t1.5727 244.796 0.21 102 0.400t- L 1 2.12207 40.6310 231.257 0.19935 0.45Ut- Cl 2.86451 42.9617 219.757 0.18943 0.5 OOE- C 1 3. 11GUUO 45. ooou 209.d32 0.18088

HtAN FILM = J.+OJE-03 INCHtS

X, IPiCHE 5 P /P ( MIlhJ PtPSl ULAV) ,FT/SEC MACH NO 0 1. JUUOG 15.uu0u 497 -38 1 0.42075 0.500t- c2 1.34368 LO. 1>52 37U .163 0.319 09 11. 1UUk- C I 1.61546 24.23 19 307 .ab8 0.26540 0.15UE- C 1 1.84136 27.71114 269.239 0 -23209 0.200t-61 2.05294 30.7Y40 24.Z.278 0.20885 0.250E- C I 2.23945 33.5917 222.099 0.19145 0.3OOk- C I 2.41133 36.1700 206.268 0.17781 0.35Ot- C 1 2.57151 38.5727 193.4 19 0.16673 11.400E- C I 2.12207 40.831 11 182.722 0.15151 0.450t- C1 2.66451 42.9677 173.635 0.14968 0.500t- C1 4.1)OUULI 45.0000 165.794 0.14292 AEAN FILM = cl.?jdt-Lj IiYLrIEb

A, INLHt 5 P/P [MINI PYPbI dIAV1 ,FT/SEC MACH NO I) 1.u00u0 15.0000 380.dU7 0.32826 0.5bOt-CL 1 -54jbQ 20.1552 283.406 0.24430 u. 1UUE- Li 1.01544 24.23 19 235.726 U -203 20 O.13Ut-LI 1. 84 734 21.7104 LU6.ljb 0.17769 u. 2uut- L 1 2.U5L94 5 0.79ru 105.494 0.15990 G.L>JE- L I 2 .2j945 33.291 7 170.345 0.14658 (;.3tiut- ci 2.41153 36.llOil 157.924 0.13613 0.33dt-Ll L.>7151 38.5727 148.U87 0.12765 0.4b0L- ci L.7LL07 4U. b31U 139.896 0.12059 b.45UE- c 1 2.86451 42.9u 7 7 132 .Y4U 0.11460 u. 5uut- c1 J.00iNO 49.u000 126.936 0.10942

MtAN F~LH= b.jUdE-u3 INiHtS

At IIUCHES P /P (MI") PYPSt U(AV) ,FT/StL MALH NO 0 I. OU0bU 15.U000 279.177 0.24117 u.5u0t- CL 1.34JOd LO. 1552 208.217 0.17949 U.1UUt-Ci I. bi540 24.L319 173.187 0.14929 0.1 SUE- C 1 1.04136 27.7104 i51.447 0.13055 ti.2UUt-Ci L.db.294 3u. 7940 136.281 0. 1 17 48 0.23Ut-Ll 2.23943 33.5917 124.931 0.10769 0.3U0€- c1 2.41133 30.17uu 116.026 0.10002 0.35dt- C1 2.57151 38.2727 108.798 0.93785E-01 0.4uut- c 1 2.72207 40.8310 102.781 0 .88598E-01 C.450t-Cl L.06451 42.9677 Y7.6b99 0.84 193E-0 1 L.5Ldt-Cl 3.uuuou 43.uu0u 93.2588 0.80390€-01

MtAi'i FlLM = U.250E-03 INCHES

Xt li\LHt 5 P/PlMIN) ?,PSI U(AV) ,FT/SEC 0.16748MACH NO 0 I.0uoou 13. uo00 194.Ld9 0.5 uuE- CL 1.343b8 iu. 152z 144.5Y5 0.12464 lj. IrJUt- GI 1 61546 24.2313 120 .2s9 0 -10367 c.150t- ci 1.U47jb 2 7.71 04 105.171 O.YO659E-01 0.L0UE- c 1 2 .U 5294 30.7940 94.6397 0.8 15 8 1E-0 1 C.25UE- Li L. 25945 33.5917 d6.7576 0 s 1.47 8 6 E- 0 1 0.300t-C1 2.41133 36.170U 80.5735 0. 69455 E- 0 1 U.35Uk-CI L. 31151 38.5727 75.5544 0.65129E-01 0.4UUt- L 1 L.7220I 40.83~0 7 1.3756 0.615 27 E-01 C.45Ut-L1 2..86451 42. 9b77 67.8263 0.58467E-01 U.500E-GI 3.000u0 45.0000 64.1b3 1 0 .558 27 E-0 1 CIEU-4 FILM = U.L00E-U3 lNCHES

Xi INCHk.5 P/P [MINI PlPSI U(AV) iFT/SEC MACH NO 0 I. 000uo 15.UUOO 124.345 0.107 19 0.501)E- L2 1.34368 20,1552 92.5409 0.79771E-01 0.lUUt- Cl 1.61546 24.2519 76 -97 19 0.663 5 1EO1 0.15Ut- C 1 1.84?36 2 T. 71 UQ 67.3996 o.~~o~zE-o~ 0.2UUE- C 1 2.05294 3 0.7’940 bo 56 9.4 0.52 2 12E-0 1 C. 250t- L 1 2.23945 33.5917 55.5249 o .47a63~-oi 0.3 (JOE--L 1 2.41133 30.1700 51.5670 0 -4445 1E-0 1 0.350E-Cl 2.57151 58.5727 +a. 3548 0.41682E-01 0.40Ut-Ll 2.72207 40. a31 u 45 .b804 0.39377501 0.450t- C 1 2.86431 42.9677 43.4086 0 -374 19E-0 1 3.5UUt-Cl 3.u0000 45.0000 41 -4464 0.35729E-01

MEAN FILM = U.15C)E-03 INTHES

XIINCHES P /P i MIN ) PIPS1 U(AV) sFT/StC MACH NO 0 1.00000 15.U00U 69.9441 0.602 93501 0.5Wt- CZ 1.34368 L0.1552 52 -0542 0 -44871 E-01 o.lou& 21 1 .61S46 24.L31Y 45.2967 0.37322E-01 L;. 15OE- C 1 1.64736 27. 71 U4 37.trb17 0.32637 E- 0 1 0.zuuc- C 1 2 .U5294 3 0.7340 34.0703 0.29369E-01 0.L50E- Cl L .23Y45 35.591 7 31.2327 0 -26923E-01 0.iOOE- Cl 2.41133 36.1700 29.0064 0.2 50 04 E-0 1 U.550E- c1 2.57151 38.5127 27.1995 U. 23446E-01 0.41)l)t- L1 L.7221)7 40. u310 25.6952 0 .22 1 50 E-0 1 0.42UE- C 1 2.66451 42.96 77 24.+175 0.2 1U48E- 01 C.500t-C1 3.u00u0 45.0Ud0 L3.3147 0. 200 9a~-o1 MEAN FlLM = O.1Odt-03 INCHES

Xv INCHt 5 P/P i MIlu) PlP51 U(AI/) ,FT/SEC MACH NO 0 1. 0owo 15.UO0U 3 1 .Dub3 0.267 97 E-0 1 c.50ut- CL I. 34368 Zd.1522 23.135Z 0.19943E-01 0.1OOE- Cl 1. 61546 24.L51Y 19.2433 0. A 65 a8E- o 1 G * 1 SUE- L I 1.84130 L 7.71 04 io. a274 0.14505E-Ot 0.2UOE- LA L.05294 50. 7Y40 15.1424 0. 1 30 53E-0 1 0.L5UE-Cl L .L3Y43 33.5917 13.8812 U.lLY66E-01 0.3UOt- C 1 2.41133 36.17dc) 12.8918 0.111 13E-01 0.33ut- Cl 2.57151 3d.5727 12. 0d 8 7 0.1042 1E- 0 1 0.40UE- LL 2.1LLOK 40. Ujld 11.423 1 0.9a443E-02 0.42ut- c 1 2.86451 42.9b77 10.8522 0.93547E-02 O.50Ut-Ll 3.C)OOUU 45.0000 10.3621 0 .a9322k-o2 PLOT OF PIJWEK VS H(M€AN)

* * * * *

HLMEAN) IN INCHtS - TO CUNVEKT 10 METERS, MULTIPLY BY 2.54E-2

FOR SHEAK HEAT IN BT~IMIN~ MULTIPLY POWER BY 42.42

W CD *

1 2.001 1 1 1 1 1 1 1 1 1 1.501 I 1 1 1 1 1 A 1 1 1. 00* 1 1 1 1 1 I 1 1 LUMPKESSIdLt StALING JAM WITH HUTATIUN AhU PPKALLEL SURFACES

SAHt'L E PKUOLEM

P21 N/M2 PI N/M2 T,0tb 1( VLSCOSITY,N-S/MZ MOLECULAR WEIGHT CP/CV 0.31UL6t Cb U.lU342t 00 311. 0.1848LE-04 28.9660 I .4D00D

KL,MtTEd 5 KlpMETtttS L,MEi t RS KHO, K G/ M3 RHOIROT) iKG/N3 NO OF GRID POINTS 0.842Ult- Cl 0. 8LYrllt-Ul U 3 0 11

IhsKYS V,M/S LPvJ/KG-Dtb K SKIP A SKIP R SKIP T 46.6U00 0 1304.78 F F F t)tC-IN OUlPUT UATA

RHO (KUT I t&G/A3 KHU L 1 ) ,Kb/M3 A(S UNO SPEED), M/ S SP E EO ,KP S 2.bULbi 1.16L17 353.591 46.6000

GAS LUNSJb~'JT~J/KG-UtGh AREA, M2 v.n/s 287 .O8b 0 -66683E-03 2 4.46 78

HEAN FiLk MIOUTJ bl RElRl KNUOSEN F xc XC F MtTtKS KC/SEC SLMS NUMBER NEWTONS METERS BAR BAR 0. i54E- 04 ANALYSIS NOT VALID C.229E-04 ANALYSIS NOT VALID 0.201)t- U4 ANALYSIS NOT VALID 0.178E-U4 ANALYSIS NOT VALID O.152E-04 ANALYSIS NOT VALID 0.1Z7E-U4 -0.183t-02 -0.149€-02 3.670 377.006 43.605 0.005 80.623 0.807E-03 0.635 0.585 0.114E-04 -U.l33t-CZ -U.lJYk-OL U.543 274.838 39.244 0.006 80.623 0.807E-03 0.635 0.5 85 O.lO2t-04 -0.937E-03 - 0. 705k-03 0.4L9 lY3.U27 34.884 0.007 80.623 0.807E-03 0.635 0.585 C b8Y E- U 5 -U .b 2 7 E-03 - U. 5 1 LE- 03 0.328 129.313 30.523 0.008 80.623 0.8C7E-03 0.635 0.585 0.76Lt-U5 -0.355E-C3 -0. 32 jk-03 U.241 d1.433 26.163 0.009 80.623 0.807E-03 0.635 0.585 0.635E-O> -0. LL9E-03 -0.16 7E-03 0.167 47.126 2 1.802 0.011 80.623 0.807E-03 0.635 0.585 0-5C8t-05 -0.lllE-03 -U.Y5bt-04 0.107 24.128 17.442 0.013 80.623 0.807E-03 0.635 0.585 0.38 IE- 05 -0.4Y'lt- C4 - 0.40,t-U4 u.L)bJ lU.179 13.081 0.018 80.6 23 0 8 07E- 03 0.635 0.585 C.254E-05 -U. lroE-C4 -U.lLOt-U4 U.UL7 3.016 8.721 0.026 80.623 0.807E-03 0.635 0.585

MEAN ttLApMC1EhS POWER #AT TS TUTAL HEATSWATTS DtLITIrDEG K TORQ UE 9 N-M 0 eZ54E-04 ANALYSIS NOT VALID 0.22YE-04 ANALYSIS NOT VALID C. 2C3E-04 ANALYSIS NOT VALID C. 178E-04 ANALYSIS NOT VALID 0.15ZE-04 ANALYSIS NOT VALID 0.127E-U4 0.5809b 0.58158 0.31616 0.12467E-01 0.114E-04 0.4455 A 0.64b20 0.48 188 0.13852E-01 0. AQLE-04 0.72 bL 0 0.7269 8 0.77188 0.15 584E-01 c .&ti9 E-05 0. b2 994 0.83083 1.31680 0.178 10E-01 (i.762t-US a. 96 826 U.96930 2.43953 0.20778E-01 0.635E-U5 1. A6191 1.16310 5.05 860 0.24934E-01 0.5G8E- U5 1.4iL39 1.45395 12.3501 0.31 l67E-01 0.38lE-05 1.93652 I. 93860 39.0324 0.41 556E-01 0-254E-05 L.YO479 2.90790 197.602 0.62334E-0 1 METEHS

Xt Mt Str( 5 P /t' 1MIN) P, h/MZ UIAV) iM/btC MACH NU 0 I.cjUUJ0 U.10342t 00 236.817 0.66992 0.1~7t-Cj I a34366 d.lj8Y7t Ub 17b -290 0.49857 0.L54t- C> I. 01546 0.1b7U7E U6 140.b31 0.41469 0.3b LL- LJ I. d4 I30 11. 191 UbE Ub 128.225 0.362b4 U.SCJt- CJ 2.J5294 11.212JLE 06 115.385 u .32bJ2 U.bj>t- C3 2.23Y45 U.23161t Ob 105.775 0.299 14 0.762t- Cj 2.41133 U.24Y3dt U6 Y6.2352 0.27782 O.t(tlYt- (3 2 .> 7151 O.Z65Y>t Ob 92.115'1 0.26052 0.1ULc-CL L.722dI O.Zd152E 06 ti7.0211 0.246 11 b.lI+t- CL 2.06431 U.29b25t 06 82.6938 0 -23387 U.IL7t-LL 3.UUUUG 0.3102bE Ob 7ti.9592 0.22331

HENq FILII = U. 11 45UE- b4 MErEni

X,MtltdS I' /I' (MINI P, h/M2 U(AV),M/StC MACH NU 0 1 .UOUU0 u.10342E 110 1'1 1.871 0.542 b3 0.117E-Cj 1.34jb6 O.13897t db 142.7'35 0.40364 U.L>+t-Lj bl>4b 0.107U7k 3b 118.771 U -33590 U.38lt-Lj I. a4 730 UslqlOt~E11b 1u3.abz 0.29373 U.51r8E- L3 2.1152'14 0.LlLjZt 36 93.461s 0.264 32 0.635t- C3 2.23945 0.2316lt 06 85.6776 0.24231 0.76k- LA 2.41133 0.24938E Uo 19.5735 0.22504 0.889t- L3 2.57A31 O.Zb595t db 74 -6139 0..21102 0. 1OLt- LL 2.12207 U.LdL52t 06 7U.vd71 0.19935 0.114t- C2 2. 8645~ O.L9625E 00 ob.9821) 0.18943 0.12 7t- L2 3.dOUU0 0.3LUZoE d6 b3.95b9 0.18088

MtAN FILh = J.lJIbOE-U4 M€ TEK S

XpMtTtdS P/P(MINl PiN/M2 U(AV1 iM/SEC MACH NO U 1 .000UU 0.10542t 00 151.b0.2 0 -428 75 0.lL7t- C3 1 .34308 0.13B97k Ob 112.626 0 - 31909 0.254E-Cj 1.6154b O.lo707E Ob 93.8441 0.26540 0.38 1€- L 3 1. d4 7 36 U.lY10bE 06 82.0639 0.23209 0.5Udt-L3 ,?.US294 U.LlL32t 06 73 .d4b2 0.20885 0.63>t-C3 2.23945 0.23161E Ub b7.bY59 0.19145 0.762E- C3 2.4 1133 0.24938t Ub b2.8705 0.17781 0.869E-C3 2.57151 0.26595E 06 56.9542 0.16673 0. GL 2.72207 U.28152E Ub 55.69 55 0.15751 0.1 14E- Ci 1. t) 6451 0.2Yb25t 06 52.9241 0.14968 O.lZ7E-CZ 5.00d00 0.310LbE 06 50.5339 0.14292 MErtKS

P, WML U IAV 1 ,WSEC MACH NO U.1034LE Ub 116.370 0.32826 u.13897E 00 Mo.3823 0 -24430 J.161U7t Jb 71.64Y4 0.20320 J.lY1UbE Jb 62.~3332 0.17769 U.21152t UlJ 56.5365 0.15990 d.23lblE Oa > 1.M7.9 7 0.14658 U.24Yjdt Ob 48. 1352 0.136 13 O.Lo5Y5t Ob 45.1368 0.12765 0.26152t 36 42.6404 0.12059 O.LYbL5E Ob 4U.5LOU 0.11460 U.31U26t Ub 38.bYOJ 0.10942

MtTtKb

P/P(MIN) P, h/M2 UIAV 1 ,M/bEC MACH NU 1 .UUOOU 0.10342t Ob 85.2759 0.24117 1.343bO U.ljMY7L 06 63.4645 0.17949 1.61>46 (1.1bliJ7E Ob 5L.7t115 0.14929 1. d473o O.19130t Ub 46. 1609 0.13055 2. J5L94 J.21132t 06 41.5585 0.11148 2.23945 0.2 31 61 E Jb 311.0789 0.10769 2.41133 U.2493dt ab 35.3647 0.10002 2.57151 0.2b395k Ub 33.1617 0.93185E-01 2. 72.207 O.Ld152t 06 51.3276 0 .d8598€-01 2.86451 JaL9625t Ob 29.1698 0.841 93 E- 01 J.UOUOU 0.31026E Ob 2M .4253 G.80390E-01

MtTEKS

XI M t T ti< 5 P /I' (MIN 1 P,IU/MZ UIAVI ,M/SEC nAcn NO 0 1 .OOiNJU U.lJ342t Ob 59.21Y4 0.16748 0.127~- C3 1.54368 G.lja97E 00 44.0726 0.12464 u.z>4t- c3 1.6 1546 0.16107k Ob 36.6579 0.10367 O.38lt-C3 1.d415o 0.191Obt Jb 32.0562 0.90659E-01 0.51;dt-Cj L .us294 O.2lZjLk Ub 2M .M462 0.81581E-01 0.635t- ill 2.23945 O.23lOlt Ub 26.4431 0.14786E-01 0.76iE- C3 L.41133 0.24938t Ob 24 -55tiM 0.69455E-Of O.Bart-c3 L.57151 U.26595E Ob 23.0290 0 -65129 E-0 1 0. IOLE- LL 2.72207 O.ZMl5LE Ob 21.7553 0.61527E-01 U.114E- C2 2.86451 0.29625t 00 20.6135 0.58467E-01 0.127E-CL 5.JOOGO 0.31026E J6 1Y.159M 0.55827E-01 kt ItKS

JIAVI tM/SkL MACH NU S7.9J04 0.10719 LtJ.2005 0.79771t-01 23.45 13 0.6635lE-01 Ld. 5160 U.5dUL2E-01 18.40 16 0 -522 12 E-0 L Lb.Y243 0.47863E-0 1 13.7175 0.44451E-01 14. 73d5 0.41682E-01 13.YL34 0.39377 E-0 1 15.2313 0.374 19E-01 12.6335 0.35729E-01

X,M E lkK 5 lJ/PlkI[u) P,N/MZ LI 4 AV I ,M/ SEC MACH NO 0 1 .u0000 0.10342t Ub 21.3lYO U.60293€-01 0. 117E- L3 L -341)bb U.13897E U6 15.8661 0.44871E-01 U.L54E-C5 1.41540 O.lb707E uo 13.1Y6d 0.37 322 E-0 1 U.361t-C3 I. 84 13b 0-1910bE Ob 11.54U2 0.32637E-01 0.50dt- L3 2.0 5L 94 0.2123Lt 06 10.3846 0.29369t-01 0. b35t- C3 L .L3Y45 0.23161E Ob 9.51974 0.26923E-01 0.762E-C3 2.41153 0.24938E U6 8.84117 0.25004E-01 0.869t-C3 2.57L51 0.26595~ u6 8.29243 0.23446E-01 0.102E- CL 2.72207 0.28152E 00 7.831YU 0.221 50E-0 L U -114E- CL 2.86451 U.29b25t 06 7 -44245 0.21048 E-01 0.lL7t-CZ 3.00GU0 U.31U26E 06 7.10b32 0 .ZOO 98E-0 1

MEAN FILM = U.L54UUE-O5 MtTERS

X,METtK 5 P/P(MINl P*N/M2 U(AVI ,M/SEC MACH NU 0 1 .UO000 U.lU342E 06 9.475 10 0.26 797 E-0 L 0.lL 7E- c5 1.34368 0.138Y7E 06 7.05161 0.19943E-01 0.254E-C3 1. b1540 0.16707E Ob 5 -86526 0.16588€-01 0.38lt-13 1.84136 0.1Y106E 06 5.1289Y 0.14505E-01 0.5 OdE- C3 2.05294 d.21232E 06 4.6 15 39 0.130 53E-0 1 I 0.655E- C5 L .2 394s 0.L3161E 06 4.23099 0 .1 19 6 6 E-'0 1 0.7blE- C3 2.41133 U.24938k 06 3.92941 0.11 1 13E-0 1 a.mYt- cj L.57151 O.L6595E 06 3.68464 0.1042lE-01 0. 1ULC- c2 2.72207 d.28152E 06 3.48985 0.98443E-02 0.1 14t- L2 2.86451 0.29625E Ub 3.30775 0.93547E-02 i O.127t-CL 3.00000 0.3102bt 06 3.15837 0.89322E-02 I

-E.- Ia _. - REFERENCES

1. Zuk, J. ; and Ludwig, L. P. : Investigation of Isothermal, Compressible Flow Across a Rotating Sealing Dam. I - Analysis. NASA TN D-5344, 1969. 2. Johnson, Robert L. ; and Ludwig, Lawrence P. : Shaft Face Seal with Self -Acting Lift Augmentation for Advanced Gas Turbine Engines. NASA TN D-5170, 1969. 3. Hughes, W. F. ; and Gaylord, E. W. : Outline of Theory and Problems of Basic Equations of Engineering Science. Schaum Publ. Co. , 1964. 4. Dellner, Lois T. ; and Moore, Betty Jo: An Optimized Printer Plotting System Con- sisting of Complementary 7090 (FORTRAN) and 1401 (SPS) Subroutines. Part I. Instructions for Users. NASA TN D-2174, 1964.

NASA-Langley, 1969 - 15 E-5109 45 NATIONALAERONAUTICS AND SPACE ADMINISTRATION WASHINGTON,D. C. 20546 OFFICIAL BUSINESS FIRST CLASS MAIL

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