NASA Contractor Report 185156

User's Guide to PMESH--A Grid-GenerationProgram for Single-Rotation and

Counterrotation Advanced Turboprops

Saif A. Warsi

Sverdrup Technology, lnc.

NASA Lewis Research Center GroupCleveland, Ohio

December 1989

Prepared for

Lewis Research Center

Under Contract NAS3-24105

National Aeronautics andSpace Administration

(NASA-CR-I,351<O) USERi5 GUfDE TO PMESH: A

G_IP,-GENEPATION PROGRAM FOR SIt_C_LF-POTATIQN

AN_ COUNT_RROTATIqN ADVANCED. TUR',3OPR;JPS

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USER'S GUIDE TO PMESH - A GRID-GENERATION

PROGRAM FOR SINGLE-ROTATION AND

COUNTERROTATION ADVANCED TURBOPROPS

Saif A. Warsi

Sverdrup Technology, Inc.

NASA Lewis Research Cen_er Group

Cleveland, Ohio 44135

ABSTRACT

This report presents a detailed operating manual for a grid-generation program that produces three-

dimensional meshes for advanced turboprops (ATP). The code uses both algebraic and elliptic partialdifferential equation (PDE) methods to generate single-rotation and counterrotation H - or C - typemeshes for the z - r planes and H - type for the z - 0 planes. The code allows easy specificationof geometrical constraints (such as blade angle, location of bounding surfaces, etc.) and mesh-controlparameters (point distribution near blades and nacelle, number of grid points desired, etc.), and it hasgood runtime diagnostics. This report provides an overview of the mesh-generation procedure, a sampleinput dataset with detailed explanation of all input, and example meshes.

INTRODUCTION

Three-dilnensional computational fluid dynamic codes require grids with suit.able resolution and smooth-

ness, These qualities are especially difficult to maintain because of the taper, twist, and sweep of realistic

turboprop geometries. Grid resolution near shocks and in shear layers allows for complex fluid physics to

be captured. Smoothness of the grid prevents truncation errors, arising from the discretization of the flow

equations, fl'orn dominating the solution.

This report describes a code for generating three-dimensional grids for advanced turboprops. The code

uses mainly algebraic methods such as (1) Ferguson's parametric cubic curves, (2) cubic splines, and (3) cubic

curves to generate meshes. Elliptic partial differential equations (PDE's) are used for further sn_oothing in

certain cases. The resulting meshes, regardless of whether tt - or C-type, have in common a two-dimensional

axisymmetric mesh (common z and r coordinates) , only varying in the 0 coordinate within the passage.

The resulting meshes may be written in a variety of formats to conform to the input required for different

flow solvers. For example, for the Adamczyk average-passage code (ref. I), a counterrotation mesh can bewritten so that each blade row has its own H-mesh which describes a full passage fl'om inlet to exit with

each respective mesh accounting for its own blade thickness while applying zero thickness to the neighboringblade row.

GEOMETRY AND MESH-GENERATION DESCRIPTIONS

The generation of computational meshes for advanced turboprops consists of a number of steps. First the

user-supplied nacelle and blade shapes, as well as geometrical and mesh quality constraints are read. Fromthis input, the common two-dimensional axisymmetric mesh is created by using a series of paramet, ric cubic

curves, cubic splines, and, in the case of C-type meshes, by limited use of PDE's for further smoothing.

Second, the resulting two-dimensional meshes are smoothed by using equal-weighted averaging. Third, the

0 - coordinate surfaces are generated, based on the 0 coordinates of the given blade and the user-specifiedblade angle. Finally, the mesh is interpolated to the periodic angle and written subject to user requirements.

The geometry for the blade and spinner is provided by the user. The spinner/hub shape is input as (z,r)

pairs with z increasing monotonically from the spinner stagnation point or inlet suffa.ce, downstream to the

outflow boundary. The data is in the same scale as the blade geometry.

Tilebladedefinitionisgivenasbladesectionsspecifiedonplanesperpendicularto astackingaxiswhichisalsothepitch-changeaxis(PCA).Thesections(stations)arespecifiedfromnearthehubto thetip withthedistancealongthestackingaxis(rb) increa.singmonotonically.At agivenstation,thesectionislocatedwith thelocaltwist angleA/3 (dbet) based on the blade angle at 75-percent blade radius /3a/4 (beta34),

leading-edge alignment (lea), face alignment (fa), and chord length (el). Tile section shape is given in anormalized coordinate system (x/el, ys/cl, yp/cl) with points on tile suction and pressure surfaces from the

leading edge to the trailing edge. Figures 1 and 2 describe this geometry.

The preceding parameters are used to convert the blade sections to a cylindrical coordinate system. Then,

user-specified point distribution (with respect to uniform unit spacing) and the following hyperbolic tangentdistribution are used to generate a distribution of normalized points . Let

A_

1B-

where [ is the number of points and As1, As2 are the fl'actions of uniform spacing.Solving the following nonlinear equation for 6

sinh J-B

6

gives the unit-segment point distribution as

,(e) = ,,(e)A + (1 - A)u({)

w]lere

1 tanh[6( - 4)],

and _ varies from 0 to I. See reference 2.

By using this normalized distribution, the points on each blade section are redistributed axially. The

sections are then converted to constant radial sections. The initial curve designs for the two-dimensional

mesh are done with Ferguson's parametric cubic curves (ref. 3). These curves are defined as follows:

r = r(u) = a 0 + ua 1 + u2a2 + vaa3

where0<u< 1.

To determine a0, al, a2, and a3, specify tile values ofr and dr/du at both ends of tile segments. Now,a's in terms of the r's may be obtained in matrix form:

the

r(u)= [ 1 u u 2 u3 ]

1 0 0 0

0 0 i 0

-3 3 -2 -1

2 -2 i I

r(0)r(1)i-(0)i,(1)

The derivatives i'(0) and i'(1) are proportional to the unit tangent vectors T(0) and T(1) at the ends of tileof the line segment under consideration. We may write

i'(0) = a0T(0) ; i'(1) = c_lT(1)

By varying the tangent vector lengths, different-shaped curves are easily generat.ed (fig. 3). These curves areused to smoothly splice the z-r curves fro,n the blades to each external boundary. Now the point distribution

on tile Mades and the hyperbolic tangent distribution flmction generate a smooth distribution of points away

from all solid surfaces. Cubic splines along with the new unit point distributions are used to obtain a very

smoothvariationof z and r coordinates everywhere. In order to further smooth the z and r coordinates, an

equal-weighted smoothing is applied. In C-type meshes, the redistribution scheme may cause a high degree

of skewness in the cone region (the rounded region up to the leading edge of the blade). Elliptic PDE's areused to smooth this area (ref. 2). The basic differential equations under consideration are

V={ = P

and

VaT/= Q

where _, 7/ are the coordinates in the uniform computational domain, and P, Q are called the "control

functions". These functions allow the user to control the placement of the grid points in the desired region.IIowever, in this report, the equations solved were

v=[ = 0 (1)aud

c (2)

Hence, tile point distribution is controlled only in the 71direction. However, the solution of equationS 1 and

2 will yield a distribution of _ and 71which is known to be a uniform rectangular two-dhnensional plane

(fig. ,t). Therefore, inverting equations 1 and 2 in order to change the role of the dependent and independentvariables gives

g22r_¢ - 2g12r{, 1 + 9nr_u = -gltQr_

where r is a vector of the physical coordinates z, r and

(3)

g12 = z_z,1 + r_r_

g22 -- zq 2 "4-r_ 2

and

G = (zer, - z, re)2

is known as the square of the Jacobian of transformation. The forcing function may be arbitrary, and theone chosen was

q = -(2 + - 1) • log(x)), log(x)1. + (r] - 1) * log(x)

This function will allow the user to increase the grid c]ustering near the r/= 0 boundary with increasing X(X >_ 1) . Equations 3 are first discretized on the computational plane by central differences and then solved

with a block relaxation scheme where the block was a line in this case (Line SOt:L).Two appendixes are provided to guide the user in the proper use of this program. Appendix A lists and

explains, in detail, all inputs required; appendix B provides a typical input dataset.

RESULTS

Figures 5 to 8 show different views of a counterrotation H-mesh generated by using the attached example

dataset with JNOSE changed to 8. Figure 5 shows a view of the z- r plane; notice the effect of the clustering

factors near the nacelle, tip, and at the edges of the blades. Figures 6(a) and 6(b) show the effect of the

clustering factors (DZLE, DZTE, DZLE2, and DZTE2) on the blade point distribution. DZLE and DZTE

were changed to 0.5 and 1.0, respectively, for the fi'ont blade. Their effect can be seen clearly in figure 6(b).

Figure 7 shows a portion of a full passage via a radial cut at the hub, with the axial index starting just a

few gridlines ahead of the front blade and finishing a few gridlines aft of the rear blade.

Figure8(a)showsthefldl passageviewfor asinglebladecaseviaaradialcutat thehub. In tiffscase,DTIIBLwas0.2;DTIIBLwasthenchangedto 1.0.Theeffectof thischangeisseenin figure8(b).Figures9(a)and9(b)showaconstantaxialcutat theinletandatapproximatelymidchordoftheblade,respectively.

Figure10showsanexampleC-mesh.Togeneratethismesh,thenacelleinputwaschangedto havenosting,CONOPTwaschangedto True, JCONE was set, and CK was set to 1.1.

Finally, Figure 11 shows the surface meshes for a swirl-recovery vane (SRV) grid, a cruise missile (CM)and an advanced single-rotation turboprop (ATP).

CONCLUSIONS

An algebraic and elliptic partial differential equation mesh generator has been developed for generation of

three-dimensional meshes for advanced turboprops and other similar geometries. H- and C-type meshes may

be generated for both single-rotation and counterrotation cases. The program has good runtime diagnostics,and the user may easily modify the mesh-control parameters.

ACKNOWLEDGEMENTS

The author would like to thank Dr. Christopher J. Miller for his valuable contributions to the debuggingand development of this code. The surface grid figures for this report were also produced by Dr. Miller.

APPENDIX AUSER'SMANUAL FORTHE ADVANCED TURBOPROP MESH GENERATOR

The mesh generator is coded in FORTRAN 77 with 34 subroutines and 2 external functions. The code

has been run on a wide variety of computer systems with no coding changes. Figure 12 shows a flow chart

of the main program structure.

The nacelle and blade geometries, the mesh size and spacing parameters, and the controls for miscel-

laneous options are all read from FORTRAN UNIT 7 in the following formats: (1) The majority of real

number fields are read in F10.5 format, while a few are read in free-format (F-F), (2) integers are read usingan I5 format, and (3) logical fields are in read L5 format. In order for the program to operate, the input file

must be named "fort.7". The uppercase lines shown in the following description of the sample input serveas comments and are skipped over by the program; however, they must be included in the input for proper

operation. All actual input lines are listed in their lowercase alphanumeric form. An explanation of all input

follows the sample. Appendix B shows a sample input data.set for a counterrotation case.

title There may be as many lines of text in the title section as the user desires. The only restriction is

that the following line with " PT10" must exist. Note that the leading space in " PT10" is significant.

The title is read with an "A" format; the maximum length of each line is 80 characters.

PT10 PT20 PT30 PT40 PT50-(5L5)

ptl0 pt20 pt30 pt40 pt50 These are logical flags which are read with a (5L5) format. The print flags

(following) print all the coordinates (z, r, 0); if PT30 or PT40 has been invoked, ignore the 0 coordinates.

Until subroutine EXTEND has been called, only the 0 on the blades are correct. When any flag is

True, the program will print the following:

ptl0

pt20

pt30

pt40

pt50

Print all input, as well as the blade geometry or geometries (if two blade rows) in normalized(diameter = 1.) cylindrical form; see subroutine MEREAD.

Print blade(s) after correct axial distribution is applied and the stations are at constant ra-

dius; see subroutine ADJBLD. Also print the fictitious base coordinates; see subroutine FICBAS.

Print the regions comprising the rest of the surface through the blade(s); see subroutines

FORBLD and MIDBLD (used only when generating two blade rows), OUTREG, and CONREG.

Print the blade surface after radial distribution is applied; see subroutine RADJST and then

after the surface not on the blade(s) is smoothed, see subroutines AVGSRF and AVG.

Print the entire, final mesh after all other processing; see subroutine MWRITE. This pro-

duces hundreds of pages of mostly useless output. Use this option only when necessary.

COUNTER-ROTATION - (L5)

cropt Logical counterrotation option flag. Use an L5 format to read. If'Ih'ue, then two blade geometries

will be read from the input, first the front and then the rear. If False, then single rotation is selected .

NACELLE GEOMETRY

NUMBER OF INPUT STATIONS FOt_ NACELLE - (I5)

nn Number of points specified on the nacelle.

zn(1),rn(1) to zn(nn),rn(nn) The actual nacelle geometry, from the nose or any extension, such as a

sting for an H-mesh (1) back to somewhere behind the blade (nn). The pitch-change axis (PCA) of

the (front) blade is used as the axial z origin; upstream of the PCA (toward the nose) is negative. Therotation axis is, of course, the origin radially r. The nacelle geometry should be in the same scale as

the blade geometry(s). The nacelle geometry is read in a 2F10.5 format.

BLADEGEOMETRYBL.DIA. BETA34 NR NC-(2F10.5,215)

diam Thediameterof theblade.Everythingisscaledbytileprogramsothat tile workingdiameterofthe(front)bladeis 1. in theoutputmesh.

beta34 Thevalueofbetaat 75-percentradius.Betais theangle,in agivenplanenormalto thePCA,betweenthechordlineandtheplaneofrotation.

nr Numberof radialstationsin theinput. Thiscanbedifferentfor thetwobladerows,if theuserisgeneratingacounterrotationgrid.Theinputstationsshouldnot includeafictitiousstationof dataatrb = 0 (see following for definition of rb). Station nr is at the tip.

nc Number of stations along the chord line at each blade cross-section in the input. Station 1 is the

leading edge and station nc is the trailing edge.

RB DBETA LEA FA CL - (5FI0.5)

X YS YP X YS YP - (10X,6F10.5)

rb The distance from the rotational axis to the plane containing tim current blade section. This shouldbe in the same units _ diameter.

dbct The angle, in degrees, to be added to beta34 to get the va.lue of beta for the current st.ation, seebeta34.

lea Leading-edge alignment. The distance along the chord line from the point on the chord line closest

to the PCA to the leading edge; lea is positive if the point closest to the PCA is aft of the leading

edge. Same units as diameter.

fa Face alignment. The perpendicular distance from the PCA to the chord line of the current station;

fa is positive if the PCA is on the face (pressure) side. Same units as diameter.

el The chord length (from leading to trailing edge) at the current station. The following blade coordi-

nates are nondimensionalized by this value. Same units as diameter.

x(i),ys(i),yp(i) The blade shape at the current station. Where x is the fractional chordwise distance

(0.0:leading edge to 1.0:trailing edge) and (ys, yp) are the distances perpendicular to the chord line,

normalized by the chord length. The blade section may be input with a finite thickness at the leading

and trailing edges; the program will, however, force the thickness to he zero at the leading and trailing

edges. The (face/lower/pressure) surface is defined by yp, while the (camber/upper/suction) surfaceis defined by ys. Note that data for two x values are on each input line.

MESIt PARAMETERS

ZUP ZDN RINF - (3F10.5)

zup The upstream boundary of the mesh, measured axially from the PCA in fractions of a diameter.

It is in a scale where the blade diameter is 1.0; hence, if the input blade diameter changes this should

stay the same to get the same relative location. It has to be negative. Note that for an H-mesh, zupmust not be beyond the upstream limit of the nacelle input.

zdn The downstream boundary of the mesh. Scaled the same _ zup. If it is beyond the downstream

limit of the nacelle input, the nacelle will be extended straight hack (at the same radius) fl'om its laststation.

The radial boundary of the mesh. If there is no outer region, .i.e., kmax = ktip (see kmax), this

will be ignored, and 0.5 (the normalized tip radius) will be used instead. It is scaled the same as zup

and has to be >_ 0.5 when used.

rinf

CONEFLAG- (L5)

conopt This is theconeoptionflag. If True,thentheconeregion (if present; see jcone) will have a

curved outer boundary (C-mesh nose). If False, then the region will have a rectangular boundary(tI-mesh).

JCONE JLE JSL JTE JMAX KTIP KMAX LMAX-(SI5)

jcone The location of cone region. J is the index in the axial direction; jcone specifies the number of

axial stations in the cone region. If it is zero, there will be no cone region; otherwise, it should be atleast 3.

jle Index of the leading edge of the blade. The region from jcone to jle is called the "fore region", so jlemust be greater than jcone.

jsl Index of the shock line clustering on the (front) blade. If this is zero, there will be no clustering. Seedzsl and cfsl.

jte Index of the trailing edge of the (fi'ont) blade. If generating a single-rotation grid, the region fi'om

here to jmax is the aft region; otherwise, fl'om here to jle2 (leading-edge index of (second) blade row)is the midregion.

j max

ktip

Index of the downstream limit of the mesh (z = zdn). J is the axial index.

Index of the tip of the blade. K is the radial index. The region from 1 to ktip is the region fromthe rotation axis to the blade tip.

kmax Index of the outer boundary of the mesh. From ktip to kmax is the outer region (excluding the

part upstream ofjcone, which is in the cone region). If kmax = ktip, there is no outer region and thetip radius will be the maximum radius instead of rinf.

lmax Number of stations in the circumferential direction, l increases ,as 0 increases.

NBLADE- (I5)

nb The number of blades on the front row.

LOCATE ZLEINF ZTEINF-(L5,2FI0.5)

locflg Logical flag which, when True, will use zleinf and zteinf for the specification of the leading- andtrailing- edge extensions at the outer boundary.

zleinf If locflg is True, this specifies, in the units used for zup, the axial location of the extension of tile

leading edge at rinf. It must be less than zdn and greater than zup. If there is a cone region, it also

should be greater than the scaled-down location of the nacelle nose (zn(1)/diam).

zteinf Same as zleinf, but for the trailing edge. Must be greater than zleinfand less than (zn(nn)/diam),

DZLE DZSL DZTE CFSL DRNAC DRTIP DTHBL - (F-F)

dzle The mesh-clustering factor in the axial direction at the leading edge of the (fi'ont) blade. This isthe fraction of an even spacing on the blade. If it is 1.0, the leading edge will have no clustering, while

if it is 0.1, the mesh will be approximately 10 times denser at the leading edge (compared to uniformunit spacing).

dzsl

dzte

Clustering factor for the shockline on the (front) blade, ifjsl is not zero. See cfsl.

Clustering factor for the trailing edge of the (front) blade.

cfsl If theshock-lineclusteringis selected(jsl isnotzero),the locationof theclusteringonthebladeisgiven,cfslstandsforchordfractionat theshockline;consequently,if thechordDactionis 0.2,timclusteringwill beone-fifthtiledistancefromtheleadingedgebackto tile trailingedge(closerto theleadingedge).

drnac Clusteringfactorin theradialdirectionat thenacellesurface.In theconeregionthisalsogivesacompressionaxiallyin frontof thenose.

drtip Clusteringfactorin theradialdirectionat thebladetip. It isphasedout in theforeregionsothat it hasnoeffectin theconeregion.

dthbl Clusteringfactorin tile circumferentialdirectionat tilebladesurfaces(andtheiraxialandradialextensions).

ZREAR REFL- (F10.5,L5)

zrear If tileuserisgeneratinga counterrotationmesh,thisspecifiesthelocationof therearPCAwithrespectto thefront.Sameunitsasdiameter.Thishasto begreaterthan0.

reflag Logicalflagfor counterrotation.If True,therearbladegeometrywill bereflectedabout0 =

0. before being used. If the front and rear blades have the same shape (i.e., identical input), only

reflected, the front geometry can be copied and this flag set. If the ys (suction side) input values are

greater than the yp values, then this option should be used. Plots of the resulting mesh can also beused as guides to determine when to use this option.

Tim rest of the input is very similar to tile input for the fi'ont blade. Some of the variables have a "2" ap-

pended to their names which indicates that the variables pertain to the rear blade row. The only difference

that should be noted is that the rear blade is scaled down by the front blade diameter for consistency of

units. This means that the rear blade tip will not necessarily be at r/d = 0.5. The user is cautioned that atthis time the option to specify tile leading- and trailing- edge extension locations for the rear blade should

not be used ( it may cause problems); therefore, set locfl2 = False. Front the input it may be interpreted that.the number of blades on tile rear row and the number of theta stations in a passage may be different than the

number from the front. Please note that this is not a general change, because the subroutine MWRITE is

now very much flow-solver specific. This change is valid only for the Adamczyk flow-solver format becauseit will output two mesh files; one with thickness for the front row and no rear blade thickness and the other

with no thickness for the front row and with thickness for the rear blade. See the flag IPRNT.

JNOSE - (F-F)

jnose If an H-mesh is being generated, then an axial index (jnose) value for the location of the stagnation

point is read. This helps maintain the original nacelle shape as specified by the input, ifjnose is specified

as 0, then a value ofjnose is computed as half of the leading-edge index (jle). Ifjnose is greater than

0, then it is taken to be the index desired ( must be greater than 3). Ifjnose is specified as less than

0, then the points are distributed axially fi'om j=l to jle, and no stagnation point is preserved. This

is important for certain types of nacelle bodies that do not have a stagnation point as such. One can

also set jnose less than 0 for bodies that do have a stagnation point, however, tile stagnation point will

be faired out. ifjnose is set greater than or equal to 0 for a body with no stagnation point, the codewill not run properly.

CK C-MESIt POISSON SMOOTtIING PARAMETER ; < 0 NO SMOOTIIING) - (F-F)

ck Used only for a C-type mesh. This is a factor used to pack points above tile tip. Values of ck should

range front 1. to 2. Since the Poisson smoothing only operates from ktip+l to kmax and j = 1 to

jcone+l, the effect of higher ck is to pack more points near ktip+l. A value of ck = 1 will give a

solution of the Laplace equation. If the mesh appears to have skewness near the leading-edge index

above the tip without smoothing, then turn on the smoothing; try an initial value of ck = 1.15. IIigher

values will cause more line contraction near the ktip+l line.

IPRNTMESItOUTPUTWRITEFLAG- (F-F)

iprnt - Thisflagcontrols the format of the mesh as it is written. IPRNT = 1 will write a mesh formatted

for NASPROP-E (ref. 4), IPRNT = 2 writes a mesh formatted for tile DENTON code (ref. 5), and

IPRNT = 3 writes a mesh formatted for the ADAMCZYK codes (ref. 1). See subroutine MWt'tITEfor actual write statements.

RAT (CIRCUMFERENTIAL PACKING RATIO; USED IF > 1) - (F-F)

rat This a circumferential clustering factor. If rat is greater than or equal to 1 then rat will be used for

the clustering in the 0 direction. This will overwrite any effect of the dthbl factor given previously. A

value of rat equal to 1 will give uniform spacing; even small increases in rat (i.e. 0.1 or less) will changethe packing considerably. In order to use rat, the number of desired mesh points in the circumferential

direction must be odd; i.e., lmax has to be odd. tIowever, if lmax has been specified as even, the

program will change lmax to odd. A message informing the user of the change will be written toUNIT 6. See dthbl which also does packing in the circumferential direction. When dthbl is specified,

a hyperbolic tangent stretching is performed; using rat gives a stretching based on series summation.

OUTPUT

UNIT 6 is the debugging output; the print flags (ptl0, pt20 , etc.) control what is printed, and informationalmessages (whether error or otherwise) are written here. Also written to UNIT 6 is the header page and any

text that the user placed in the title portion of the input file. The output should be self-explanatory. UNIT

11 (and perhaps also UNIT 12, if generating a counterrotation mesh for the Adameyzk flow-solver) is the

final output (mesh). Please note that the final output file or files are always named "fort.ll" and "fort.12".

Files by these names should not exist before the mesh generation process because the program will abort

prematurely. The output files are unformatted. The first record contains the size and location parameters

and has two forms depending upon whether it is a single-rotation or couuterrotation mesh. The actual mesh

coordinates are then written. See subroutine MWRITE for the actual write statements since they will vary

depending upon the flag IPRNT. However, all write so that the z, then r, and finally, the 0 (in radians)coordinates are written.

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13

REFERENCES

1. Adamczyk, J.J.: Model Equation for Sinmlating Flows in Multistage Turbomachinery. ASME Paper

85-GT-226, Mar. 1985 (NASA TM-86869).

2. Thompson, J.F., Warsi, Z.U.A., and Mastin, C.W.: Numerical Grid Generation: Foundations and Appli-

_. Elsevier Science Publishing Co., 1985.

3. Faux, I.D., and Pratt, M.A.: Computational Geometry for Design and Manufacture. Ellis ttorwood Ltd.,1979.

4. Bober, L.J., Chaussee, D.S., and Kutler, P.: Prediction of IIigh Speed Propeller Flow Fields Using a

Three-Dimensional Euler Analysis. AIAA Paper 83-0188, Jan. 1983 (NASA TM-83065).

5. Denton, J.D.: Time Marching Methods for 2hlrbomachinery Flow Calculations. Numerical Methods in Ap-

plied Fluid Dynamics, B. tIunt, ed., Academic Press, New York, 1980, pp. 473-493.

14

Plane of rotation

Axis of rotation

Figure 1. - Description of nacelle and blade geometries.

PCA

= /33/4 + A,q _ Plane of rotation

Figure 2. - Description of sectional blade geometry.

15

,I' (Xo.Or1increasing

_ simultar_ously

Z ,x,,, To

Figure 3. - Effect of tangent vector lengths on shape of Ferguson cubic curves.

77= _?rna= ""X

t[ = 0 --,'"

,--- rl "- r/t==#

,tf

##

##

x._ rl=0

Figure 4. - Physical and computational planes.

16

Figure5. - z - r plane of counterrotatiou It-mesh.

!(a) DZTE = 0.5 (b) DZTE = 1.0

Figure 6 - Effect of clustering factors oll blade point distribution.

17

Figure7. - Constmatradialcutat hub(counterrotationcase).

(a)DTHBL= 0.1 (b)DTIIBL= 1.0

Figure8. - Effectof DTIIBLoncircumferentialpointdistribution.

18

(a) At inlet. (b) At midchord.

Figure 9. - Constant axial cut.

Figure 10. - z - r plane of typicM C-mesh.

19

(a)Swirl-recoveryvane(SRV)

(b) Cruisemissile(CM)

Figure11.- Surfacegrids.

2O

(c)Advancedturboprop(ATP)

Figure11.- Concluded.

21

/.=Ad)usl B_ i

Extend Blade 1

tot-0

No

Yes

Read input

Blade 2

ME!_,JtD

J Adiust Blade 2_D,,TBLD

Extend Blade 2

tor=Q

FICBAS

)

C)

Yes

Create rounded

region

_G

Adjust radial

spacing

RADJST

Adjust spacing

adore tip

FIXTIP

+ No )

Fix spacing ahead

leading edge

FIX

Yes

Extend Blade io

Jnose

No >

Extend Blade 2

1o exit

Do between

blades

_DBLD

Fix spacing ahead

teachng ec_ge

FIXFOR

>

Extend Blade

to inlet or Jcone

FOR.B_

Extend Blade 1

to exit

&rI"B_D

O_T'£P,.EG

©

Figure 12. - Flow chart of main program structure.

22

Yes

Correct spacing

between blades

MIDFIX

Correct spacing

aft of blade

FZXJ_'T

Correct spacing

eft of blade

FIXAFT

Equal weighted J

averaging

&I/GSI_IP

Theta extensions

¢XTID_

Yes

Check and pnnl

maximum ratio ceil

spaong

_PC

/ writ. .0a,!--

Figure 12 - Concluded.

23

i

Report Documentation PageNational Aeronautics and

Space Administralion

1. Report No. 2. Government Accession No.

NASA CR-185156

4. Title and Subtitle

User's Guide to PMESH--A Grid-Generation Program for Single-Rotation

and Counterrotation Advanced Turboprops

7. Author(s)

Saif A. Warsi

9. Performing Organization Name and Address

Sverdrup Technology, Inc.NASA Lewis Research Center Group

Cleveland, Ohio 44135

12. Sponsoring Agency Name and Address

National Aeronautics and Space AdministrationLewis Research Center

Cleveland, Ohio 44135-3191

3. Recipient's Catalog No.

5. Report Date

December 1989

6. Performing Organization Code

8. Performing Organization Report No.

None (E-5152)

10. Work Unit No.

535-05-01

11. Contract or Grant No.

NAS3-24105

13. Type of Report and Period Covered

Con-tractor ReportFinal

14. Sponsoring Agency Code

15. Supplementary Notes

Project Manager, Lawrence J. Bober, Propulsion Systems Division, NASA Lewis Research Center.

16, Abstract

This report presents a detailed operating manual for a grid-generation program that produces three-dimensionalmeshes for advanced turboprops. The code uses both algebraic and elliptic partial differential equation (PDE)

methods to generate single-rotation and counterrotation, H- or C-type meshes for the z - r planes and H-type for

the z - 0 planes. The code allows easy specification of geometrical constraints (such as blade angle, location of

bounding surfaces, etc.), mesh control parameters (point distribution near blades and nacelle, number of gridpoints desired, etc.), and it has good runtime diagnostics. This report provides an overview of the mesh-

generation procedure, sample input dataset with detailed explanation of all input, and example meshes.

17. Key Words (Suggested by Author(s))

Mesh generator

Propeller

Propfan

18. Distribution Statement

Unclassified - Unlimited

Subject Category 02

19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of pages

Unclassified Unclassified 24

NASAFORM1626OCT86 *For sale by the National Technical Information Service, Springfield, Virginia 22161

22. Price"

A02