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VELOCITY FIELD NEAR THE JET ORIFICE

OF A ROUND JET IN A CROSSFLOW

Richard L. Fearn and J. Paul BensonUniversity of Florida

NASA Contractor Report

(NASA-CE-152293) VELOCITY FIELD NEAB THEJET ORIFICE OF A R O U N D JET IM A CBOSSFLOW(Florida State Univ., Gainesville.) 72 p

UC A O U / M F A01 CSCL 20D

N81-18319

Unclas16386

ecember, 1979

This work was performed under Grant NSn-2288 and NGL 10-005-12"for the National Aeronautics and Space Administration, AmesResearch Center, Moffett Field, CA, and Langley Research Center,Hampton, YA

https://ntrs.nasa.gov/search.jsp?R=19810009794 2020-03-19T05:03:57+00:00Z

VELOCITY FIELD NEAR THE JET ORIFICEOF A ROUND JET IN A CROSSFLOW

Richard L. Fearn and J. Paul BensonUniversity of Florida

SUMMARY

Experimentally determined velocities at selected locations near thejet orifice are presented and analyzed for a round jet in a crossflow.Jet-to-crossflow velocity ratios of four and eight were studied experimentallyfor a round subsonic jet of air exhausting perpendicularly through a flatplate into a subsonic crosswind of the same temperature. Velocity measurementswere made in cross sections to the jet plume located from one to four jetdiameters from the orifice. Jet centerline and vortex properties arepresented and utilized to extend the results of a previous study into theregion close to the jet orifice.

INTRODUCTION

In the transition from hover to conventional flight, vertical take-offand landing (VTOL) aircraft supplement wing-generated lift with direct thrustfrom lift jets, lift fans or tilt-proprotars. Proposed configurationsinvolve the injection of relatively high-velocity jets of air and/or exhaustgases into the crosswind caused by the forward motion of the aircraft. Theinteraction between these jets in a crossflow and the aerodynamic surface ofthe aircraft can be described in terms of an interference effect. Qualitatively,this interference effect results in a loss of lift and an increment of nose-up pitching moment, both of which tend to increase with increasing forwardvelocity of the aircraft. This jet/aerodynamic-surface interference effectis one of the significant problems in V/STOL aerodynamics.

In an effort to understand the basic flow phenomenon of a jet in across-flow, a series of wind tunnel experiments has been conducted in theV/STOL tunnel at Langley Research Center. A round subsonic jet of air10.16cm in diameter exhausted through a flat plate into a subsonic crosswindof the same temperature. For perpendicular jet injection into the crossflowand for a range of jet to crossflow velocity ratios, the pressure distributionwas measured on the flat plate (ref. 1). An extensive investigation of theflow properties in the plume of the jet was conducted. For each jet tocrossflow velocity ratio studied, the velocity, static pressure and totalpressure were determined at numerous locations in each of several crosssections to the jet plume (ref. 2).

Based on the results of the first wind-tunnel experiment studying thejet plume, a contrarotating pair of diffuse vortices was identified as asignificant and persistent feature of the flow field. These vortices weremodeled in such a way that the vortex properties could be inferred fromselected velocity measurements in the jet plume (ref. 3). It has also beendemonstrated that the properties of this vortex pair associated with a jet ina crossflow can be utilized to calculate the pressure distribution on the flatplate for a jet to crossflow velocity ratio of 8 (ref. A).

Similar experiments in the jet plume and data analysis have been conductedto study the effect of jet injection on the vortex properties associated witha jet in a crossflow (Refs. 5 and 6).

The purpose of this report is to present and analyze experimental datathat were acquired in a region closer to the jet orifice than that described inreference 2. Experimental velocities and pressures are presented for crosssections to the jet plume located in the region from one to four jetdiameters from the jet orifice. The test conditions were perpendicular jetinjection into the crossflow and jet-to-crossflow velocity ratios of fourand eight. Analysis of this data provides experimental information on thevortex properties in the important region of vortex roll-up near the jetorifice.

LIST SYMBOLS

D Diameter of the jet orifice, cm.

efl , efl , e Unit vectors in vortex coordinate system1 2 v (see figure 3).

F Integrated strength of a single Gaussianvortex, cm2/s.

T Effective vortex strength, cm2/s.

Y Effective vortex strength nondimensionalized by2DU .

CO

h Effective vortex half-spacing, cm.

h Half-spacing between vortex centers, cm.

<(> Angle of rake of yaw pitch probes with the Z-axis,B deg.

w Angle of vortex cross section with the Z-axis,deg.

c R Effective jet to crossflow velocity ratio.

r, r.. , r_ Radii in vortex coordinate system (see figure 3), cm.

r Radius of vortex core, cm.

S ' Arc length along vortex curve, cm.

«o Speed of the cross flow , cm/s.

V Projection of velocity vector onto cross section,cm/s.

X, Y, Z Coordinate axes for tunnel coordinate system.

Y , Z or YB, ZB Coordinate axes for cross section ofmeasurement.

Y , Z or XV, ZV Coordinate axes for cross section to vortexcurve.

8 Diffusion constant for Gaussian vortex, cm

0) Vorticity, s'1.

APPARATUS

This experiment was conducted in the Langley V/STOL wind tunnel whichis a closed return atmospheric tunnel with a test section 4.42 m by 6.63 m.Test-section airspeeds for this investigation were approximately 43 m/s forR = 4 and 21 m/s for R = 8.

The jet of air exhausted perpendicularly from a rectangular flat plat17.7 D x 29.5 D which was mounted 3.0 D above the tunnel floor ( D=10.16 cm is the diameter of the jet). The center of the jet orifice waslocated 11.8 D downstream of the rounded leading edge of the plate and on thelongitudinal centerline of the plate.

The jet of air was formed by using a plenum chamber and a 20:1convergent nozzle designed to provide a flat velocity profile at the nozzleexit. Supply air for the jet was heated so that the temperature at thejet orifice would be approximately the same as that of the crossflow.

Velocity measurements were made with a rake of seven parallel yaw-pitch probes mounted 5.08 cm apart on the leading edge of an airfoil. Eachprobe was 20.32 cm long and 0.64 cm in diameter. Five pressure orificeswere located on the hemispherical tip of each proble, and a ring of sixinterconnected static-pressure ports was located 5.08 cm aft of the probe tip.

All pressures were measured with pressure transducers which were cali-brated with water or mercury manometers. The leads from the pressure portson the probes were connected by plastic tubing to a pressure scanning devicemounted inside the wind-tunnel sting. Each device consisted of a singlepressure transducer which could be connected sequentially to each of 48pressure tubes. The output of each pressure transducer was fed into a lowpass filter to attenuate fluctuations in the transducer output signal. Onesecond after each static-pressure port was connected to the pressure transducer,the signal from the filter was sampled and recorded on magnetic tape.

A more detailed discussion of the apparatus utilized in this series ofexperiments is presented in references 2 and 5.

TEST PROCEDURES AND CONDITIONS

The probe system utilized for velocity measurements in this series ofexperiments (refs. 2 and 5) is not well-suited for use in the region nearthe jet orifice. The physical size of the probes and their spacing onthe rake (1/2 D) are too great for the severe velocity gradients encounteredin this region. Also, there was excessive vibration in the probe supportsystem under normal operating conditions when the rake of probes was placedin the jet plume near the jet orifice.

Selected velocity measurements in the region near the jet orifice, however,would provide useful information concerning the initial distortion of thevortex field and its roll-up into a pair of contrarotating vortices. In anattempt to acquire preliminary measurements in this important region withthe existing probe system, an overlapping placement of the rake of probes wasutilized to provide a measurement spacing less than 1/2 D, and probe vibrationwas reduced by using guy wires to stiffen the probe support system. The useof guy wires reduced the precision of probe placement and disabled twodegrees of freedom in the remote control of probe location, tunnel yaw andtunnel height. Remote control of a limited range of longitudinal motion wasavailable.

Jet to crossflow velocity ratios of 4 and 8 were studied for perpendicularjet injection into the crossflow. For each of these velocity ratios,measurements were made in one cross section approximately 1 D from the jetorifice. For a velocity ratio of 4, measurements were also made in a groupof 5 closely-spaced cross sections located approximately 2 1/2 D from thejet orifice (see figure 1). For a velocity ratio of 8, velocity measurementswere also made in two groups of closely spaced cross sections to the jetplume; a group of 3 cross sections located approximately 3 D and a group of: ross sections located approximately 4 D from the jet orifice (see figure 2).Tne remote control of the longitudinal motion of the probe was utilized tomove the rake from one cross section to another within a group of closely-spaced cross sections. Overlapping placement of the rake of probes wasutilized to obtain a measurement spacing of 1/16 D for the cross sectionsnearest to the jet orifice and a spacing of 1/4 D for the other cross sections(see figures 1 and 2). Lack of remote control of tunnel yaw made it ex-cessively time consuming to achieve a fine measurement spacing out of theplane of flow symmetry. Measurements out of the plane of flow-symmetry wereaccomplished with two to four wind tunnel yaw locations of the rake of probes.

VORTEX MODELS

The contrarotating vortex pair associated with a jet in a crossflow canbe modeled so that the vortex properties are inferred from selected velocitymeasurements (ref. 3). The velocity measurements presented in this reportwere utilized in these models to infer properties of the contrarotating vortexpair in the region near the jet orifice. A brief summary of the vortexmodels presented in reference 3 will serve to define the parameters used todescribe the vortex properties and as a basis for evaluating the validity ofthe results obtained.

Filament Vortex Model. The strength and location of two infinitestraight vortex filaments are determined by the measured velocities alongthe line of intersection of a cross section of measurement with the planeof flow symmetry (ZB axis). This two-dimensional filament vortex model isassumed to indicate the properties of the vortex pair at the location of thecross section. Although this model provides no description of the distri-bution of vorticity in the cross section, it has the advantage of requiringrelatively few velocity measurements.

Diffuse Vortex Model. In the diffuse vortex model, the restrictionthat the vorticity be concentrated in a filament is relaxed, and it isassumed that each vortex is composed of a Gaussian distribution of vorticity.The strength, location, and diffuseness of the vortex pair is determined bymany measured velocities in a cross section. A sketch of the geometry forthe diffuse vortex model is shown in figure 3. The projection of the measuredvelocity onto the plane of the cross section is assumed to be the vector sumof the velocity induced by the contrarotating diffuse vortex pair and thecomponent of the crossflow velocity in the plane of the cross section

- U sin<}> eco Tv Z (1)

where TO is strength of a single isolated diffuse vortex; 6 is the diffusionconstant; r-^ and T£ are distances to a point from the two vortex centers;ee , CQ , ez ; are unit vectors (see figure 3). The parameters describingvortex |eomeYry and vortex strength in the velocity equation are varied toobtain the least squares best fit between the velocity data and the model.

For the presentation of results, it is convenient to define the followingvortex properties: Effective vortex stength is defined as the flux ofvorticity across the half plane Yv < 0

' /-

7T/2

Tr/2/o Yv (2)

where u(ri9) is the distribution of vorticity for the contrarotating pair ofGaussian vortices. Effective vortex spacing is defined as the centroid ofvorticity in a half plane of the cross section

h = w(rie)r dr de (3)

Vortex core size (i. is defined as the distance from the axis of a singleGaussian distribtuion of vorticity to the location of maximum tangential speed.The effective vortex strength, effective vortex spacing, and vortex coresize are related to the diffuse vortex model parameters by

F = T erf (Bh0), h - h,,/ erf (6ho), r£ = 1.121/3

where 6hferf (Bh0) = J0

is the error function.

dt

(4)

(5)

RESULTS

Measured velocities and pressures are presented in the appendix. Foreach point of measurement the three velocity components, static pressure,and total pressure are presented in tabular form. Measurements are groupedaccording to jet to crossflow velocity ratio and cross section of measure-ment. Graphs representing the velocity measurements in the plane of flowsymmetry serves to locate the cross sections of measurements. Graphsshowing also indicate the measurement grid for each cross section.

The velocity measurements of the present study can be used in thediffuse vortex model (ref. 3) to extend the model-inferred vortex propertiesinto the region near the jet orifice. Results of this analysis are shownin table 1. The five groups of cross sections are separated by horizontallines in the table. The first three columns of the table serve to identifythe test conditions by stating the effective jet to crossflow velocityratio, the crossflow velocity and the angle of inclination of the crosssection of measurement. The results of utilizing selected measured velocitiesfrom the cross section in the diffuse vortex model are displayed by statingthe geometry of the vortex distribution and the vortex strength: vortexcurve location (S/D, Z/D), effective vortex half-spacing (h/d), radiusof vortex core (r /D), vortex curve cross section angle (£ ), and effectivevortex strength (Y = T/2DU ). For use in the diffuse vortex model, it isdesirable to acquire the velocity measurements in cross sections to thevortex curve (4>B = $ ). The model results, however, are not sensitive torelatively small changes in cross section angle. The vortex core radiusfor a Gaussian distribution of vorticity can be related to the parameter6 in Eq. 1, r = 1.121/8. The number of velocity measurements from thecross section used in the diffuse vortex model (NPTS) were selected fromthe region near the intersection of the vortex curve and the cross section;velocities in the high axial velocity component jet core were avoided.The vortex properties are considered to be functions primarily of effectivevelocity ratio (R) and arc length along the vortex curve (S/D) measuredfrom the jet orifice. Also presented in the table is an indication of theability of the model to fit the experimental data as measured by thestandard deviation expressed as a percentage of the maximum vortexinduced velocity in the cross section (SIGMA).

The vortex properties listed in table 1 and the results of previousstudies in the far field of the jet plume are shown graphically in figures4 through 8. Vortex curves for R = 4 and R = 8 are shown in figures 4 and 5.Figure 6 presents the vortex half-spacing and figure 7, the vortex coresize. The effective vortex strength for R = 4 and R B 8 is presented infigure 8. Note that the effective vortex strength for R « 8 reaches ahigher maximum value than for R = 4, but that the initial development ofthe streamwise vortex is more rapid for R » 4 than for R * 8.

The diffuse vortex model is two-dimensional and describes streamwisevorticity only. In the region near the jet orifice it provides an in-complete description of the vorticity field. The numerical values forthe vortex parameters presented in this report should then be consideredas a rough description of the streamwise vorticity.

It is emphasized that the results presented in the report do Dot serveas an adequate description of the flow field in the near jet region.They are Intended to be a "first look" to be used for planning moredetailed experiments utilizing a probe system that is suitable for use inthe extremely high velocity gradients encountered in this region. Theresults indicate that there is a rapid development of the streamvise vortexpair, but the measurement grid is not sufficiently small to calculatewith sufficient precision the three-dimensional vorticity field.

'REFERENCES

1. Fearn, R. L.; and Weston, R. P.: Induced Pressure Distribution of aJet in a Crossflow, NASA TND-7916, 1975.

2. Fearn, R. L.; and Weston, R. P.: Induced Velocity Field of a Jetin a Crossflow, NASA TP-1087, 1978.

3. Fearn, R. L.; and Weston, R. P.: Vorticity Associated with a Jetin a Crossflow, AIAA S. Vol. 12, No. 12, Dec. 1974, pp. 1666-1671.

4. Dietz, W.; A Method for Calculating the Induced Pressure DistributionAssociated with a Jet in a Crossflow, M. S. Thesis, University ofFlorida, 1975.

5. Fearn, R. L.; and Weston, R. P.: Velocity Field of a Round Jet in aCross flow for Various Jet Injection Angles and Velocity Ratios,NASA TP-1506, 1979.

6. Krausche, D.; Ream, R. L.; and Weston, R. P.: Round Jet in aCrossflow: Influence of Jet Injection Angle on Vortex Properties,AIAA J., Vol. 16, No. 6, June 1978, pp. 636-637.

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APPENDIX

EXPERIMENTALLY DETERMINED VELOCITIES AND PRESSURES

Presentation of Results

The basic results of this investigation are the measured pressures and thevelocities determined from them. For presentation, these measurements aregrouped by cross sections of measurement. Data for R = 4 is presented first,followed by data for R = 8. For each jet to crossflow velocity ratio, crosssections are presented in order of increasing distance from the jet orifice.The results for each cross section of measurement are presented as a singlefigure and a correspondingly numbered table. The (a) part of the figure presentsthe velocity measurements in the plane of flow symmetry and serves to locate thecross section of measurement relative to the jet plume. In the (b) part of eachfigure are shown the projections of the measured velocities onto the cross sectionof measurement which serve to indicate the extent of measurement in the crosssection and to illustrate the development of the contrarotating vortex pair. Thecorrespondingly numbered table presents the numerical values for measured velocitiesand pressures. Multiple parts to the table, (a), (b), (c), etc. indicate over-lapping placements of the rake of seven probes to provide a measurement spacingsmaller than the probe spacing of the rake. The location of a cross section isgiven by the location of the tip of probe A of the rake in the wind-tunnelcoordinate system (X/D,0,Z/D) and the inclination PHI of the rake with the Z-axis.The locations of points within a cross section are given by their coordinates(XB.YB.ZB) in a system obtained by rotating the wind-tunnel coordinate systemthrough an angle PHI and locating the origin at the tip of probe 4 of the rake ofseven yaw-pitch probes (See sketch). All coordinates are nondimensionalized bythe jet diameter D. The velocity determined at each location in a cross section

UINF

Sketch

is specified by the three components (UB,VB,WB) relative to the coordinate system(XB.YB.ZB) and is nondimensionalized by the cross-flow speed UINF. The staticand total pressures are presented as dimensionless coefficients CP and CPT.

SYMBOLS

CP static pressure coefficient, (p - p )/q

CPT total pressure coefficient, (pt - Pt,{o)/qa)

17

Symbols (continued)

D jet diameter, cm

PHI angle between Z and AB axes (same as $ in main text), deg.B

p static pressure, Pa

p total pressure, Pa

q dynamic pressure, Pa

R effective jet to crossflow velocity ratio

THETA angle that local fluid velocity makes with probe, deg

UB.VB.WB XB, YB and ZB components of velocity, m/zec.

UINF cross-flow speed (same as U in main text and figures), m/sGO

X,Y,Z Cartesian coordinate system; denotes wind-tunnel coordinatesystem when no subscript is used

XB,YB,ZB Cartesian coordinate system fixed to rake of probes

Subscript:

oo refers to cross-flow condition

18

Index to Figures

Each figure has a corresponding table which presents the numerical values

for the experimentally determined velocities and pressures.

Figure R PHI Commentsdeg

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<Id

1. Report No. . ^

NASA CR-:'/j22^32. Government Accession No.

4. Title and Subtitle

VELOCITY FIELD NEAR THE JET ORIFICE OF A ROUNDJET IN A CROSSFLOW

7. Authorlt)

Richard L. Fearn and J. Paul Benson

9. Performing Organization Namt and Address

Engineering SciencesUniversity of FloridaGainesville, FL 32611

12. Sponsoring Agency Name and Address

National Aeronautics and Space AdministrationWashington, D.C. 20546

3. Recipient's Catalog No.

6. Report DateDecember 1979

6. Performing Organization Code

6. Performing Organization Report No.

10. Work Unit No.

11. Contract or Grant No. NSG— 2288

and NGL 10-005-127^3. Type of Report and Period Covered

Contractor Report14. Sponsoring Agency Code

15. Supplementary Notes _, . . . . .. . , .This report supplements the information presented inNASA TP 1087, INDUCED VELOCITY FIELD OF A JET IN A CROSSFLOW by Richard L.Fearn and Robert P. Weston.

16. Abstract Experimentally determined velocities at selected locations near the

jet orifice are presented and analyzed for a round jet in crossflow. Jet-to-

crossflow velocity ratios of four and eight were studied experimentally for a

round subsonic jet of air exhausting perpendicularly through a flat plate into

a subsonic crosswind of the same temperature. Velocity measurements were

made in cross sections to the jet plume located from one to four jet diameters

from the orifice. Jet centerline and vortex properties are presented and

utilized to extend the results of a previous study into the region close to

the jet orifice.

17. Key Words (Suggested by Author(tl)

Jet in a crossflow

19. Security Omit, (of this report)

Unclassified

18. Distribution Statement

Unclassified - Unlimited

20. Security CUtsil. (of this page)

Unclassified21. No. of Pages 22. Price*

70

'For sale by the National Technics) Information Service. Springfield. Virginia 22161