Thanks are also due to the technical staff of the Fluid Mechanics Group in the Jet Propul- sion Laboratory, especially to chief technician Mr

Growth of the maximum shear stress in the cavity shear layer with downstream distance: Mode II,. Growth of the maximum shear stress in the cavity shear layer with downstream distance: Mode III,. Growth of the maximum streamwise and transverse rms velocity fluctuations in the cavity shear layer with downstream distance; Mode III, 1;J' R:l 3.

Variation of the maximum shear stress in the foam layer with force frequency, constant power.

Chapter 1

Statement of the Problem

Previous work involving the control of flow oscillation in a cavity considered changing the geometry of the bottom or top corner of the cavity by rounding the corners (Ethembabaoglu 1973) or by placing external objects in the cavity such as flaps. A need arose for a clean technique that can control oscillations simply by introducing external disturbances into the shear layer. The connection between the state of the shear layer and the resistance of the cavitation system can be established by studying the quantities responsible for the transfer of momentum into and out of the cavity (u'v' and uv).

These quantities carry the necessary information about the nature of the instabilities in the shear layer and play an intrinsic role in the formation of the pressure distribution inside the cavity system.

Chapter 2

lfater Channel
Model
Pressure Measurements
Frequency, Phase and Corrolation Measurement
Velocity Measurements by Laser Doppler Velocimetry
Flow Visualization

The common end of the Scanivalve was connected to the low pressure side of a pressure transducer (type Validyne Wet-Wet DP-103-12) which was able. In the present experiments the gain was set to 2 or 4 depending on the signal condition. By using Us instead of U. the free-stream velocity ahead of the model nose eliminated the need for the blockage correction.

This also made the results independent of the shape of the front nose (provided there was no significant pressure gradient over the length of the cavity).

Chapter 3

Phase Measurements
Mean Velocity Distributions in the Shear Layer
Growth Rate of the Shear Layer
Shear Stress and Velocity F1uctuation Distributions of the Cavity Shear Layer Measurements of shear stress and fluctuating components of the velocity
Mean and Fluctuating Velocity Field of the Cavity Flow

Unsteady mass transfer into and out of the cavity is minimal due to the lack of significant oscillations in the shear layer. Figures 20 to 22 show the non-dimensionalized mean transverse component of the velocity, g, in the shear layer. The lack of similarity in the i-profiles of the cavity shear layers may be due.

Shear stress The profile shows a monotonic decrease in the maximum value of the profile when the shear layer is transformed into the boundary layer.

Chapter 4

SKETCH 5.1

Cavity Pressure Distribution
Observation of Sudden Drag and Pressure Change in Other Flows
Estimate of C» by Evaluation of ii~ and ~ Terms Along y = 0 Line
Distribution of ; Along y = 0 Line
Evaluation of u~ Along y = 0 Line Ue
A Possible Flow :Model

At the beginning of the oscillating modes (Jode II in this study), the drag coefficient has a value of 0. Thus, the contribution to the total drag of these two sections of the cavity walls cancel each other. This leaves the outer edge of the downstream plane ¥iith Cji > 0 , the main contributor to the cavity drag.

The pressure build-up near the upstream corner is apparently due to the deflection of the shear layer in the cavity. The negative v region is balanced by a wider region of the outflow from the cavity +v near the upstream corner. Consequently, this deflection will cause the stagnation of the high velocity portion of the shear layer velocity profile at the downstream corner.

It appears that natural shear layer diffusion due to increased cavity width (shear layer length) plays a less important role in bringing the fluid at higher velocity into the stagnation region. The cavity drag coefficient remains low as long as self-sustained fluctuations are present in the flow. Therefore, the degree of shear layer deflection depends on the nature of the instability growth in the shear layer.

The severity of the shear layer deflection is decisive in the nature of the interaction of the shear layer with the bottom corner. It is possible that due to the existence of such a restoring mechanism, some low-frequency oscillations appear in the shear layer.

Chapter 5

Forcing of the Shear layers
Surf ace Heating Technique
Effect of External Forcing on a Naturally Oscillating Cavity Flow [b/0 > b/0lmm]·
Cancellation Experiment

Linear theory can predict the exponential growth of the (T-S) waves based on the parameters Fe. In the final version of the experimental model, a single strip heater was flush mounted at s = 9.2 with ; = 5.3. For case A, Figure 60 shows the response of the cavity shear layer to a wide band of the forcing frequencies at different levels of forcing force.

It can be concluded that external frequencies can be imposed on natural non-oscillatory cavity flow, within the receptivity range of the shear layer. The first is the appearance of a small amplitude wave in the shear layer of the forced envelope. It is interesting to note that the response of the cavity flow to external forcing is not instantaneous.

This drag coefficient was an order of magnitude higher than that of the same case, but in the absence of forcing. The spectra reveal that as the amplitude of the force increases, the amplitude of the natural oscillation decreases and eventually disappears. At the forced power of 40 watts, the forced frequency becomes the dominant frequency of oscillation.

With this rule, it is possible to force the cavity shear layer frequencies within the shear layer acceptance range. A reduction in effective oscillation was achieved by a factor of 2 during 30 cycles of cavity shear layer oscillations.

Chapter 6

Summary of Results

An independent estimate of the drag coefficient by measurement of the shear stress and average momentum transfer terms. uv along the y = 0 line confirmed the exponential growth of the cavity drag. In the oscillatory modes of the cavity flow, the maximum pressure coefficient (CP) always occurs at the upstream angle and remains so until the. Thus, shear stress development along the shear layer has a direct effect on the drag of the cavity as well as an indirect effect through its role in the development of the uv term.

The type of shear layer interaction with the downstream corner, which depends on the deflection of the shear layer, determines the development of the shear stress throughout the entire shear layer of the cavity. Based on the findings of previous experiments, it is proposed that inward displacements of the shear layer relative to the downstream corner will result in an overall decrease in the shear stress level. Consequently, the mass balance of the cavity requires less shear deflection in the cavity.

It also requires the shear layer to bend back and restore the position of the shear layer. This mechanism keeps the position of r"'Pmax fixed at the upstream corner, and it may also introduce some low-frequency components to the oscillations. k) The control of the cavity flow oscillation is facilitated by external forcing of the cavity shear layer. Thus, a transformation of the boundary layer T-S waves to the Kelvin-Helmholtz waves of the shear layer is possible.

It is also possible to generate shear stress levels several orders of magnitude higher than that of the laminar shear layer by external forcing. However, spectral analysis shows that the amplitude of the forcing frequency has a direct effect on the growth of the natural frequency.

Concluding Remarks

Mode switching or transition to wake state can be delayed by amplifying the self-sustained oscillations through external forcing. Various mode expansions and simulations are possible by providing the correct forcing frequency to the cavity shear layer. The most important result of external forcing is the ability to cancel or dampen the established self-sustained oscillations.

An external forcing frequency corresponding to that of the cavity with an amplitude less than the threshold level, which has a correct phase angle with respect to the self-supporting one, was able to reduce the rms fluctuations by a factor of 2.

Appendix A

Period

Appendix B

Appendix C

This generates a header containing information relevant to the conditions of the experiment and the LDV setup. Dewey, C.F., Jr. 1976 ''Qualitative and Quantitative Flow Field Visualization Using Laser Induced Fluorescence." AGARD-CP-193, pp. Goree, J.A., Dimotakis, P.E. and Koochesfahani, M.M. Measurements of Two Velocity Components in the Two-Dimensional Mixed Layer."

Heller, H.H. and Bliss, D.B. 1975 'Physical Mechanism of Flow-Induced Pressure Fluctuations in Cavities and Concepts for Their Suppression.' Hussain, A.K.M.F. Coherent structures and studies of perturbed and unperturbed jets.” Lecture Notes in Physics, 136, Springer-Verlag, Berlin. Johannesen, N.H. Experiments of Supersonic Flow Past Rotating Bodies with Annular Slots of Rectangular Section.” Phil.

Ph.D. Thesis, California Institute of Technology, Pasadena, CA. Kendall, J.M. 1967 ``Supersonic Boundary Layer Stability Experiments''. of Boundary Layer Transition Study Group Meeting, II, Aerospace Corp, San Bernardino, CA. Kistler, A.L. ". Knisely, C.W An Experimental Investigation of Low-Frequency Self-Modulation of Improper Impingement Cavity Shear Layers." NACA representative. McGregor, D.W. and White, R.A. 1970 ``Drag of rectangular cavities in supersonic and transonic flow including cavity resonance effect.'' AIAA J. 8, p.

Plumblee, HE, Gibson, JS, and Lassiter, LW 1962 ''A theoretical experimental investigation of the acoustic response of cavities in an aerodynamic flow. '. White, RA Some results on heat transfer within resonant cavities at subsonic and supersonic Mach numbers.' J. Basic Eng., trans.

Fig. 2 Power spectrum of the velocity fluctuations.

Drain

Transducer

Arbitrary Scale

Mode JI

Mode E

Flow Direction

Modem

31 Growth of the maximum streamwise and transverse wgp velocity fluctuations in the cavity shear layer with downstream distance;. Mode II, ~b Growth of the maximum streamwise and transverse rms velocity fluctuations in the cavity shear layer with dovJnstream distance;. Mode III, ~b ~ 3. Cl Cle, CICI Cl Cl. 38 Effect of the downstream angle on the velocity fluctuations and shear stress profiles of incident cavity shear layer;.

39 Variation of axisymmetric cavity resistance coefficient with dimensionless cavity width, b/0 0 •. estimated C 0 based on boundary layer friction in the absence of a cavity.

162----....-~_..,__--A, _ _...__.....,__ 0 20 40 60 80 100 120 140 X/80 Fig. 31 Growth of the maximum streamwise and transverse rms velocity fluctuations in the cavity shear layer with downstream distance; Mode II, ~b !:::: 2

4 7 Variation of cavity resistance coefficient with b/R; @ current study; • Koenig (1978) optimal drag coefficient of a disc and cylinder combination·. 130 140 Contribution of shear stress to the net resistance in the cavity Contribution of UV uz-therm to the net resistance in the cavity e.

1.6 1.8 2 2.2 Fig. 46 Variation of pressure coefficient at the middle of the downstream face with b/0 0 •

7 Ff (Forcing Frequency) (Hz)

Case A)

Case B)

62 Distribution of maximum shear stress with distance in the direction of flow along the shear layer of the cavity; a) three different binding frequencies, constant power; b) 2 different binding powers, constant frequency; b/00 = 77. 63 Flow visualization of a non-oscillating natural cavity flow; b/0 • 66. a) unforced, (b) forced at F = 4 Hz, simulating mode I of oscillation.