Cavity-flow wall effects and correction rules

This paper is intended to evaluate the wall effects in the pure-drag case of plane cavity flow past an arbitrary body held in a closed tunnel, and to establish an accurate correction rule. The three theoretical models in common use, namely, the open-wake, Riabouchinsky and re-entrant-jet models, are employed to provide solutions in the form of some functional equations. From these theoretical solutions several different rules for the correction of wall effects are derived for symmetric wedges. These simple correction rules are found to be accurate, as compared with their corresponding exact numerical solutions, for all wedge angles and for small to moderate 'tunnel-spacing ratio' (the ratio of body frontal width to tunnel spacing). According to these correction rules, conversion of a drag coefficient, measured experimentally in a closed tunnel, to the corresponding unbounded flow case requires only the data of the conventional cavitation number and the tunnel-spacing ratio if based on the open-wake model, though using the Riabouchinsky model it requires an additional measurement of the minimum pressure along the tunnel wall. The numerical results for symmetric wedges show that the wall effects invariably result in a lower drag coefficient than in an unbounded flow at the same cavitation number, and that this percentage drag reduction increases with decreasing wedge angle and/or with decreasing tunnel spacing relative to the body frontal width. This indicates that the wall effects are generally more significant for thinner bodies in cavity flows, and they become exceedingly small for sufficiently blunt bodies. Physical explanations for these remarkable features of cavity-flow wall effects are sought; they are supported by the present experimental investigation of the pressure distribution on the wetted body surface as the flow parameters are varied. It is also found that the theoretical drag coefficient based on the Riabouchinsky model is smaller than that predicted by the open-wake model, all the flow parameters being equal, except when the flow approaches the choked state (with the cavity becoming infinitely long in a closed tunnel), which is the limiting case common to all theoretical models. This difference between the two flow models becomes especially pronounced for smaller wedge angles, shorter cavities, and with tunnel walls farther apart. In order to gauge the degree of accuracy of these theoretical models in approximating the real flows, and to ascertain the validity of the correction rules, a series of definitive experiments was carefully designed to complement the theory, and then carried out in a high-speed water tunnel. The measurements on a series of fully cavitating wedges at zero incidence suggest that, of the theoretical models, that due to Riabouchinsky is superior throughout the range tested. The accuracy of the correction rule based on that model has also been firmly established. Although the experimental investigation has been limited to symmetric wedges only, this correction rule (equations (85), (86) of the text) is expected to possess a general validity, at least for symmetric bodies without too large curvatures, since the geometry of the body profile is only implicitly involved in the correction formula. This experimental study is perhaps one of a very few with the particular objective of scrutinizing various theoretical cavity-flow models

The wall effect in cavity flow

A non-linear theory for the calculation of the flow field of an oblique flat plate under blockage condition is given using the techniques of integral equations. Numerical results are obtained with the aid of a high speed digital computer for the plate situated mid-channel at values of the angle of attack from 50 to 90° and the channel width-chord ratio from 3 to 20. Also obtained are results for the plate situated at two different off-center positions for a channel width-chord ratio 5 and angles of attack less than 30°

Final Report: Wall Effects in Cavity Flows

The wall effects in cavity flows past an arbitrary two-dimensional body is investigated for both pure-drag and lifting cases based on an inviscid nonlinear flow theory. The over-all features of various theoretical flow models for inviscid cavity flows under the wall effects are discussed from the general momentum consideration in comparison with typical viscous, incompressible wake flows in a channel. In the case of pure drag cavity flows, three theoretical models in common use, namely, the open-wake, Riabouchinsky and re-entrant jet models, are applied to evaluate the solution. Methods of numerical computation are discussed for bodies of arbitrary shape, and are carried out in detail for wedges of all angles. The final numerical results are compared between the different flow models, and the differences pointed out. Further analysis of the results has led to development of several useful formulas for correcting the wall effect. In the lifting flow case, the wall effect on the pressure and hydrodynamic forces acting on arbitrary body is formulated for the choked cavity flow in a closed water tunnel of arbitrary shape, and computed for the flat plate with a finite cavity in a straight tunnel

The Dynamics of Ventilated Partial Cavities over a Wide Range of Reynolds Numbers and Quantitative 2D X-ray Densitometry for Multiphase Flow.

Ventilated partial cavity drag reduction is a technique that could potentially enable reduction of a ship's frictional drag, leading to a 5 to 20% net fuel savings, and thus providing economic and environmental benefits. Ventilated partial cavity drag reduction experiments were conducted using two geometrically similar experimental setups. First, experiments were performed at the world's largest re-circulating water channel, the U.S. Navy's Large Cavitation Channel (LCC), at Reynolds numbers to 80 million. For these experiments the LCC was adapted to allow free surface testing, which in itself was a major effort. The effect of the cavity closure geometry, and the cavity's robustness in the presence of global flow perturbations mimicking the effect of ambient waves were studied. Next, the experiments were reproduced at 1:14th size scale at Reynolds numbers of the order of one million, and in these small scale experiments the effect of Weber number was also investigated by reducing the surface tension by a factor of two. Results from these two sets of experiments were compared, and a potential scaling of required ventilation gas flux discussed. In addition the energy economics of the partial cavity drag reduction technique were analyzed. We can note that for partial cavities, the air entrainment is dominated by the cavity closure dynamics. To gain a better understanding of these dynamics, knowing the void fraction distribution, both spatially and temporally, would be very useful. In the cavity's closure region, as well as in most cavitating flows, any intrusive probe would perturb the flow greatly. X-ray densitometry offers a way to obtain a two dimensional time-resolved projection of the void fraction distribution, and a quantitative measure of the void fraction along the beam paths. An x-ray densitometry system was developed for use with a pre-existing cavitation tunnel. The limitations of the x-ray system were investigated, methods to contend with the imaging artifacts found, and the measured void fraction profiles compared against those obtained employing dual fiber optical probes and high speed video.Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91443/1/smakihar_1.pd

New Advances of Cavitation Instabilities

Cavitation refers to the formation of vapor cavities in a liquid when the local pressure becomes lower than the saturation pressure. In many hydraulic applications, cavitation is considered as a non-desirable phenomenon, as far as it may cause performance degradation, vibration problems, enhance broad-band noise-emission, and eventually trigger erosion. In this Special Issue, recent findings about cavitation instabilities are reported. More precisely, the dynamics of cavitation sheets are explored at very low Reynolds numbers in laminar flows, and in microscale applications. Both experimental and numerical approach are used. For the latter, original methods are assessed, such as smooth particles hydrodynamics or detached eddy simulations coupled to a compressible approach

Nonlinear free-surface flows, waterfalls and related free-boundary problems

Many works have considered two-dimensional free-surface flow over the edge of a horizontal plate, forming a waterfall, and with uniform horizontal flow far upstream. The flow is assumed to be steady and irrotational, whilst the fluid is assumed to be inviscid and incompressible. Gravity is also taken into account. In particular, amongst these works, numerical solutions for supercritical flows have been computed, utilising conformal mappings as well as a series truncation and collocation method. Here, an extension to this work is presented where a more appropriate expression is taken for the assumed form of the complex velocity. The justification of this lies in the behaviour of the flows far downstream and the wish to better encapsulate the parabolic nature of such a free-falling jet. New numerical results will be presented, demonstrating the improved shape of the new free-surface profiles. Further adjustments to the method are presented which lead to enhanced coefficient decay. The aforementioned adjustments are also applied to other supercritical flows (such as weir flows) and similar improvements to the jet shape can be observed. Flows that are still horizontal upstream but instead negotiate a convex corner and then run along an angled supporting bed (i.e. spillway flows) are also surveyed. New spillway problems and results are presented, where the spillway’s angled wall is more complex than a linear path; and, again, series truncation and collocation are utilised. Finally, a wake model for potential flow past a finite plate, perpendicular to the oncoming flow and below a free surface, is pursued. The approach here is to adopt a closure model of horizontal flow far downstream and use the boundary integral equation method to obtain a solution numerically. Related free-boundary problems are included to progress from a case of zero-gravity, unbounded flow to the full problem

The Specialist Committee on Detailed Flow Measurements. Final Report and Recommendations to the 26th ITTC

The scope of this report is to review up-todate measurement systems and methods available for flow-field and wave-field measurements and describe applications of Particle Image Velocimetry (PIV), stereoscopic PIV (SPIV), Laser Doppler Velocimetry (LDV),Particle Tracking Velocimetry (PTV),holography, and other emergent methods, for the measurements of flow separation, wake,vortex strength, etc, for ship hydrodynamics problems. Furthermore, practical issues related to the application of these measurement techniques, especially PIV and SPIV, in largescale tow tank facilities and cavitation tunnels will be discussed, with recommendations for future work for the ITTC in these areas

Biomedical and cooling applications of micro flows

Micro flows find applications in a variety of topics covering biomedical, cooling, electronics and MEMS (micro-electro-mechanical-systems) applications. In this work, the destructive effects of hydrodynamic cavitation for biomedical treatment, heat transfer enhancement with nanostructures and nanofluids for small scale cooling applications were investigated. The research performed in this study includes results from bubbly cavitation experiments and findings showing the destructive effects of bubbly cavitating flow on selected solid specimens, live cells and proteins. Our results showed that cavitation could induce damage both on chalk pieces (and possibly kidney stones) and leukemia/lymphoma cells while the secondary structure content, the hydrodynamic diameter and enzymatic activity of lysozyme were unaffected by cavitation. For the purpose of making compact and efficient heat exchangers, heat transfer enhancement with nanostructures could be considered as a futuristic candidate. Thus, heat transfer characteristics of nanostructured plates, on which an array of vertical and tilted copper nanorods with an average diameter ranging from 100 to 150 nm and length 500 to 600 nm are integrated to a planar copper thin film coated silicon wafer surface, were compared to planar copper thin film coated silicon wafer surfaces via three different heat transfer techniques (pool boiling, forced convection and jet impingement). Three different heat sinks were developed for this purpose. Surface temperatures were measured and heat transfer coefficients were calculated for the designed heat sinks and an average of 22% single-phase heat transfer enhancement was realized with the nanostructured plates. A miniature heat transfer enhancement system is also developed based on the actuation of magnetic nanoparticles dispersed in a base fluid (water). The ferromagnetic particles within the pool were actuated with the magnetic stirrers and this resulted in an average heat transfer enhancement of 37.5% compared to the stationary fluid. In the light of the performed stuides, hydrodynamic cavitation was shown to be a strong heat-free and energy efficient future alternative to ultrasonic cavitation which is being extensively used in biomedical treatment. Also nanostructured surfaces and magnetically actuated nanofluids were proven to contribute to heat transfer enhancement significantly

Experimental Study of the Effects of a Gap Clearance on the Performance of a Fully Cavitating Flat Plate with and without a Flap

Experimental results are presented for the effect of a hinge gap on the fully cavitating performance of a flat plate hydrofoil without and with a flap. From the results of the tests it is concluded that for the zero flap deflection, no significant effects of the gap are apparent for the range of the parameters investigated. However, for a 20% flap-to-chord ratio and a 20° flap deflection a significant drop occurs in the lift and moment coefficients for a given gap ratio. This effect increases with increase in gap width. The drag on the other hand is unaffected for the range of values tested. Certain qualitative effects of the jet, arising from the gap, on the cavity appearance are discussed. Comparison of the experimental results for zero gap, with established non-linear theories, show very good agreement

The Design and Development of a Recirculating Water Channel: A Critical Assessment

The thesis critically assesses the design, development and equipment of a recirculating water channel: the channel in the Department of Engineering at the University of Liverpool It is intended to provide a valuable reference manual for such facilities. The channel is a versatile item of equipment wliich can be used in four different configurations:- as a free surface water channel, including the ability to simulate shallow water and also to generate regular head waves; as a water tunnel; as a free surface cavitation channel or as a cavitation tunnel, with a minimum pressure of 1/30 atmosphere. Uie working section is 3.66m long, 1.4m wide and 0.84m deep with a maximum water speed of 5.7 m/s. The thesis includes: 1. A description of the water channel in its four configurations and earlier development of a jet injection system to overcome a velocity defect at the water surface. The flow velocity in tlie working section and methods of flow measurement are discussed together with new measurements of turbulence velocity and the time to reach equilibrium speed. The wavemaker has been shown to produce waves which are good approximations to a sinusoidal shape at low water speeds and can be maintained over a long period of time. At higher speeds it was found that the wave shape progressively degenerated; methods for improving the wave-maker are suggested. 2. The force measuring equipment is reviewed including a dynamometer for ship models and a miniature version for much smaller forces obtained on sea shells at low water speeds. 3. The principles of model testing are discussed together with a technique for measuring the actual wetted surface area in the case of fast ships. A new experimental and theoretical investigation into the effect of model size relative to the size of the working section is reported. 4. A final chapter reviews the design of the flume and all its equipment. Suggestions are made for further improvements suitable for a future water channel