# Experimental Investigation of Ventilated Cavity Flow Over a 3D Wall Mounted Fence

Luka Barbaca, Bryce W Pearce, Paul A Brandner

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Luka Barbaca, Bryce W Pearce, Paul A Brandner. Experimental Investigation of Ventilated Cavity Flow Over a 3D Wall Mounted Fence. 16th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery (ISROMAC 2016), Apr 2016, Honolulu, United States. hal-01521586

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# Experimental Investigation of Ventilated Cavity Flow Over a 3D Wall Mounted Fence

Luka Barbaca<fnref n="1" />*, Bryce W. Pearce<fnref n="1" />, Paul A. Brandner<fnref n="1" />

<figure><img src="image_2.png" /></figure>

ISROMAC 2016

International
Symposium on
Transport

Phenomena and
Dynamics of

Rotating Machinery

Hawaii, Honolulu

April 10-15, 2016

## Abstract

Ventilated cavity flow over a 3-D wall mounted fence is experimentally investigated in a cavitation tunnel. The influence of air ventilation rate, fence height based Froude number and vapour pressure based cavitation number on the resulting cavity and associated drag coefficient is determined. Three different flow regimes are identified throughout the range of cavitation numbers for a constant set of free-stream conditions. The geometry of a fully formed ventilated cavity is described. The re-entrant jet cavity closure is observed as the primary mechanism for entrainment of ventilated air into the flow.

## Keywords

Ventilated cavity — Wall mounted fence — Cavitation tunnel

## INTRODUCTION

The need for faster and more efficient sea transport is more prominent than ever in today's world. As vessel speed increases the occurrence of cavitation becomes unavoidable. Cavitation in this context being the formation and interaction of vaporous volumes (or cavities) with the flowing liquid. The phase change occurs in regions where the liquid is subjected to pressures at or below vapor pressure. It is mostly an undesirable phenomenon as it can lead to performance loss, vibration, noise and surface erosion of the cavitating body. Depending on the application, various techniques have been investigated to minimize these detrimental effects. One of the techniques that has been extensively studied is the use of artificial ventilation.

Ventilated supercavities (also termed ‘artificial’) are created when incondensable gas (typically air) is injected into the low pressure region of the liquid flow. The injection of gas induces the creation of a ventilated supercavity with the closure located in the wake of the cavitating body. Two main benefits from ventilated cavities are drag reduction and increased flow stability. The use of ventilated cavities has been investigated extensively from the middle of last century for mainly military, but also for commercial application [1, 2, 3].

Axisymmetric ventilated supercavities have been investigated for drag reduction purposes on underwater projectiles (i.e. torpedoes). By enveloping the body in an air bubble, and thereby reducing its wetted area, the skin friction is significantly reduced. A comprehensive review of axisymmetric

ventilated cavity flow is presented in [4]. ‘Air-lubrication’ is a similar method used for hull drag reduction where an air layer is created to reduce the contact area between the hull and water [5].

The injection of air on the downstream face of a wedge shaped hydrofoil (i.e. a ‘base-ventilated hydrofoil’) was first proposed as a method to reduce drag in the 1950’s [6]. Due to the increased pressure on the blunt base, the resulting streamwise pressure integral over the foil surface is reduced. More recently, Elms [7] proposed an intercepted base-ventilated hydrofoil, equipped with a rotating tail section, for ride control of high-speed craft. Also, the flow around a transom mounted interceptor [8], can be considered as a ventilated cavity flow with an ‘infinite’ cavity, subjected to atmospheric pressure, detaching from the interceptor tip.

Ventilated cavity flows have been of interest at the Australian Maritime College (AMC) Cavitation Research Laboratory (CRL) in recent years. The cavitating flow over a wall mounted fence has been investigated numerically, both using a potential flow Boundary Element Method (BEM) [9] and Computational Fluid Dynamics (CFD) [10]. A comprehensive numerical study (using BEM) of intercepted base-ventilated hydrofoils has been reported by Pearce and Brandner [11] and a limited set of experimental data has been presented by the same authors [12].

In this report, ventilated cavity flow over a 3D wall mounted fence has been examined experimentally in the CRL cavitation tunnel. This flow is of interest for the generation of forces

<footnote n="1">¹Australian Maritime Collage, University of Tasmania, Launceston, Tasmania, Australia</footnote>

<footnote>*Corresponding author: Luka.Barbaca@utas.edu.au</footnote>
from geometric discontinuities/interceptor type devices as well as being a cavitating flow of basic interest. The parameters that control cavity geometry are investigated and basic cavity physics are described.

# 1. EXPERIMENTAL OVERVIEW

A schematic representation of ventilated cavity flow over a wall mounted fence is shown in figure 1. A fence, of a height $h$, is immersed in the upstream wall boundary layer of thickness $\delta$. $\delta$ is defined as the distance from the wall where $U$ is 99% of the freestream velocity $U_\infty$. Air is supplied to the wake region of the flow through a manifold on the downstream face of the fence. A ventilated cavity, with re-entrant jet closure, is shown detaching from the sharp fence tip.

<figure><img src="image_3.png" /><figcaption>**Figure 1.** Sketch of a wall mounted fence immersed in the upstream wall boundary layer with a ventilated cavity detaching from the sharp tip. Air is supplied through the downstream face of the fence.</figcaption></figure>

The fundamental dimensionless parameter characterizing cavitating flows is the cavitation number, which in general form can be expressed as $\sigma_c = (p_\infty - p_c) / 0.5 \rho U_\infty^2$, where $p_c$ is the pressure inside the cavity, $p_\infty$ is the reference free-stream pressure, $\rho$ is the liquid density and $U_\infty$ is the reference freestream velocity. The experimental setup was developed to examine the dependence of cavitation number on the flux of injected air, fence height based Froude number ($Fr = U_\infty / \sqrt{gh}$, where $g$ is the gravitational acceleration) and vapour pressure, $p_v$, based free-stream cavitation number ($\sigma_v = (p_\infty - p_v) / 0.5 \rho U_\infty^2$). The rate at which air is injected in the flow is characterized by a volumetric flowrate coefficient $C_{Qv} = Q_m / \rho_{air} U_\infty S$, where $Q_m$ is the mass flow of the injected air, $\rho_{air}$ is the air density and $S$ is the reference area (for the present case it is the surface of the fence face). Alongside the cavitation number, the drag $D$ is examined with respect to the aforementioned parameters. The drag is expressed in its non-dimensionalised form, as the drag coefficient $C_D = D / 0.5 U_\infty^2 \rho S$. The cavity length $l_c$ dependence on $C_{Qv}$ was also investigated.

The experiments were performed in the CRL water tunnel. The tunnel design [13, 14] incorporates a large tank downstream of the test section for bubble coalescence and separation. This feature, combined with auxiliary systems for the rapid degassing and continuous evacuation of the large quantities of incondensable gas, enables efficient conduct of tests involving ventilation (i.e. injection and continuous removal of large quantities of air). The tunnel test section measures 0.6 x 0.6 m square, by 2.6 m long. The operating

velocity and pressure ranges are 2 to 12 m/s and 4 to 400 kPa absolute respectively. The tunnel volume is $365 \text{ m}^3$ and is filled with demineralised water. Optical access is provided through acrylic windows on each side of the test section.

The experimental setup has been developed to study ventilated cavity flow over 2D and 3D wall mounted fences. For the present study only results obtained with the 3D fence model are presented. The fence model (figure 2), equipped with an internal manifold for air distribution, is machined from a single stainless steel bar. The fence is 10 mm high, with a V-notch machined at the fence front tip to ensure a stable cavity detachment. The model is 0.156 m wide and spans approximately a quarter of the test section. The shape of the rear part of the fence does not have an influence on the flow, as it is located completely inside the cavity. The air distribution system consists of an internal channel and 10 equi-spaced streamwise outlets distributing air into the wake of the fence. The model is mounted on a six-component force balance, attached to the test section ceiling. A tube is routed through the balance for the air supply.

<figure><img src="image_4.png" /><figcaption>**Figure 2.** A rear view of the fence model. Ten equi-spaced passages for the air supply can be seen on the downstream face of the fence. A V-notch is machined at the fence front tip to ensure a stable cavity detachment.</figcaption></figure>

A scani-valve system used for pressure measurement is represented schematically in figure 3. This setup allows use of a single pressure transducer for all measurements, eliminating the need to apply corrections arising from transducer zero and span errors. The freestream dynamic pressure and pressure inside the cavity are measured relative to the freestream static pressure, from which $\sigma_c$ can be derived. The cavity pressure is measured with a wall taping located just downstream of the model, with a tube routed through the balance.

The test section absolute pressure is measured, depending on the value, from high or low range Siemens Sitransp absolute pressure transducers models 7MF4333-1FA02-2AB1 and 7MF4333-1GA02-2AB1 with estimated precision of 0.13 and 0.48 kPa respectively. The test section velocity is measured from the calibrated contraction differential pressure. Depending on the value, a high and low range Siemens Sitransp differential pressure transducers models 7MF4433-1DA02-2AB1-Z and 7MF4433-1FA02-2AB1-Z are used, with estimated precisions of 0.007 and 0.018 m/s respectively. The air mass
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Schematic of the scani-valve system used for obtaining the cavitation number, $\sigma_c$. Air injection is via a mass flow meter. Gas pressure measured from the taping inside the ventilated cavity is converted to a liquid pressure (necessary for the differential pressure transducer operation) using the cavity-water interface.</figcaption></figure>

flow rate is controlled and measured using an Alicat Scientific model MCR-500-SLPM-D (flow rate range 0-500 SLPM) mass flow meter with an estimated precision of 3 SLPM. The ventilated cavitation number is measured using a Validyne model DP15TL differential pressure transducer (estimated precision of 0.2 kPa) via Swagelok model SS-43Z6FS1 7-way valve actuated using a stepper motor controlled from the data acquisition system. The force balance used to measure the model drag has a maximum rated load of 2 kN and an estimated precision of 0.15 N. The dissolved gas content of the water is measured using an Endress+Hauser OxyMax WCOS 41 membrane sensor.

The three independently prescribed variables that control ventilated cavity flow over a fence are; air ventilation rate, Froude number and free-stream cavitation number. Due to the air flow rate being measured via a mass flow meter, the volumetric flowrate coefficient could not be prescribed (it depends on the gas pressure inside the cavity and the free-stream conditions), and it had to be calculated using the cavity pressure derived from the measured ventilated cavitation number. To determine the range of $Q_m$ values (for a particular free-stream condition), cavity length was increased beyond the test section outlet to establish the $Q_m$ upper bound. Approximately ten $Q_m$ values were examined for each set of the free-stream conditions.

Tests were conducted for three $Fr$ values (controlled with the test section velocity) and three values of $\sigma_v$ (controlled with the test section static pressure). The examined values were 20.1, 25.3 and 30.3 for the $Fr$ and 0.55, 0.75 and 0.95 for the $\sigma_v$. The fence model was fully immersed in the oncom-

ing upstream wall boundary layer, with the boundary layer thickness to fence height ratio of approximately 1.9. The tests were conducted with a dissolved $O_2$ content between 2 and 6 ppm. Cavity length has been obtained using still forward-lit photography as the average from at least ten images.

## 2. RESULTS AND DISCUSSION

### 2.1 Cavity geometry

A typical geometry of a fully formed ventilated cavity is shown in figure 4. The cavity has a stable detachment from the fence upstream face sharp tip and sides. The cavity can be divided into two regions along its length. The region closer to the fence is almost entirely filled with air and the zone with a smooth cavity/water interface. In the rear part of the cavity injected air is entrained into the main flow. The closure of the cavity exhibits re-entrant jet behaviour [15]. The re-entrant jet can be described as a wave penetrating into the cavity and transporting liquid upstream along the wall. The liquid falls under gravity, engulfing air into bubbles. These are then entrained into the main flow predominantly through the shedding process at the cavity closure and, to a lesser extent, via the re-entrant jet/water interface. Depending on the cavity length and free-stream conditions, the re-entrant jet can extend all the way to the fence, or be contained to only a portion of the cavity length. In figure 4, re-entrant jet region can be seen as a chaotic region with a broken cavity/water interface. The wake of the ventilated cavity consists of a continuous stream of air bubbles entrained in the main flow. The unattached bubbles on the sides of the cavity illustrate
<figure><img src="image_6.png" /><figcaption>**Figure 4.** A typical geometry of a fully formed ventilated cavity. The upstream region of cavity is filled with the air and has a smooth cavity/water interface. The closure region exhibits re-entrant jet behaviour. The re-entrant jet causes cavity break-up and resulting bubbles are entrained in the main flow predominantly through shedding process at the closure and, to a lesser extent, via the re-entrant affected cavity interface. The wake consists of a constant stream of entrained bubbles.</figcaption></figure>

the effect of three-dimensional flow with vortices entraining a small portion of the ventilated air into the flow. These vortices also cause cavity necking (reduction in width) along the cavity length.

For ventilated cavity flows, at particular free-stream conditions, $\sigma_c$ is controlled solely by the air ventilation rate, $C_{Qv}$. The dependence of $\sigma_c$ on $C_{Qv}$ can be derived from figure 5 (with $Fr = 25.3, \sigma_v = 0.95$). Along the curve, three regimes

can be identified. In regime (a), a ventilated cavity is not yet fully formed. The short cavity present has a typical shear layer cavitation appearance. In regime (b), cavitation number has a linear dependence on the ventilation rate. A ventilated cavity is fully formed and a re-entrant jet closure is present. At the beginning of this region the re-entrant jet impinges on the downstream face of the fence. With reduction in cavitation number and increase in cavity length, the re-entrant jet no longer impinges on the fence. Despite these differences there remains a linear relationship between $\sigma_c$ and $C_{Qv}$. In regime (c), the flow is said to be ‘blocked’ [16]. On the left hand side of the curve a vertical asymptote is present, representing the minimum cavitation number value obtainable, $\sigma_{min}$. When this minimum cavitation number is reached the cavity grows ‘infinitely’ with even the slightest increase in $C_{Qv}$. The blocked cavitation number is a function of the degree of confinement of the flow domain, which in this case is the ratio between the maximum cavity and tunnel test section cross-sectional areas normal to the flow direction.

Figure 6 shows the relation between $l_c/h$ and $\sigma_c$ (for $Fr = 20.1, \sigma_v = 0.95$). It can be seen that the data follows a power law ($l_c/h = 0.7369\sigma_c^{-2.142}$). This power law behaviour is characteristic of an unbounded flow [17]. This indicates that any blockage effect present does not significantly affect the results obtained.

The influence of a change in free-stream conditions, i.e. $Fr$ and $\sigma_v$, on the dependence of $\sigma_c$ on $C_{Qv}$ has also been investigated. In figure 7 curves of $\sigma_c$ versus $C_{Qv}$ are shown for three $Fr$ values (for $\sigma_v = 0.95$). It can be seen that with the increase in $Fr$ a higher $C_{Qv}$ is needed to obtain the same

<figure><img src="image_7.png" /><figcaption>**Figure 5.** Dependence of cavitation number on the volumetric flowrate coefficient (for $Fr = 25.3, \sigma_v = 0.95$). Three regimes can be differentiated along the curve: a) shear layer cavitation, b) fully formed ventilated cavity with a linear dependence and c) cavity in ‘blocked’ conditions. The vertical asymptote represents a minimum cavitation number obtainable under the examined conditions.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Figure 6.** Non-dimensional cavity length as a function of cavitation number (for $Fr = 20.1$, $\sigma_v = 0.95$). The curve exhibits a power law behaviour ($l_c/h = 0.7369\sigma_c^{-2.142}$), which is characteristic of an unbounded flow.</figcaption></figure>

$\sigma_c$, i.e. more air needs to be injected into the cavity. With the increase in $Fr$ the slope of the linear region is increased. $\sigma_{min}$ also increases with an increase in $Fr$, which suggests a higher degree of confinement with increased free-stream velocity. This may be attributable to an increase in the cavity thickness due to the higher vertical velocity component at the detachment point at the fence tip.

<figure><img src="image_9.png" /><figcaption>**Figure 7.** Relation between $\sigma_c$ and $C_{Qv}$ for the cases with different Froude number and constant free-stream cavitation number ($\sigma_v = 0.95$)</figcaption></figure>

Figure 8 shows the alternate case of varying $\sigma_v$ for a fixed $Fr$ ($Fr = 25.3$). With the increase in $\sigma_v$ more air has to be injected to achieve the same $\sigma_c$ value. The linear part of the curves has relatively constant slope for all $\sigma_v$ values. $\sigma_{min}$ is approximately constant, which is expected as the free stream velocity is held constant.

<figure><img src="image_10.png" /><figcaption>**Figure 8.** Dependence of $\sigma_c$ on $C_{Qv}$ for different free-stream cavitation number and constant Froude number value ($Fr = 25.3$).</figcaption></figure>

## 2.2 Drag

Traditionally, the main interest in devices utilizing ventilated cavities has been for drag reduction. In figure 9 the dependence of $C_D$ on $\sigma_c$ is shown for three values of $Fr$ (for $\sigma_v = 0.95$). The drag coefficient decreases approximately linearly with the decrease in cavitation number. The non-linearity present for high $\sigma_c$ is due to the shear layer cavity behaviour, as a fully formed cavity in not yet present. It can be seen that for $\sigma_c = \sigma_{min}$ the drag also has a minimum value ($C_{Dmin}$). Drag slightly decreases with increase in $Fr$ (figure 9). The difference in $C_{Dmin}$ through the range of examined $Fr$ is approximately 1.5%. Figure 10 gives the alternate case of varying $\sigma_v$ for a fixed $Fr$ ($Fr = 25.3$). It can be seen that $C_D$ is independent of $\sigma_v$ in the region where ventilated cavity is fully formed. A slight difference exists for high $\sigma_c$ values, again where the shear layer cavitation regime is present.

## 3. CONCLUSIONS

Ventilated cavity flow over a three-dimensional wall mounted fence has been investigated experimentally in a cavitation tunnel. An experimental setup has been developed to examine the influence of air ventilation rate and free-stream conditions on the cavitation number, cavity length and drag. It was found that three flow regimes can be differentiated as cavitation number varies: a) shear layer cavitation for high $\sigma_c$ values, b) for intermediate $\sigma_c$ values, a fully formed ventilated cavity with a linear dependence of $\sigma_c$ on $C_{Qv}$, and c) ‘blocked’ cavity flow when $\sigma_c \to \sigma_{min}$. In the case of a fully formed ventilated cavity the cavity closure exhibits a re-entrant jet behaviour. The re-entrant jet shedding is primarily responsible for air entrainment into the flow. Cavity length as function of $\sigma_c$ follows a power law behaviour.
<figure><img src="image_11.png" /><figcaption>**Figure 9.** Drag coefficient as a function of cavitation number for three values of Froude number and constant free-stream cavitation number value ($\sigma_v$ = 0.95).</figcaption></figure>

With an increase in $Fr$ and/or $\sigma_v$, significantly more air is needed to obtain the same $\sigma_c$ value. With a decrease in $\sigma_c$, drag coefficient decreases linearly until it reaches a minimum value when $\sigma_c = \sigma_{min}$. The $C_D$ shows a mild dependence with $Fr$ and is independent of $\sigma_v$.

A companion study is planned to investigate the effect of fence immersion in the upstream wall boundary layer. A series of unsteady pressure measurements in the closure region is also to be conducted, coupled with the high-speed camera imaging, to gain a deeper insight into the re-entrant jet closure physics. These 3-D wall mounted fence results will also be compared with a future study of ventilated cavity flow over a 2-D wall mounted fence.

## ACKNOWLEDGMENTS

The authors wish to acknowledge the assistance of Mr Robert Wrigley and Mr Steven Kent in carrying out the experiments and the support of the Australian Maritime College.

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