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%%                           CHAPTER 2 - Experimental setup
%%				updated			6 May 2013
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\chapter{\uppercase {Experimental setup}}

\section{Main tank}

The experiment was conducted in the Hydrodynamic Laboratory Building in the Ocean Engineering Program at Texas A \& M University at College Station. The experimental tank is an open and elevated glass-fronted steel tank measuring $1.30 m$ in height, $1.32 m$ in width and $3.00 m$ in length. A top-mounted rack allows steady, precise three-dimensional instrument placement within the tank. To remedy unevenness in the tank bottom, a false floor was installed, thus providing a plane and level surface for placement of rigid simulated vegetation and the jet outlet stand.

\section{Jet assembly and constant head tank} \label{sec:jet assembly}

A constant head tank is a simple and reliable means of establishing and maintaining a jet with reproducible initial conditions. In this study, an open five-gallon bucket of a ten-inch diameter is suspended by a crane above the main tank, see Figure \ref{fig:supply}. Supplied by a high-speed and -volume bilge pump positioned under the false floor in the far downstream portion of the main tank, the water level in the bucket is held constant at $0.229 m$ above the bucket bottom. Surplus water exits the bucket through perforations above the target water level and falls into a pan that returns the excess water to the experimental tank through a diffuser situated under the false floor and isolated from the upper jet flow chamber by horsehair lining. 
	
\begin{figure}
\centering
\includegraphics[width=0.65\textwidth]{Supply}
\caption[Constant head tank design]{Suspended constant head tank at maximum vertical extent and experimental tank}
\label{fig:supply}
\end{figure}
	
	Water is drawn continuously from the bottom of the bucket through a $3.66 m$ long flexible tube with a $1.27 cm$ inner diameter and expelled from a $0.12 m$ rigid plastic tube with an inner diameter of $6.35 cm$. This extended nozzle was designed to ease calibration and reduce tangential motion of the fluid. Although the main tank was filled to $0.387 m$, the jet outlet was positioned so that the expanding jet cone remained sufficiently distant from walls, floor and free surface within the measurement domain.
	
	 Effectively, the jet vertical centerline is $0.187 m$ above the false floor and $0.200 m$ under the free surface throughout the measured range. \citet{Shinneeb2011} employed a similar main tank and jet setup, but varied the jet centerline and measurement plane vertically at a ratio of $H/d$, where $H/2$ is distance from free surface to jet centerline and $d$ is jet nozzle diameter. That study considered $5 \le H/d \le 15$; the present study, for reference, has a fixed $H/d = 59$ \citep{Shinneeb2011}.
	 
\begin{figure}
\centering
\includegraphics[width=0.65\textwidth]{Props_f}
\caption[Coordinate system definition]{Plan view of measurement plane coordinate system}
\label{fig:Props_f}
\end{figure}
	 
	It is known that the halfwidth of an axisymmetric, incompressible non-buoyant jet will expand at an angle of 5.43$^{\circ}$ with respect to the jet centerline \citep{Lipari2011}. The jet height was chosen so that the maximum streamwise extent of measurements at $0.914 m$ occurs at twice the halfwidth $b$, see Figure \ref{fig:Props_f},  and well before wall effects have measurable influence on self-similarity. Necessitated by irregularities in the shape of the tank bottom, placement of the false floor resulted in the mounted jet centerline measuring $73.7 cm$  from the left wall and $58.4 cm$ from the right wall. Though the jet cone does not contact either wall, the offset produces a slight variance in the tank recirculation current that is discernible in the resultant spanwise velocity profiles.
	
	The constant head tank is raised or lowered to produce a range of turbulent initial nozzle velocities, of which five were chosen to generate collapsible profiles to improve experiment accuracy and permit the determination of experimental error. The highest tank placement $\Delta h$, $1.93 m$ difference between water level of constant-head tank and water level of main tank, was the maximum vertical extent of the crane, and the lowest tank placement, $0.71 m$, was the minimum elevation for which the return pan siphon would function. Intermediate placements occurred at $1.63 m$, $1.32 m$ and $1.02 m$. 
	
	After measuring flow volumes for these volumes at the water surface in the main tank, the various placement heights produced the bulk velocities $u_0$ in Table \ref{tab:speeds}, assuming a  top-hat initial nozzle velocity profile \citep{Xu2002}. Each jet exhibits fully turbulent initial conditions, $Re_{\overline{M_0}} \ge 4000$, where $Re_{\overline{M_0}}$, non-dimensional momentum Reynolds-like number, is defined by  
	\begin{eqnarray}
	Re_{\overline{M_0}}=\sqrt{\frac{\overline{M_0}}{\rho}} \frac{1}{\nu} \label{eq:ReMom}
	\end{eqnarray}
	where $\overline{M_0}$ is mean initial momentum at the nozzle, $\rho$ is density and $\nu$ is kinematic viscosity  \citep{Lipari2011}. An alternate form of the Reynolds number with bulk discharge velocity as characteristic velocity scale is occasionally used and is defined by  
	\begin{eqnarray}	
	Re_{\overline{u_0}}=\frac{\overline{u_0} d}{\nu} \label{eq:ReBulk} 
	\end{eqnarray}
	where $\overline{u_0}$ is mean initial velocity at the nozzle and $d$ is the jet outlet diameter. By geometry, $Re_{\overline{u_0}} / Re_{\overline{M_0}} = 1.13$ for radially axisymmetric jets \citep{Lipari2011}. 
	
	\begin{table}
\caption[Constant-head tank placement and speed]{Constant-head tank placement and speed}
\centering
\begin{tabular}{ccccc}
Speed & $\Delta h$ m & $\overline{u_0}$ m/s & $Re_{\overline{M_0}}$ \\ 
\hline
1 & $ 1.93 $ & $ 3.31 $ & $18600 $  \\ 
2 & $ 1.63 $ & $ 3.06 $ & $17200$  \\
3 & $ 1.32 $ & $ 2.77 $ & $15500$ \\
4 & $ 1.02 $ & $ 2.45 $ & $13700$  \\
5 & $ 0.71 $ & $ 2.08 $ & $11700$  \\
\end{tabular}
\label{tab:speeds}
\end{table}
	
	The described jet and tank setup is typical of modern jet studies. Due to the wealth of literature regarding free jets, it is important to reproduce accepted jet self-similarity in the present measurements before extending analysis to vegetated arrays, presented in Chapter \ref{sec:Theory}.

\section{Plant array}
	
	Without installation of vegetation, this study confirms accepted self-similarity and conservation parameters of axisymmetric jets. In this study, however, this initial analysis serves as a calibration and a necessary stepping stone to studying the effects of introducing simulated vegetation as an obstacle to flow. Once validated as a self-similar, conserving jet, arrays of simulated \textit{Spartina alterniflora}, smooth cordgrass, are inserted in three configurations for each of the five test speeds.
	
	 \textit{Spartina alterniflora} is a common rigid, emergent wetland plant and is simulated here by smooth acrylic rods of $6.35 mm$ diameter vertically mounted on $0.305 m$ by $0.914 m$ acrylic sheets in an equidistant staggered pattern so that each interior plant is $8.8 cm$ from each of its six neighbors, similar to the mathematical model proposed by \citet{BRAUN1995}, though sparser. Stem oscillation produces random fluid-elastic instabilities and thus produces undesirable symmetric vortex shedding \citep{A.1986} and \citep{J.1979}. This undesired velocity-induced vibration was eliminated by mounting an aluminum c-channel atop rows of vegetation for $24 \le x/d \le 72$ perpendicular to the jet centerline. 

	  Although relatively sparse compared to recent open-channel vegetation studies---vegetation density per meter $a$, given by
	  \begin{eqnarray}	
	a=\frac{d}{\Delta S^2} \label{eq:vegDensity} 
	\end{eqnarray}
	where $\Delta S$ is inter-plant spacing and compared with other studies in Table \ref{tab:plant_studies}---it is this sparseness that retains the basic shape of the jet cone and enables comparison\citep{Nepf1999}. In nearly all studies of emergent, rigid vegetation, only plant stems---actual or simulated---are installed; in at least two instances, however, arrays of both simulated \textit{Spartina alterniflora} stems and leaves were studied \citep{Nepf1997} and \citep{Lightbody2006}. \citet{Yagci2010} found that the accuracy of a rigid cylinder representing an actual plant in terms of axial velocity reduction depended on the depth of the measurement plane.
	
	\begin{table}
\caption[Related studies]{Studies involving flow through vegetated arrays}
\centering
\begin{tabular}{ccccc}
Study & $a d$ & Sensor type \\ 
\hline
present study & $ 0.0052 $ & ADV  \\ 
\citet{A.1986} & $0.5$ & Tracer particles and camera \\
\citet{Balachandar2002} & --- & Numerical model \\
\citet{BRAUN1995} & $0.25$ & Numerical model \\
\citet{HUAI2009} & $0.0036$ & ADV \\
\citet{Leonard1995} & $0.003 - 0.083$ & LDV \\
\citet{Lightbody2006} & $0.01$ & ADV \\
\citet{Liu2008a} & $0.016$ & LDV \\
\citet{Murphy2007} & $0.015 - 0.048$ & ADV, LDV and FVA \\
\citet{Neary2003} & --- & Numerical model \\
\citet{Nepf1999} & $ 0.008 - 0.07$ & ADV and LDV \\
\citet{Nepf1997} & $0.007 - 0.288  $  & ADV and LDV  \\
\citet{Neumeier2004} & --- & ADV \\
\citet{Pye1995} & $ 0.006$ & Current meter \\
\citet{Stoesser2009-07-01} & $ 0.02$ & Numerical model \\
\citet{Tanino2008} & $0.12 - 0.45 $ & ADV\\
\end{tabular}
\label{tab:plant_studies}
\end{table}
	  
	  In addition to the non-dimensional parameter $a d$, where $d$ is stem diameter, plant density can be expressed by the dimensionless parameter $\phi$, defined as 
	  \begin{eqnarray}	
	\phi= m A_S \label{eq:vegDensityphi} 
	\end{eqnarray} 
	where $m$ is number of plants per horizontal area and $A_S$ is stem cross-sectional area \citep{Tanino2008}. There is no simple conversion from one parameter to another. By definition, $ad$ is the preferred dimensionless vegetation density parameter for equidistant regular arrays, whereas $\phi$ is well suited for dense, random placements, such as simulated mangroves \citep{Tanino2009}. For the present study, $ad=0.0052$ and $\phi = 0.00477$.  This $ad$ was chosen to compare with other studies investigating \textit{Spartina alterniflora}. The typical density of emergent marsh grasses with rounded stems is typically $0.01 \le a \le 0.07 \frac{1}{cm}$ \citep{Nepf2008}.
	 
Vortices shed from upstream cylinders attach to downstream inline cylinders, whereas side-by-side cylinders favor a mode of vortex shedding equivalent to an isolated cylinder if spacing is adequate \citep{Kiya1980} and \citep{Akilli2004}. If $\Delta S \le 1.4 d$, no matter the orientation, as is the case in very dense arrays, the same study found that adjacent cylinders act as a single body in terms of vortex shedding \citep{Kiya1980}. In the present study, the staggered cylinder placement is between both of these extremes, so that while the first rows of plant stems appear to shed vortices as isolated cylinders; stems in the interior of the array not only shed their own vortices but also are subjected to vortices shed by upstream rows. Staggered arrays produce more flow resistance than inline arrays \citep{Liu2008a}.

\begin{figure}
\centering
\includegraphics[width=1\textwidth]{Configs_f}
\caption[Measurement stations and array configurations]{Plan view of measurement stations with sections and configurations indicated}
\label{fig:Configs_f}
\end{figure}

	Vegetated plates were installed in three configurations, see Figure \ref{fig:Configs_f}. In the free-jet configuration, no simulated vegetation is present; this configuration serves to validate the setup and analysis. This jet assembly was specifically chosen to replicate the most prevalent jet in literature, the axisymmetric radial jet. In Configuration 1, two vegetated arrays are inserted so that the free jet cone enters vegetation for $x/d > 120$ and all but Section 4 are within the free jet region. In configurations 2 and 3, the free jet cone enters vegetation at a smaller $x/d$, as described in Table \ref{tab:configurations}. 
	
\begin{table}
\caption[Configurations]{Extent of vegetation by configuration}
\centering
\begin{tabular}{ccccccc}
Configuration & Free jet range &  & Vegetated range &\\ 
 &  $x/d$ & Sections &  $x/d$ & Sections \\ 
\hline
Free jet & $ 0-216 $ & $1-4$ &  --- &  ---\\ 
1 & $ 0-120 $ & $1-3$ & $120-216$ & $4$ \\
2 & $ 0-72 $ & $1$ & $ 72-216 $ &  $2-4$ \\
3 & $ 0-24 $ &  --- &  $24-216$&  $1-4$  \\
\end{tabular}
\label{tab:configurations}
\end{table}	

	Therefore, Configuration 1 represents a fully developed and self-similar jet flow in the distant zone of established flow at the point of impingement with vegetation. By contrast, the point of impingement for Configuration 3 is early within the zone of flow establishment. Configuration 2 is an intermediate stage between configurations 1 and 3, in which the flow impinges on vegetation within the early zone of established flow. The zone of established flow, as determined by this study, occurs between $12 < x/d < 24$, as is discussed in Chapter \ref{sec:SS_free}.
	
\section{Measurement and record length}
	
	A 3D Nortek Vectrino ADV, with the control volume vertically centered on a measurement plane parallel to the water surface and vertically coincident with the jet centerline, recorded velocity in streamwise, spanwise and tangential directions. The addition of a fourth acoustic leg permitted the measurement of two vertical velocities; these were averaged to produce a single tangential velocity, thus the terms tangential and vertical are equivalent due to alignment. 
	
	The initial axial nozzle velocity was on the order of $1 m/s$; therefore, a sampling rate of $50 Hz$ was chosen to capture statistically independent samples and the main tank was seeded with seeding particles to ensure sufficiently high signal-to-noise ratio and signal correlation. Initial attempts to reduce tank recirculation with horsehair mounted on the far downstream wall resulting in substantial loss of ADV seed particles. Removal of the horsehair did result in a visible recirculation current visually estimated at no more than $0.01 m/s$, which, as results will demonstrate, has a minimal effect on velocity profiles and no clear effect on momentum conservation or entrainment halfwidth. The sampling frequency should be at least twice as high as the highest frequency of interest, the so-called Nyquist frequency \citep{Atta1974}. In order to determine optimal record length, the ADV was positioned in the wake of a cylinder at a downstream position in fully vegetated flow. Allowing a maximum 10\% deviation threshold for any realization from the full record axial mean, the minimum sample length at $50 Hz$ was $36.3 s$. Because the mean axial centerline velocity serves as a characteristic velocity scale, it is important to achieve an accurate mean. 
	
	In general, however, the record length at each station was $140-180 s$. Radial and tangential velocities are considerably smaller in magnitude and variable and are not characteristic length scales; therefore, higher deviation is permitted. At this sample length, maximum deviation of radial and tangential velocity realizations from mean are approximately 75\% and 200\%, respectively, due to the small magnitude of these velocities and a raw mean of zero, see figures \ref{fig:Comparesect1Ui}-- \ref{fig:Comparesect4Ui} in Appendix \ref{sec:velplots}. Over all sections and configuration, $\frac{\overline{v}}{\overline{u_c}} < 0.1 $ and $\frac{\overline{w}}{\overline{u_c}} \ll 0.1$.  
	
	In order to capture adequate spatially varying velocity data, the selected testing pattern, see Figure \ref{fig:Configs_f} and Table \ref{tab:sections}, consisted of 64 axial and radial measurement stations. Twelve equidistant centerline measure stations at a spacing of $7.62 cm$, the first of which is placed $7.62 cm$ downstream of the jet nozzle, record axial decay. Radial measurement stations resemble perpendicular branches off of the axial measurement line and extend a distance of twice the anticipated free-jet halfwidth---defined as the radial distance at which $u(\eta)=u_c/2$---each side of the centerline at a spacing of $2 cm$. Aside from Section 1, which has only 9 stations total, this radial measurement spacing produced sufficient radial resolution to demonstrate momentum conservation of the free jet case with low error. 	
	
\begin{table}
\caption[Measurement stations]{Location and extent of measurement sections}
\centering
\begin{tabular}{ccccc}
Section & Alignment & Stations & $x/d$  & $\left(r/r_{1/2}\right)_{max}$\\ 
\hline
1 & radial & $ 9 $ &  $48$ & $2.70$\\ 
2 & radial & $13$ & $84$ &   $2.25$\\
3 & radial & $15$ & $120$ &  $1.71$ \\
4 & radial & $17$ &  $132$ &   $1.85$ \\
5 & axial &  $12$ &  $12-144$&  $0$ \\
\end{tabular}
\label{tab:sections}
\end{table}

\section{Postprocessing} \label{sec:postproc}

	Raw ADV output includes instantaneous velocity, correlation and signal-to-noise ratio in three Cartesian directions. Although there is value to this raw velocity and its mean over the entire record, it is common practice to compute the root-mean-square (RMS) to obtain turbulent strength according to 	
	\begin{eqnarray}
		u' = \sqrt{\frac{1}{N}\sum_{i=1}^{N}\left(u'_i\right)^2} = \sqrt{\frac{1}{N}\sum_{i=1}^{N}\left(u - \overline{u}\right)^2} \label{eq:turbintensity} 
		\end{eqnarray} 
		where $u'$ is a turbulent fluctuation and $\overline{u}$ is a mean velocity \citep{Carollo2002}. 
		Figures \ref{fig:CompareC0sect4Ui_special} and \ref{fig:CompareC0sect4ujui_special} illustrate the comparative amplitudes of mean and RMS velocity profiles of the same data set, Section 4 of the free jet, normalized to centerline axial velocity. 
	
\begin{figure}
\centering
\begin{subfigure}[b]{0.5\textwidth}
\centering
\includegraphics[width=\textwidth]{CompareC0sect4UiMEAN_special}
\caption{$\mathrm{\overline{u_i} \; mean}$ \\ $\overline{u}(+)\; \overline{v}(\times)\; \overline{w}(\bigcirc)$}
\label{fig:CompareC0sect4UiMEAN_special}
\end{subfigure}%
\begin{subfigure}[b]{0.5\textwidth}
\centering
\includegraphics[width=\textwidth]{CompareC0sect4UiRMS_special}
\caption{$\mathrm{\overline{u_i} \; RMS}$ \\ $\overline{u}(+)\; \overline{v}(\times)\; \overline{w}(\bigcirc)$}
\label{fig:CompareC0sect4UiRMS_special}
\end{subfigure} 
\caption[Normalized spanwise mean velocity profiles]{Normalized spanwise mean velocity profiles for Section 4 of the free jet}\label{fig:CompareC0sect4Ui_special}
\end{figure}

\begin{figure}
\centering
\begin{subfigure}[b]{0.5\textwidth}
\centering
\includegraphics[width=\textwidth]{CompareC0sect4ujuiMEAN_special}
\caption{$\mathrm{\overline{u_j' u_i'} \; mean}$ \\ $\overline{u'u'}(+)\; \overline{v'v'}(\times)\; \overline{w'w'}(\bigcirc)$ \\ $\overline{u'v'}(\ast)\; \overline{u'w'}(\Box)\; \overline{v'w'}(\Diamond)$}
\label{fig:CompareC0sect4ujuiMEAN_special}
\end{subfigure}%
\begin{subfigure}[b]{0.5\textwidth}
\centering
\includegraphics[width=\textwidth]{CompareC0sect4ujuiRMS_special}
\caption{$\mathrm{\overline{u_j' u_i'} \; RMS}$ \\ $\overline{u'u'}(+)\; \overline{v'v'}(\times)\; \overline{w'w'}(\bigcirc)$ \\ $\overline{u'v'}(\ast)\; \overline{u'w'}(\Box)\; \overline{v'w'}(\Diamond)$}
\label{fig:CompareC0sect4ujuiRMS_special}
\end{subfigure} 
\caption[Normalized spanwise Reynolds stress profiles]{Normalized spanwise Reynolds stress profiles for Section 4 of the free jet}\label{fig:CompareC0sect4ujui_special}
\end{figure}
			
	In many cases, it may be preferable to despike ADV data prior to use. Based on the physics-based approach to detect and smooth spikes described in \citet{Goring2002}, the present study initially used a modified version of this algorithm that maintains peaks of a user-defined minimum peak width. Additional spatial and temporal despiking techniques are available for particle image velocimetry (PIV) \citep{Weisgraber1998}. Although error was marginally reduced in unobstructed near-centerline flow, peak preservation modifications failed to retain sufficient detail of large-scale turbulent structures along the entrainment boundary, as well as behind stem wakes within the plant array. Overall, an average 5\% of momentum was lost at sections 3 and 4, see Figure \ref{fig:despike133}. In addition, there was no physical justification for the removal of turbulent peaks; therefore, it was decided to retain all raw velocity data, though the occasional aberrant reading may have insignificantly elevated averaged derived quantities, such as volumetric flow rate, momentum and energy. 
	
\begin{figure}
\centering
\begin{subfigure}[b]{0.5\textwidth}
\centering
\includegraphics[width=\textwidth]{133400pstsample}
\caption{Centerline (Configuration 3 Speed 3 Section 4 Station 00)}
\label{fig:despike133400}
\end{subfigure}%
\begin{subfigure}[b]{0.5\textwidth}
\centering
\includegraphics[width=\textwidth]{133418pstsample}
\caption{Entrainment boundary (Configuration 3 Speed 3 Section 4 Station 18)}
\label{fig:despike133417}
\end{subfigure} 
\caption[ADV despiking]{Despiked set with identified points in blue }\label{fig:despike133}
\end{figure}	
		
	As described in Chapter \ref{sec:jet assembly}, the slight offset of the jet centerline within the main tank resulted in unequal recirculation currents. This effect, visible in all spanwise velocity profiles, is small and consistent across all cross-section and does not displace the jet mean from the centerline. Jet self-similarity parameters are defined for a presumed Gaussian curve with a maximum mean coincident with the jet centerline; therefore, the curve is folded and averaged about the centerline to produce a spanwise Gaussian profile with symmetric sides, see Figure \ref{fig:thesisUspanwisedatafitfull}. During early alignment of the jet, the ADV was set to record at varying distances along the jet centerline; records were processed and Gaussian fitted to ensure vertical and horizontal centerline alignment. Due to the slight unequal recirculation present within the tank, most radial profiles exhibit variability at extreme radial stations.
	
\begin{figure}
\centering
\includegraphics[width=0.6\textwidth]{thesisUspanwisedatafitfull}
\caption[Gaussian fit to spanwise axial velocity profile]{Example Gaussian fit to spanwise axial velocity profile \\ $\mathrm{realization}(\cdot)\; \mathrm{raw \;mean}(\times)\; \mathrm{folded \;mean}(\ast) \; \mathrm{halfwidth}(\bigcirc) \; \mathrm{Gaussian \;fit}(-)$}
\label{fig:thesisUspanwisedatafitfull}
\end{figure}	

	Each measurement station was tested under three configurations at five speeds, in addition to free jet configurations,  across each of the 64 stations. All five jet speeds are well-developed turbulent flows, and therefore, as expected from jet theory, collapse upon normalization with respect to respective initial nozzle velocity. Thus, after collapse, the fifteen vegetated runs produce three collapsed data sets---one for each configuration---as well as the free jet validation runs. Throughout the remainder of this study, referenced quantities are speed averaged, and the corresponding errors are the Gaussian standard deviation of the normalized five speeds prior to averaging. To obtain the collapsed velocity, each computed mean value is normalized  with respect to its bulk nozzle velocity. These five non-dimensional mean values are then averaged to obtain the collapsed value. This procedure is applied to mean velocities, Reynolds stresses and turbulent transport triple products, though the power of the normalizing bulk velocity is adjusted to obtain a non-dimensional mean. Figure \ref{fig:thesisUspanwisedatafitfull} illustrates the collapsing of the five speeds to a single raw mean value and demonstrates the effect of the recirculation at extreme radial measurement stations. 
	

