Acoustic Doppler Velocimeters (ADV) Performance Curves (APCs) sampling the flow turbulence

The capability of Acoustic Doppler Velocimeters (ADV) to resolve flow turbulence is analyzed by mean of a new tool denoted ADV Perfomance Curves (APCs). These curves can be used to define optimal flow and sampling conditions for turbulence measurements using an ADV. To generate these curves, a conceptual model is developed which simulates both, different flow conditions (flow component) and the instrument operation (instrument component). Different scenarios (ranges of flow conditions and sampling frequencies) are simulated using the conceptual model to generate several synthetic time series of water velocity and corresponding sampled signals. For the sake of comparison, the main turbulence statistics parameters of the synthetically generated sampled and non-sampled time series are plotted in dimensionless form; these plots are called APCs. The performance of the developed tools is validated using experimental results. Using the APCs a new criterion is proposed to perform ADV measurements with good resolution of the flow turbulence. In cases where this criterion can not be satisfied these curves can be used to make the corrections. Introduction Acoustic Doppler Velocimeters are capable of reporting accurate mean values of water velocities in three directions (Kraus et al.,1994; Lohrman et al., 1994; Voulgaris et al.,1998) even in low flow conditions (Lohrman et al.,1994). On the other hand, the ability of this instrument to accurately resolve flow turbulence is still uncertain (Barkdoll, 2002). Lohrman et al. (1994) argue that the ADV resolution is sufficient to capture a significant fraction of the flow turbulent kinetic energy (TKE), but they identify the Doppler noise as a problem that causes the TKE to be biased high. Most of the research related to the capability of an ADV to resolve turbulence (specifically TKE and spectra) has focused on the definition of this noise level present in the signal and how it can be removed (Lohrman et al.,1994; Anderson et al., 1995; Voulgaris et al., 1998, Nikora et al., 1998, Lemmin et al.,1999 and Mc Lelland et al., 2000). However, little attention has been dedicated to evaluating the filtering effects of the sampling strategy (spatial and temporal averaging) on the turbulent parameters (moments, spectra, autocorrelation functions, etc.). Only Voulgaris et al. (1998) discusses some issues related with the effects of the spatial averaging. As an initial approach, it can be argued that the ADV’s ability to resolve the turbulence will depend on the flow conditions. The objective of this paper is to introduce novel tools, denoted here ADV Perfomance Curves (APCs), which can be used to define optimal flow and sampling conditions for doing turbulence measurements using an ADV. These tools are validated analyzing water velocity signals sampled with ADVs in 10 different experimental setups and flow conditions at the University of Illinois at Urbana–Champaign, USA. Description of ADV operation An ADV measures three-dimensional flow velocities using the Doppler shift principle and consists, basically, of a sound emitter, three sound receivers and a signal conditioning electronic module. The emitter of the instrument generates an acoustic signal that is reflected back by sound-scattering particles present in the water (assumed to move at the water velocity). This scattered sound signal is detected by the instrument receivers and used to compute the signal Doppler phase shift with which the radial flow velocity component is calculated. The ADV uses a dual pulse-pair scheme with different pulse repetition rates (McLelland et al., 2000). The radial velocities vi (i=1, 2, 3) are computed using the Doppler relation. This process of sampling the radial velocities for the three receiver is done by ADV as a whole with frequency fS (equal to 1/T), which is between 100 and 263 Hz depending on the velocity range and the user-set frequency. Then, the radial velocities computed from each receiver are converted to a local Cartesian coordinate system (ux, uy, uz) using a transformation matrix that is determined empirically (through calibration) by the manufacturer (McLelland et al., 2000). During the time it takes to make a three-dimensional velocity measurement (T) the flow may vary, however, these high frequency variations are smoothed out in the process of signal acquisition and cannot be captured by the instrument. The direct implication of these features is that the Cartesian flow velocity represents an averaged value, over an interval time T, of the real flow velocity. In this sense T can be though as the instrument response time, and the process of acquisition itself can be seen as an analog filter with cut-off frequency 1/T (or fS). Two main conclusions can be drawn from the considerations above. The first one is that energy in the signal with frequency larger than fS is filtered out (acquisition process acts as a low-pass filter). The second one is related with aliasing of the signal. Since the velocity signal is sampled at a frequency fS the largest frequency that can be resolved by the instrument is fS/2 (Nyquist theorem, see Bendat et al., 2000). This indicates that energy in the frequency range fS/2<f< fS is folded back in the range 0<f< fS/2. The level of aliased energy will depend on the flow characteristics. After the digital velocity signal is obtained (with frequency fS), the instrument performs an average of N values of this signal producing a digital signal with frequency fR = fS /N, which is the ADV’s user-set frequency with which velocity data is recorded. This averaging process is a digital non-recursive filter (Bendat et al., 2000; Hamming,1983). The consequences of the digital treatment of the signal are analyzed in the following section. Conceptual model A conceptual model is developed here to evaluate the performance of the ADV based on the turbulence characteristics of the flows to be measured with this instrument. The model includes two components, the instrument and the flow components, which simulate both the instrument operation (based on the previous description of how the ADV works) and the power spectrum of flow velocities associated with different flow conditions, respectively. A description of each component is presented next. Instrument component For the purpose of our research, the ADV can be conceptually modeled as a twomodule linear system. The first module is the data acquisition module (DAM). This module encompasses the sound emitter and receivers, the analog to digital converter (ADC), which works at frequency fS, and the computation of flow velocities from the acquired signal. The second module is the data preprocessing module (DPM), which encompasses the averaging of the digital velocity signal that produces data at the user-set frequency fR. The DAM produces a digital signal from the flow velocity, i.e. the input is the flow velocity and the output is a digital signal with frequency fS. This module is modeled through the sampling of synthetic water velocity series produced in the flow component of the conceptual model. The DPM basically performs a time averaging of the output of the DAM in order to produce data at the user-set frequency fR. The output is the water velocity digital signal that the ADV users receive. The low-pass filtering of the signal (in the DPM) has implications in the computation of the spectrum and moments from the signal. The quantification of this effect is discussed later in this paper. Flow component Synthetic water velocities signals need to be generated to represent different ranges of flow conditions. These signals must have turbulence characteristics that resemble realistic conditions. In order to accomplish that a three dimensional model power spectrum is adopted which include all the turbulence characteristics for specified flow conditions. The model power spectrum used in this paper was proposed by Pope (2000). The input parameters of the model are energy-containing-eddy length scale, L, and Kolmogorov length scale η (which can be estimated from the value of the rate of dissipation of turbulent kinetic energy, ε, of the flow). The three dimensional energy-spectrum function, E(κ) predicted by Popé s model is given by ) ( ) ( ) ( 3 / 5 3 / 2 κη κ κ ε κ η f L f C E L − = where C = constant, κ is the wavenumber and fL and fη are shape functions defined as