TECHNICAL NOTE:
Noise of Acoustic Doppler Velocimeter Data in Bubbly Flows

Nobuhito Mori, M.ASCE ¹ , Takuma Suzuki ² and Shohachi Kakuno, M.ASCE ³

February 21, 2007

Abstract

Acoustic Doppler velocimeters (ADV) measurements are useful and powerful for measurements of mean and turbulent components of fluids in both hydraulic experimental facilities and fields. However, it is difficult to use the ADV in bubbly flows because air bubbles generate spike noise in the ADV velocity data. This study describes the validity of the ADV measurements in bubbly flows. The true 3D phase space method originally developed by () is significantly useful to eliminate spike noise of ADV recorded data in bubbly flow in comparison with classical low correlation method.

CE Database subject headings: two phase flow, turbulent flow, bubbles, experimental data, noise

Introduction

Acoustic Doppler velocimeters (ADV) are very popular instruments for measuring flow velocity in both hydraulic experiments and field observations. ADV are very easy to setup and handle but the ADV recorded data contains spike noise due to Doppler signal aliasing, air bubble effects and etc. (i.e. , ). A major problem is that the spike noise looks similar to turbulent components in the velocity data. Therefore, several despiking algorithms have been proposed to remove spike noise from ADV recorded velocity data (, ,). Generally, Fourier low-pass filtering, moving averaging, and acceleration threshold (first differential of velocity) methods are used for removing spike noise from ADV data. The 3D phase space method proposed by () is an excellent method for despiking ADV data because it is efficient and does not require empirical coefficients. Modification of the 3D phase space method was evaluated by ().

ADV measurements are useful, but difficult to analyze in bubbly flows such as the surf zone or aerated flows. Air bubbles are thought to be the source of the spike noise in the ADV velocity data. There have been no quantitative studies to examine the relationship between ADV measured velocity and air bubbles.

In this study, we perform ADV velocity measurements in bubbly flows and examine the validity of despiking, the relationship between spike noise and air bubbles. Finally, the relationship between the air void fraction and mean and fluctuating flow characteristics is discussed.

Experimental Setup

The experiments were conducted in a small circular tank with an air bubble generator. A rotor was placed in the middle of the tank to generate a circular flow around the tank. The ADV (ADVLab, Nortek) was placed in the middle point between the center of the tank and wall. The bubble generator was connected to an air pump with a valve to control airflow rate. The void fractions $\alpha$ at the ADV measurement point were measured by a conventional void probe calibrated with a laser sensor before the experiments. The mean diameter of generated bubbles was measured by high-speed camera and was 1.7mm approximately. A schematic view of the experiments is shown in Figure . The sampling frequency of the ADV was 25Hz, the sampling volume was 9mm and a total of 30000 data points were collected for each case. Thus, the sampling volume was enough larger than the generated bubbles. Seven experiments were conducted with void fractions ranging from 0 to 2.75% but keeping bubble size.

The mean water velocity without bubbles was 6cm/s and the void fractions ranged from 0 to 2.75%. Figure shows the relationship between the void fraction $\alpha$ and the time averaged correlation (unit [%]; COR), and signal-to-noise ratio (unit [db]; SNR). The COR is the value of the signal correlation coefficient for each of the three ADV receivers and the SNR is the signal-to-noise ratio measured at each of the three receivers in ADV (Nortek ADVLab manual). The correlation of ADV data predicts velocity uncertainty; a higher correlation predicts lower uncertainty. Following the manufacturer's instructions, data points were excluded if the correlation was less than 70%. The correlation value is almost 100% in cases without bubbles and is monotonically decreased as the void fraction increased. Finally, COR is dropped to 70% for $\alpha>1\sim1.5$%. On the other hand, the SNR is increased as void fraction increased. In general, as long as the SNR is above 20db, SNR has little effect on data quality (, ), although the data should be excluded for SNR$<20$ db. Therefore, the SNR is improved when measuring flow with air bubbles compared to single phase water flow.

Methods of Data Processing

Despiking

The 3D phase space method is the most efficient algorithm available for despiking for ADV measured velocity data. The 3D phase space method was originally proposed by () and modified by (). The 3D phase space method uses the concept of a 3D Poincare map in which the variable, velocity $u$, and its first and second derivatives, $\Delta u$ and $\Delta^2 u$, are plotted against each other. The points located outside of the ellipsoid in the Poincare map are excluded and the method iterates until the number of detected spikes becomes zero. The procedure for despiking by the 3D phase space method is summarized in the following steps.

1. Calculate the first and second derivatives of velocity $u$.
2. Calculate the universal threshold as $\lambda=\sqrt{2\ln N}$ from the number of data $N$.
3. Calculate the correlation between $u$ and the second derivative $\Delta^2 u$.
4. Produce an inclined ellipsoid of $u$, $\Delta u$ and $\Delta^2 u$ with the angle calculated from the correlation between $u-\Delta^2u$.
5. Major and minor axes of ellipsoid are given by $\lambda\sigma_{u}$, $\lambda\sigma_{\Delta u}$ and $\lambda\sigma_{\Delta^2u}$, respectively.
6. Identify the points that lie outside of the ellipsoid and replace them. Continue the above procedure until further spike replacement is not required.

The original 3D phase space method proposed by () uses a projection plane in 2D space, but we use the true 3D phase space modified by () in the present study. The differences between the pseudo 3D (original phase space method) and the true 3D (modified phase space method) for bubbly flows is discussed below.

Figure shows an example of despiking results for $\alpha=0.1$%. Figure (a) shows the relationship between the ellipsoid defined by the universal threshold in 3D space by () and outlier points. Figure (b) shows the relationship between ellipses defined by the universal threshold in the pseudo 3D space by () and outlier points. If the correlation between velocity $u$ and its second derivative $\Delta^2 u$ is small enough, there is little difference between the true 3D and pseudo 3D phase space method. If the correlation becomes larger, however, the ellipsoid tends to be inclined in $u$ and $\Delta^2 u$ axes. The shade space of the ellipsoid is then no longer negligible.

Correlation and Signal-to-Noise Ratio

Following the manufacturer's instructions, data points should be excluded if the correlation (COR) of ADV data is less than 70% or the SNR is less than 20 db. The relationship between the spike noise and COR or SNR is verified. Figure shows an example of the time histories of velocity (top), correlation (middle), and SNR (bottom) in the case of $\alpha=0.1$%. The stars $*$ and circles $\circ$ in the figure indicate the points detected as spikes by the true 3D and pseudo-3D phase space methods, respectively. The true 3D phase space method is in fair agreement with the pseudo 3D method. The point at which the correlation is less than 70% is not located at the same point detected by the despiking method. Figure shows the relationship between velocity and correlation/SNR in the case of $\alpha=0.6\%$. Small filled dots $\bullet$ in the figure indicate all data, open circles $\circ$ are points detected point by the true 3D phase space method, open squares $\square$ are points detected point by the pseudo 3D phase space method, and triangles $\triangle$ are the low correlation points, respectively. There is no clear relation between the despiked velocity point and correlation/SNR in the bubbly flow. In particular, the spike noise randomly distributed in the whole range of the velocity field. Therefore, the COR and SNR cannot regard the parameters for filtering spike noise in ADV recorded data.

Results and Discussion

The effects of despiking and low correlation filtering methods on the mean and turbulence characteristics of flows are studied. No interpolation is employed to avoid introducing the effects of the interpolation method itself. Figure shows the valid data rate dependence on void fraction. The valid data rate is defined as the excluded data divided by the whole data. The open circles $\circ$, asterisks $*$ and squares $\square$ indicate the true 3D phase space, pseudo 3D, and correlation methods, respectively. The number of data points removed due to low correlation is monotonically increased as the void fraction increased, although the number of data points removed by the despiking algorithms are decreased as the void fraction increased. The reason for the increased removed data rate by despiking in the low void fraction case compared to the high void fraction case is the Doppler noise floor due to the slow mean velocity field ($\bar{u}$=6cm/s). The signal condition is also improved for high void fraction cases due to bubble generated turbulence. Therefore, SNR is increased as the void fraction increased as shown in Figure . The removed data rate due to the low correlation exceeded 50% for a void fraction greater than 1.5%. The correlation between despiking points and low correlation points is very weak as shown in Figure . Therefore, low correlation points can be regarded as independent from spiking noise for bubbly flow. The tendencies towards despiking and low SNR point and despiking and low correlation point are similar. On the other hand, there is a statistically significant difference between the true 3D phase space and pseudo 3D phase space method for the low void fraction case, but the difference is not significant if the void fraction is larger than 1.5%. In addition, this relationship depends on mean flow velocity due to the signal condition of the ADV data, but we neglected the influence of mean velocity on spike noise in here.

Finally, the effects of despiking and low correlation filtering methods on the mean and turbulence characteristics of flow are verified as shown in Figure . Figure (a) and (b) shows the mean velocity and its standard deviation normalized by the raw data set. Low correlation filtering significantly reduces mean velocity, but the mean velocity for both the 3D and pseudo 3D phase space methods is very close to 1. The standard deviations are affected for the true 3D and pseudo 3D methods only in low void fraction cases. The differences in the standard deviation between raw data and true 3D phase space method or pseudo 3D phase space method are 4.5% and 3.5% in the case of $\alpha=0.04$%. These values strongly depend on the number of recorded spikes. Although, it is difficult to generalize the above discussion, these results can be applied to ADV velocity data in bubbly flows.

Conclusion

In this study, the Acoustic Doppler velocimeter (ADV) velocity measurements in bubbly flows were examined. The despiking methods based on 3D phase space method were applied and bubble effects on ADV velocity were discussed. The results of the data analysis suggests the following:

• There is no clear relationship between velocity and ADV's correlation/signal-to-noise ratio in bubbly flow.
• Spike noise filtering methods based on low correlation and signal-to-noise ratio are not adequate for bubbly flow.
• The true 3D phase space method significantly remove spike noise of ADV velocity in comparison with the original 3D phase space method.

In addition the ADV measurements can be valid for 1-3 % void flows. The limitation of the ADV measurements for high void fraction flows is further question of this study. Additional quantitative verification and further extension of the method will be studied in the future.

This research was partially supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Young Scientists (B) No.17760409.