# Laboratory Modeling of an Axial Flow Micro Hydraulic Turbine
## 2 Research Methods
The measured velocity fields for different modes help us to understand the degree of variation in efficiency, and these velocity fields will allow the formulation of recommendations for increasing the range of efficient micro hydraulic turbine operation. The averaged flow velocity distributions were obtained using a LAD-06I laser Doppler anemometer. Paraffin oil aerosol particles produced by a Laskin atomizer were used as tracer particles for flow seeding, which made it possible to obtain droplets with a characteristic size of 1-3 \(\upmu\)m [22]. Part of the cone wall was replaced by a transparent film to allow the laser beams to pass into the cone. Position control of the LDA system in three axes was implemented. This provided an automated experiment to obtain an extensive amount of flow velocity data. The main errors are related to inaccuracy of flow rate setting, servo drive speed and measuring accuracy of LAD-06I system. The flow rate was controlled by IRVIS-RS4M-ULTRA flow meter with accuracy of flow measurement 1.5% (data from the instrument manual). The accuracy of setting the servo drive speed was 0.5% (data from the device manual). The LDA system measured the velocity of a single particle with an error of 0.2%. In order to measure the velocity in steady-state modes at a particular point of space, statistics of reliable flashes of at least 10,000 per point were  
Figure 1: Air model of a micro hydraulic turbine: **(a)** Diagram of the experiment system; **(b)** Detailed diagram. 1—inlet pipe, 2—shaft, 3—servo drive, 4—guide vane (stationary swirler), 5—runner (rotating swirler), 6—streamline body, 7—conical draft tube, 8—nozzle, 9—wind tunnel. accumulated. This allowed the flow rate at a given point to be determined with 99.7% certainty because each velocity component at each individual point in space was averaged over at least 3000 credible bursts. The LDA system was tuned so that the signal received from the flashes was close to Gaussian, with the RMS of the velocity for both components not exceeding 2-3 m/s. Based on an uncertainty analysis [31] in the present experiment, the total errors in the velocity measurements and their pulsations can be estimated as no more than 5% and 2%, respectively. Using linear interpolation with the minimum interval time given by the average data rate, the signal with a random tracer arrival time was converted into an equidistant signal in the time array. The spectrum was then calculated using fast Fourier transform. The maximum error for the measured fundamental frequency in the LDA spectra did not exceed 0.05 Hz. The flow ahead of the stationary swirler is shown in Figure 2. Away from the walls, the mean velocity distribution upstream of the bend shows good uniformity with a turbulence level of around 10-12%. When the operating regime is shifted from the BEP, the flow behind the runner becomes swirling. The degree of swirl is described by the swirl number \(S\) which is defined as the ratio of the axial flux of the angular momentum \(M\) to the product of the axial flux of the axial momentum \(K\) and the characteristic flow radius \(R\)[32]:  
\[S=M/RK, \tag{1}\]  
The moment \(M\) and \(K\) in Equation (1) can be determined from the measured velocity distributions:  
\[S=\frac{\int\limits_{0}^{R}UWr^{2}dr}{R\int\limits_{0}^{R}U^{2}rdr}, \tag{2}\]  
where \(U\) is the axial component and \(W\) is the tangential component, the integration is performed at downstream position \(z\), from the flow axis to the wall. An interesting approach is to calculate the swirl number based on the swirler geometry [33]. If the impeller rotation speed is constant, the swirl number can be calculated according to the one-dimensional model presented in [34]:  
\[S=\frac{\pi D\omega_{n}}{16}(D^{2}-d^{2})(\frac{1}{Q}-\frac{1}{Q_{0}}), \tag{3}\]  
where \(Q_{0}\) is flow rate corresponding to zero swirl number. For a certain runner speed, the flow rate \(Q_{0}\) can be determined empirically. Equation (3) shows that \(S\) is inversely proportional to the flow rate.