Performance optimization of low-head vertical axis impulse turbine runners for nozzle angle nozzle d

Abstract

Keywords: 3D Printed Buckets; Hydraulic Nozzles; Pico Hydro; Response Surface Methodology; Turgo Turbine

Introduction

With a permanent magnet, a Pico turbine combines a 220V single-phase alternator with a hydraulic turbine

nator. Pelton waterwheel for the high heads is seated, Francis turbine is horizontal, and Run of the River Kaplan

*Corresponding author. *E-mail address: hnlgecs@gmail.com This paper was recommended for publication in revised form by Assigned Editor-in-Chief Ahmet Selim Dalkilic Published by Yıldız Technical University Press, İstanbul, Turkey Yıldız Technical University. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

is a vertical Pico hydro turbine, one of the three hydraulic turbine varieties. The hydro impulse turbine is a popular, dependable, and sustainable option in hydroelectric plants, especially well-suited for moderate and high head applications. Technologies exploiting low and ultra-low head water potential sites have become popular due to their minimal environmental impact. Furthermore, putting small, creative water-related projects into action offers underdeveloped nations a cost-effective way to produce renewable energy. A high-pressure water jet with kinetic energy is key in producing impulses. The performance of the impulse turbine suffers due to alterations in jet characteristics. The jet size and shape affect the performance of the impulse turbine. The turbine’s efficiency was mainly influenced by the nozzle opening diameter or the jet diameter, speed ratio, blade count, and jet angle or the nozzle tilt angle [1]. The variability in the length-to-diameter ratio of the jet provides a method for controlling jet surface roughness over a substantial range [2]. The exact calculation of a Turgo turbine’s wheel-to-nozzle diameter ratio, or D/d, is necessary since it influences wheel velocity, which influences efficiency and performance [3]. Smaller jet diameters and higher flow rates can be used to obtain the ideal operating state since the maximum brake power increases with increased discharge due to an increase in torque [4]. Higher water heads lead to increased power generation, while electric power increases linearly with nozzle diameter enlargement [5]. In descending order, the circular water jet exhibits the highest peak pressure at identical inlet pressures, followed by the common fractal shapes like square, triangular, cross-shaped, and elliptical water jets[6]. At the minimum standoff distance of the nozzle, axial flow predominates in the water jet; otherwise, radial flow is more dominant [7]. The main jet diffusion factors influencing jet quality are eccentricity-induced pressure fluctuations and jet velocity imbalance. [8]. Apart from the primary flow in the bucket, the weak secondary flows from bends or bifurcations in the Pelton turbine distributor cause minor disturbances, affecting the type of jet shape, alignment of the jet with the bucket, and shifting of the water jet core from the nozzle centerline [9]. The efficiency of Turgo and Pelton turbine runners, used in Pico hydro applications, suffers from variations in speed ratio and jet misalignment [10]. The hydrodynamically designed buckets of the Turgo impulse turbine with an optimum jet angle are required for maximum power with the best efficiency [11]. According to numerical modeling, the needle tip’s position changed the velocity distribution of a Pelton turbine’s free jet [12]. The variation in available head and water discharge through the turbine affects the hydraulic performance of turbine runners. In a novel way, the Turgo impulse turbine boosts a hydraulic impulse turbine’s capacity while regulating flow with the nozzle and spear injector mechanism of the Pelton turbine [13]. The single-jet Turgo turbine was found to have improved performance over the

baseline design, with optimized parameters by multi-criteria analysis [14,15]. Also, for a Turgo impulse turbine, the discharge plays a vital role; as the discharge increases, the specific speed rises, while with a higher net head, the specific speed decreases. Additionally, increasing the net head boosts power output [16], and reducing the water head decreases water discharge, decreasing rotational speed, torque, brake power, and efficiency [17]. The water flow rate is the only factor affecting pressure, the power produced at the alternator, and the sufficient torque applied to the shaft [18]. The Pico hydro Turgo turbine has hill charts similar to the regular turbine for low-head applications at the constant head for varying flow conditions and optimized jet angle for remote area applications [19,20]. Nowadays, researchers are attracted to the lowhead operation of the Pelton runner. With a flow rate of 33 liters per minute and a static pressure head (very low) of

Method And Materials

Test Configuration The delivery line comprises 4-inch galvanized iron pipes, and a flexible hose connects to the nozzle spear mechanism assembly and header tapping. The sucked water through the collecting water sump at the water by the pump is discharged to the delivery line with a high head in an upward direction. The valve position is regulated, allowing water to flow further in the test rig. The head of 10 m is kept constant with the help of pressure gauges mounted on the header pipe. The pressure gauge measures the pressure before delivery to the flexible hose. The flow line is facilitated with overflow protection and controlled water flow. The test rig setup is depicted in Figure 2, with all the instruments for measuring quantities using different runners and with the same pitch circle diameter (PCD), i.e., 100 mm. The turbine runners are struck with a tangentially arranged set of nozzles placed at PCD. The nozzles of 10,12,

and 14 mm of aluminum have been attached to the nozzle hub. The variable flow condition is achieved with the help of the spear mechanism. The spear mechanism and the body were made from SS 304. The square acrylic frame of 1000 mm in length and width houses the vertical shaft and bearings. The runner is kept with a vertical turbine axis configuration. Also, the steel shaft has a pulley of 50 mm effective diameter fixed midway above the transparent acrylic casing to measure shaft power with absorption-type dynamometer elements connected to it. The rope, pulley, and dead weight constitute the absorption type diameter for torque measurement. The non-contact type tachometer was attached to the frame to measure runner speed. Flow measurement was achieved with the Electromagnetic type flow meter (Flowtech Digital Water Flow Meter, Model: MAG EMFM-0634, maximum process pressure 25 kg/cm2)

Table 1. Characteristic parameters of the centrifugal pump used in the experimental setup Description of parameter

3. The runner material, aluminum, was selected for its

lightweight and manufacturing ease for the present study. The close conduit of the test setup consists of a flow measuring device, a pressure sensor, and a spear nozzle assembly at the end. An electric motor-driven impeller pump circulates the water in the entire test rig. The buckets of PTR and TTR were designed for micro Pelton turbines and suitable for Pico hydro application for a 10 m head. The buckets were designed and 3D printed using PLA material on a Prusa i3 FDM 3D Printer (Bed dimensions 200 x 200 x 200 mm, material layer thickness 0.05 to 0.4mm, article printing speed 20 to 200 mm/s, 3D Printer Standard Extruder

Table 2. Pelton and Turgo turbine runner with the 3D printed Polylactic Acid (PLA) bucket Sr.No.

Figure 3. Designed and manufactured Turgo and Pelton turbine runners with 3D-printed buckets.

Diameter: 0.4mm, 3D Printing Software: CURA, RepetierHost simplify3D, 3D Printing Filament Material: Polylactic Acid (PLA), Acrylonitrile Butadiene Styrene (ABS), HighImpact Polystyrene (HIPS), WOOD, Polycarbonate (PC), Poly Vinyl Chloride (PVC) and more, 3D Printing Material Diameter: 1.75mm, 3D Printing Accuracy: ± 0.1mm) manufactured by Make3d at the AFMFP laboratory, SV NIT Surat. The steel vertical shaft of 15 mm diameter is stepped to 8 mm diameter for 50 mm length at one end to accommodate the runners, as shown in Figure 4. The hub of the runner accommodates the M4 grub screw to prevent relative motion between the runner and shaft. The aluminum pulley with a rope wound measured the shaft torque. The deadweight and spring balance arrangement was used to measure the rope’s differential tensions and shaft power. The optimum buckets for any given PCD are about 19 to 21 because no significant flow separation at the cutout edge occurs. For the experiment, 21 buckets were selected for the Pelton and 24 buckets for the Turgo turbines. The runners’

design and buckets were carried as per the micro hydro Pelton wheel turbine manual [49]. Study of Nozzle Standoff Distance and Jet Incidence Angle The linear distance between the bucket’s splitter edge and the nozzle tip is known as the “nozzle standoff distance” in PTR. On the other hand, the surface inside the bucket has a point where the jet hits in the TTR. The arrangement shown in Figure 5 depicts the jet deviation for three steps (Normal, +2.5°, and +5°. So, from normal jet incidence (perpendicular to the bucket radial axis) at 90°, it varies between 92.5 and 95 degrees in the present study. Study of Nozzle Diameter The aluminum nozzle hub is machined to make the dimensions shown in Figure 6(a) to reduce the spear rod assembly weight and ease machining. An orifice plate of thickness 4.77 mm acts as a nozzle with 80 degrees of divergence provided to the different concentrically drilled jet sizes.

Figure 4. Experimental setup and tangential nozzle arrangement (a) the torque measuring arrangement, (b) the flow line and flow meter, (c) the test section-runner arrangement concerning nozzles, (d) the tested nozzles of diameters 10, 12, and 14 mm.

Figure 5. Concept of jet deviation (ηh) and Nozzle standoff distance (Nsod).

Figure 6. The specifications of (a) Nozzle hub and (b) Adjustable nozzle plate. The nozzle(jet) sizes used in the current study are 10, 12, and 14 mm, as depicted in Figure 6(b). The sitting position of the orifice plate on the nozzle hub with the help of an M4 screw is shown with the red dotted arrow. The inside threaded side of the nozzle hub can be fitted to the spear rod mechanism. The interchangeable plates of different diameters produce jets of different sizes. The standoff distance, which is typically 4 to 5 dj between the jet exit (nozzle tip) from the spear assembly and the jet striking point on the bucket, is used. Investigation of Hydraulic Efficiency (ηh) The various essential variables from the study’s point of view are listed below in Table 3 with operating ranges. The dimensionless quantities compare the runner’s operation range under investigation. In the case of the Turgo turbine runner (TTR), a point on the bucket is considered a normal

jet incidence point, and variation in angle is carried with respect to that point located from the bucket’s outer edge. The parameters shown in the above table are available for evaluation. The potential Energy provided to the turbine, or the hydraulic power to the turbine, is the product of the mass flow rate of fluid flowing through it and the test-specific Energy . The values for range calculations are based on the direct effect on the evaluated parameter of the incurred parameter in the equations above. The data collected upon experimentation in the present study is reduced using equations mentioned in Table 4 below. An uncertainty analysis is essential to envisage the correctness of measurements. The instruments measuring various physical quantities always suffer from inherent characteristics leading to false readings. According to the study, uncertainty was found for the head of water, angular

Table 3. Recorded input key global parameters with a range of work Parameters

PTR, TTR

In the above equation, M is the number of required runs, and mt is the number of categorical elements. The number of replications is denoted with mc, while the number of numerical factors is m. So, for the present study, factorial design is 2m composed of 3 numerical factors 23 = 8; the axial section included 2m(2 x 3 = 6) points, and 3 test replications as center points are considered. Hence, it yields 80 test runs as per the above calculations. A face-centered Central Composite Design (CCD) can be achieved by selecting Alpha = 1.0; each of the five levels at which each element in the research study operates can be altered. This method reduces the complexity of implementation to three tiers for each element. With this arrangement, a quadratic model may be estimated, with the linear (first-order) terms being addressed by the 2m factorial points and the quadratic terms being accommodated by the 2m axial points. A complete factorial design provides a simple, organized approach that thoroughly assesses the primary effects and interactions of variables. Model And Data Analysis (ANOVA) Equation (5) shows a second-order (quadratic) model for n parameters. In this equation, β0 denotes the constant term, βi signifies the linear coefficient, βii represents the quadratic coefficient, βij indicates the interaction coefficient, and ε accounts for the experimental error. (5) The Design Expert 13.0 software is used in this study to estimate model coefficients and conduct a statistical analysis of the experimental data. The coefficients of the developed model were determined by this program using independent data and constant variance to distributions, one-way Analysis of Variance (ANOVA). The ANOVA method was employed to evaluate the appropriateness and adequacy of the responses concerning the model’s functions and variables. The models that achieved statistical significance have a P-value below 0.05. The model’s statistical importance was assessed using the signal-to-noise (F value), and its validity was confirmed using the coefficient of determination (R2). The residuals and pure errors at duplicate locations were evaluated using a lack of fit test.

The formulas and processes used in the research were used to confirm the model’s fit using the anticipated residual sum of squares, or PRESS. The experiments were performed with the nozzle diameters of 10 mm, 12 mm, and 14 mm at 90° jet incidence (normal incidence), 92.5°, and 95° for both PTR and TTR. The RSM simulation–optimization method optimized the input parameters to maximize hydraulic efficiency. The CCD of RSM techniques developed a model with a standard deviation of 0.053. Regression analysis validated the model, confirming its reliability in determining input parameters for maximum hydraulic efficiency. The value of ANOVA is depicted in Table 7, corresponding to the test in Table 6, with different combinations of parameters studied under the present investigation, representing the quadratic model. The parameters considered for the present study, like nozzle angle (α), nozzle diameter (dj), nozzle standoff distance (Nsod), PTR, TTR, and the number of nozzles (n), are found to affect the hydraulic efficiency (ηh) of turbine runners significantly, as experimentally. The factor coding and the sum of squares are coded as type III – partial, respectively. The sum of squares provides the total for each variable entered last in the model. In other words, each variable’s impact is assessed by considering all other variables. The significance of the model is indicated by its F-value of 90.49. An enormous F-value could only result from noise in 0.01% of cases. Significant model terms are indicated by P-values below 0.0500. Important model terms include A, B, C, D, E, AB, AC, BC, BD, CD, A², and C². If a model term’s value is more than 0.1000, it is not meaningful. If the model has many superfluous terms (aside from those required to preserve hierarchy), model reduction may improve the model. The lack of fit, F-value of 0.97, indicates that the lack of fit is minimal compared to the pure error. The likelihood that noise is the cause of a significant lack of fit F-value is 54.54%. A non-significant lack of fit is preferred because the model must fit. According to Appendix A2, the proposed model in the present study is quadratic. Fitting a multivariate linear regression model with all independent variables included is the first step in the backward elimination process. The model is then refitted after the variable with the greatest p-value is eliminated. This iterative process is repeated until all of the model’s remaining

Table 6. Design of Experiments (DoE) Central Composite Designs (CCD) matrix and results Test Run (M)

C.F. 2 Results for hydraulic efficiency (ηh) Number of Regression model nozzles Exp. Pred. Residual (n)

Table 6. Design of Experiments (DoE) Central Composite Designs (CCD) matrix and results (continued) Test Run (M)

C.F. 2 Results for hydraulic efficiency (ηh) Number of Regression model nozzles Exp. Pred. Residual (n)

Table 7. Present work - ANOVA for response surface quadratic model for the hydraulic efficiency of runners Source

*1n= Single nozzle, 2n= Double nozzle, df = Degree of freedom, SoS= Sum of squares, MS= Mean square

variables show p-values below a given threshold—typically set at 0.05. In RSM with CCD, normal probability plots and externally studentized residuals are essential for model diagnostics and validation Figure 9(a). Figure 9(b) compares the predicted values from the model to the actual observed values for model accuracy and validation, detecting outliers and identifying patterns like non-linearity. Additionally, the internally studentized, as shown in Figure 9(c), also describes the outliers and pattern; moreover, it checks the assumption of constant variance (homoscedasticity). Also, describe the heteroscedasticity of the spread of residuals with a change in run number. Figure 9(d) shows an incorrect functional form and missing variables in the systematic pattern in the residuals.

Results And Discussions

Measurement of Hydraulic Efficiency (ηh) The hydraulic performance was measured by measuring various parameters like runner speed (N), flow rate through nozzles(Q), dead weight (W), and spring balance

reading (S). The experimental work is carried out with varying flow conditions through the spear nozzle mechanism. An absorption-type rope brake dynamometer was used to measure the torque available on the shaft. The experiments were performed continuously for the various parameters, and different combinations of variables were considered for the present study. The results found with different configurations are given in terms of range in Table 5. Comparison of PTR and TTR Based on Hydraulic Efficiency (ηh) According to theoretical analysis, hydraulic efficiency (ηh) depends on parameters like flow rate, head, and fluid density. However, density remains constant for water as a fluid, so it merely depends on the remaining parameters. The runners are geometrically identical except for the bucket. The effect of independent parameters considered for the present study on the hydraulic efficiency of both runners is as follows. Effect of Nozzle Angle (Jet Incidence Angle, α) In the present study, the nozzle angle varied from 90 to 95 degrees in two steps of 2.5 degrees due to limitations. The normal jet incidence is desirable in the case of PTR. In

Figure 9. The graph for (a) Normal probability vs. Externally studentized residuals, (b) Predicted efficiency vs. Actual efficiency, (c) Internally studentized residual vs. Run number, and (d) Externally studentized residual vs. Run number.

contrast, TTR’s hydraulic performance changes with nozzle angle variation.The larger the jet incidence angle variation from the design location, the greater the hydraulic efficiency (ηh) within a specific limit of jet incidence angle. For the present study, equations (6) to (9) revealed that the negative coefficient associated with nozzle angle tends to reduce the runner efficiency in both the runners considered here with either a single or double nozzle arrangement. The present

study describes the situations where the jet misalignment contributes less to torque generation. Effect of Nozzle Diameter (Jet Diameter, dj) The jet of three different sizes, 10 mm, 12 mm, and 14 mm, equal to the nozzle diameter, strikes the runner bucket in different inclinations and distances, yielding different torques on the vertical shaft attached to the runner. With an increase in jet diameter, the fluid flow rate also increases.

Conversely, the jet is more focused with a smaller diameter and more diffusion with surroundings found with a 14 mm diameter. The hydraulic efficiency (ηh) increases with a decrease in nozzle diameter(dj) in the case of PTR with a single nozzle (1n). It is found more with a double nozzle (2n), keeping the nozzle standoff distance (Nsod) constant but a low value of nozzle angle(α). For TTR, compared to PTR, the hydraulic efficiency (ηh) is found to be higher with low inlet angle (design point) and nozzle diameter (dj). From equations (6) and (7), the nozzle diameter (dj) is found to have a positive coefficient in the case of PTR for both single and double nozzle operations. Still, its contribution is less due to the minor terms involved than the nozzle angle(α). From equations (8) and (9), the nozzle diameter (dj) is found to have a negative coefficient in the case of TTR for both single and double nozzle operations, with less effect on hydraulic performance than the minor terms involved, such as nozzle angle(α). Effect of Nozzle Standoff Distance (Nsod) For an impulse turbine, the nozzle tip distance from the runner is crucial for jet incidence. Typically, this distance is maintained between 4dj and 6dj to prevent flow separation at the jet surface. It must be optimized to avoid interference with water from the bucket. In this study, the nozzle standoff distance (Nsod) was varied between 40 and 60 mm in 10 mm increments. Quadratic equations (6) to (9) indicate that a 40 mm standoff distance is more effective, as it has a negative coefficient for both runners investigated. However, standoff distance(Nsod) is more negatively dominant for TTR than for PTR. The standoff distance is kept constant for the further evaluation of other parameters as attributed by RSM. The Response Surface Methodology (RSM) with the CCD model was adopted to systematically investigate the influence of independent variables on hydraulic efficiency (ηh). This study examined three critical numerical parameters: the angle of the jet (≈ nozzle angle) (A), the diameter of the jet (≈ nozzle diameter) (B), and nozzle standoff distance (C) alongside a two categorical parameter turbine runner type (D) and number of nozzles (E), designated as independent variables. The output hydraulic efficiency (Y) was selected as the dependent variable (response). The experimental design includes two categorical and three numerical components. To ensure the readings were repeatable, 80 experimental tests were conducted thrice, with eight test points and three replications for each category. Table 6 lists the experimental design elements and related experimental responses for the constructed model. An adequate regression model was constructed by analyzing the experimental data. An Analysis of Variance (ANOVA) was performed, a response surface model was constructed, and the Central Composite Design (CCD) responses were evaluated using “Design Expert 13.0” software. According to the different turbine types, the software determined the

most important models, as explained below: Pelton Turbine Runner (PTR)-Single nozzle(1n)

A and B represent the current study’s coded values for nozzle angle(α) and diameter(dj). AB denotes the interaction between these parameters, while A² and B² are the squared terms corresponding to the studied parameters. In the equations derived from the analysis, a positive coefficient indicates an increasing effect of the respective factor on the hydraulic efficiency (response) (ηh). In contrast, a negative coefficient signifies a decreasing impact. Table 7 represents the results of the ANOVA alongside the relevant statistical parameters for hydraulic efficiency (ηh). The experimental data align well with the model’s predictions, particularly when the model exhibits significant regression and an insignificant lack of fit. A strong F-value of 90.49 denotes that the model has a substantial statistical impact on the response variable. Its reliability is further reinforced by the p-value, which indicates only a 0.01% likelihood that such a high F-value could be attributed to random noise. The low error probability confirms that the proposed model effectively captures the experimental data. P-values below 0.05 indicate the significance of model

terms, while values under 0.001 indicate high importance for certain variables. Conversely, p-values exceeding 0.1 suggest that neither the model nor its components carry statistical significance. Furthermore, the model demonstrates minimal lack of fit concerning pure error, as evidenced by the lack of fit F-value of 0.9733. It is a positive outcome since the lack of fit is insignificant, indicating that the model aligns well with the predicted data. The R2 value, or the coefficient of determination, measures the dataset variance corresponding to the built model. In particular, R2 is the percentage of the dependent variable’s (response) variance that can be accounted for by the independent variables (predictors). An intense match between the model and the data is indicated by an R2 value close to

1. According to Appendix A3, R2 values greater than 0.95

indicate the model matched the data quite well, with only 0.14% of the data being unexpected. The created model’s ability to predict the runners’ hydraulic performance across a variety of independent variables is demonstrated by its high adjusted R2 value. There is less than a 0.2 discrepancy between the adjusted and the predicted R2, having a value of 0.9532 and 0.9375, respectively. With an acceptable threshold of > 4, the correlation’s suitable precision of 44.3384 indicates that the noise ratio of the model is within an acceptable range, confirming its usefulness for examining the design space. Additionally, the comparatively low coefficient of variation (0.8090) and standard deviation (0.0053) show better model validity and accuracy.

(d) Figure 10. The response 3D surface and contour plots of hydraulic efficiency as a function of nozzle angle (α), nozzle diameter (dj), and nozzle standoff distance (Nsod) in different turbine rotor types and the number of nozzles (n) of (a) PTR-1n, (d) TTR-1n, (c) PTR-2n, and (d) TTR-2n.

Table 8. Optimum values for input parameters and corresponding response Sr. Runner type No.

Standoff distance Response: Hydraulic (Nsod), mm efficiency (ηh)

that the developed model fits the experimental data, validat-

The evaluation of the correlational relationship between the

ing its applicability for predicting the hydraulic efficiency

Figure 11. Desirability solution ramp for optimization of parameters for maximum hydraulic efficiency. Table 9. Summary for comparison of present and similar past work Sr. No.

PTR, Maximum head =110 m, Runner diameter =275 mm, nozzle diameter = 9.5 to 12.5 mm (4 nos. in equal steps ), number of nozzles =1

Experimental

PTR, Head = 3 m, Runner diameter = 275 mm, nozzle diameter= 8 ,9, 10 mm, Number of nozzles=1

Experimental

PTR, Head = 2.5 m, Runner pitch circle diameter =123 mm, nozzle diameter= 9 mm, Number of nozzles=8

Experimental

TTR, Head = 42 m, Runner diameter =100 mm, nozzle diameter= 10,15,20 mm,Number of nozzles =2

PTR,Head = 4 m, Runner diameter =260 mm, nozzle diameter= 51 mm, Number of nozzles=1

PTR,Head =10 m, Runner diameter =220 mm, nozzle diameter= 21 mm, Number of nozzles=2

Experimental

PTR,Head = 47.5 m, Runner pitch circle diameter = 500 mm, nozzle diameter= 38.50 mm, Number of nozzles=4

TTR, Head =2.7 m, Runner diameter =120 mm, nozzle diameter= 63.9 mm, Number of nozzles=1

TTR, Head =35 m, Runner pitch circle diameter =130 mm, nozzle diameter= 7.125, 12.85 and 18.59 mm, Number of nozzles=1

PTR, Runner pitch circle diameter =100 mm, TTR, Runner pitch circle diameter =131 & 169 mm ,Head =17-25 m & 18- 28 m, nozzle diameter= 7.94 to 12.70 mm, Number of nozzles=1

Experimental

Williamson et al., 2013 TTR, head = 0.5 – 3.5 m, runner pitch circle diameter = 150 mm, nozzle diameter =15- 35 mm (5 nos. in equal steps )

Experimental

PTR,TTR, Head =10 m, Runner pitch circle diameter Experimental & =100 mm, nozzle diameter= 10, 12 and 14 mm, Number RSM with CCD model of nozzles=2

Table 10. Comparison of hydraulic efficiency ηh between experimental and RSM results for optimum values of parameters Runner type Turgo turbine runner (TTR)

the hydraulic efficiency (ηh) for PTR and TTR is illustrated in Figure 10, utilizing contour and 3D plots generated through Response Surface Methodology (RSM). Figure 10 depicts these visualizations for the hydraulic efficiency (ηh) (response) as a function of nozzle diameter (mm), nozzle angle (α), and the nozzle standoff distance (Nsod), with variations in turbine runner types and also with single or two nozzle arrangements. From the 3D plots with the response contour of the hydraulic performance in Figure 10 (a), it was observed that the nozzle angle(α) significantly influences the hydraulic efficiency (ηh) for the PTR, with both low and medium values of the nozzle angle(α) yielding maximized hydraulic efficiency (ηh). Positioning a nozzle angle(α) with reference to the bucket allows the generation of adequate torque and non-interference for the bucket flow to recover before reaching the exit. Consequently, following a decrease in the hydraulic efficiency (ηh) with the high standoff distance (Nsod) and nozzle diameter(dj), an increase is noted in the low range of standoff distance and nozzle diameter. Figure 10 (b) presents the contour and 3D plots of the hydraulic efficiency (ηh) for the TTR single-nozzle operation. In contrast to the previous scenario, the nozzle angle(α) and nozzle diameter(dj) are more dominant than the standoff distance (Nsod). With an increase in the nozzle angle(α), the efficiency decreases and increases with the nozzle diameter(dj). Figure 10 (c) illustrates the contour and 3D surface plots of the hydraulic efficiency (ηh) for PTR with double nozzles tangentially arranged at the PCD of runners. The 3D surface pattern resembles a curve for the PTR turbine type; however, this configuration harvested and converted more hydraulic Energy than the TTR single-nozzle operation. The similarities between the response surfaces for the TTR and PTR indicate a comparable effect of nozzle positioning, nozzle size, and tip distance of a nozzle under single and double nozzle on the hydraulic performance of the runner. The contour plot and three-dimensional response surface illustrating the hydraulic efficiency (ηh) for the TTR with double nozzle (2n) are presented in Figure 10 (d). This visualization demonstrates that the amount of Energy extracted efficiently by the runner is superior to that of alternative turbine runner types, with a notable finding that reducing the nozzle standoff distance (Nsod) leads to increased hydraulic efficiency (ηh). The contour plots and 3D response surfaces shown in Figure 10(a, b, c, and d) further emphasize the significant correlation between nozzle angle(α) and nozzle diameter (dj).

Moreover, the interaction analysis between nozzle standoff distance (Nsod) and hydraulic efficiency (ηh) also indicates that variations in the number of nozzles(n) notably influence hydraulic efficiency (ηh). These findings suggest that alterations in the nozzle angle(α) exert a more pronounced impact on the hydraulic efficiency (ηh) of TTR than changes in nozzle diameter(dj) and nozzle standoff distance (Nsod), with lower hydraulic efficiency (ηh) achieved at lower nozzle diameter(dj), nozzle standoff distance (Nsod) and single nozzle (1n). Overall, by optimizing the nozzle angle(α), nozzle diameter(dj), nozzle standoff distance (Nsod), and the number of nozzles(n)for the two runners, it is feasible to enhance the hydraulic efficiency (ηh) of the PTR by up to 10% and TTR by up to 13%. The study utilizing Response Surface Methodology (RSM) yielded several key findings regarding the influence of independent variables on the output, which is considered the hydraulic efficiency (ηh) of the turbine runner for Pico hydro application. It was determined that nozzle angle (A), nozzle diameter (B), nozzle standoff distance (C), and the number of nozzles (E) significantly affect the hydraulic efficiency (Y) of both the runners (D), with specific combinations of these variables identified as optimal for maximizing efficiency. The regression model developed from the experimental data demonstrated a robust fit and predictive capability. It was validated through ANOVA, which highlighted the statistical significance of both the types of factors and their interactions. The response surface plots provided a visual representation of these interactions, indicating how variations in one parameter can influence hydraulic efficiency in conjunction with others. Furthermore, the findings have practical implications for turbine operation and design, suggesting that strategic adjustments to nozzle angle(α), nozzle diameter(dj), nozzle standoff distance (Nsod), and the number of nozzles (n), alongside careful consideration of turbine runner type, can enhance performance. Lastly, the study recommends avenues for future research, including further exploring additional variables like debris and fluid density, as it is to be used for Pico hydro off-grid applications and turbine configurations to refine the understanding of their impacts on hydraulic performance. The TTR has a half bucket compared to the PTR and a much better tendency to accommodate a higher flow rate with a half bucket width. The speed of TTR was found to be higher compared to PTR. One of the objectives was to find the optimal hydraulic efficiency as a response to the

allied design parameters. The values found in the current study for the range of parameters investigated are shown in Figure 11 for the quadratic model with red and blue balls on the graph. It has been observed that the optimal values of the numerical parameters, nozzle angle(α), nozzle diameter(dj), and nozzle standoff distance (Nsod), are within the range and around the model’s highest expectation.. The condition of optimality for TTR is depicted in Table 8 below. The solution is found with the objective of maximum hydraulic efficiency under given head and variable flow rate conditions. For validating the model, desirability is close to 1, and in the present study, it is found to be about 0.905, which shows good agreement between output and the desired output. The optimum value of hydraulic efficiency achieved to maximize the hydraulic efficiency was found when the double nozzle configuration had a 40 mm nozzle standoff distance, nozzle angle, and nozzle diameter of 95° and 14, respectively. Optimum Conditions for Maximum Hydraulic Efficiency (ηh)max The main objective of this investigation is to identify the maximum hydraulic efficiency by determining the operating and geometrical parameters that facilitate the most efficient operation of the system. The designed parameters and the required model responses for the optimization process are comprehensively detailed in Table 8. This table specifies that the response hydraulic efficiency (ηh) is integral to the optimization efforts. The input parameters

were constrained within predetermined ranges to maximize the identified response. Under these conditions, the TTR achieved the maximum hydraulic efficiency of 66.19% (as illustrated in Table 8 and Figure 11). For TTR, it corresponds to a 95° nozzle angle,14 mm nozzle diameter, a 40 mm standoff distance, and the PTR turbine type with double nozzle (2n). The experiment, RSM-based input parameter optimization work, and the corresponding responses in hydraulic efficiency (ηh) carried out by various researchers are highlighted in Table 9 for comparison. The variation in maximum hydraulic efficiency (ηh)max in the last column is a relative term, as the variation in geometrical and operating parameters of the turbine runner is considered for research. The current research found that the hydraulic efficiency (ηh) for TTR was significantly higher than previously reported findings(Sr No.6, Table 9). It is also noted that most of the past work tabulated is done on horizontal axis turbine runners, unlike the vertical axis considered in the present study. This research shows that jet diameter, angle, and nozzle standoff distance significantly improve impulse turbine hydraulic efficiency (ηh). On the other hand, for Pico hydro applications, the RSM optimization method can enhance the vertical axis TTR’s performance. When considering the PTR double nozzle configuration, the TTR configuration yielded a higher gain in hydraulic efficiency(ηh). However, there isn’t a recognized way to compare the abilities of various hydroturbine runners. This study developed an RSM model for impulse turbine runners to achieve these objectives.

Figure 12. Comparison between similar previous work and the present study for maximum hydraulic efficiency.

The RSM model’s output is compared with experimental data to validate the ideal conditions for the anticipated parameters, as Table 10 illustrates. Excellent agreement between the experimental data and the suggested RSM model is demonstrated by the results of the confirmation test, which show a slight discrepancy (0.54%) between the predicted and real hydraulic efficiency (ηh). The results of the present investigations have been compared with

similar previous work on a bar chart for maximum hydraulic efficiency. Figure 12 shows that the present study yielded hydraulic efficiency under optimized conditions under a head of 10 m compared to a lower runner PCD of 100 mm in earlier studies. The comparison revealed higher efficiency bars in the previous work due to increased head, number of nozzles, nozzle diameter, runner type, or runner diameter.

(b) Figure 13. Turbine runner with a hydraulic performance comparison between similar previous and the present work findings (a) based on runner speed (b) based on nozzle diameter

The hydraulic performance of the PTR in the present investigation has been compared with similar previous work carried out by Alomar et al. in 2022, which had a 110 m head and 10.5 mm nozzle diameter. The trendline for the present work has been shown with error bars for the 10 mm nozzle diameter, 40 mm nozzle standoff distance, and double nozzle arrangement in Figure 13 (a). The trend lines match, and it has been found that the 65% hydraulic efficiency in the present study is higher than 33.3% of the parameters studied compared to those reported by authors in their previous work. The nozzle diameters are also checked for the findings obtained in the present study, as depicted in Figure 13 (b) in the case of TTR. The TTR in the present study is compared with the TTR for a similar trend reported by Gaiser et al. in 2016, with a head of 35 m, a runner pitch circle diameter of 130 mm, and a single nozzle. The highest efficiency observed in their study was 64.7% with a 12.85 mm nozzle. In their work, the head, runner diameter, and flow rate are more than those investigated in the current study. However, the current curve with 100 mm PCD,14 mm nozzle diameter, and 10 m head follows the same trendline. So, the present study has the least value of parameters, with the increased value of the hydraulic performance for the runners investigated. Thus, it suggests improved hydraulic efficiency with optimized parameters. It has been found that the vertical axis turbines investigated in the present study are more suitable for low head conditions for the given set of design and operating parameters considered. It indicates that the present study is suitable for installing off-grid Pico hydro applications for power generation in remote areas.

compared to metallic bucket material for power generation at low head. With a standoff distance of more than 4dj, the jet deviates due to diffusion in the surrounding environment, resulting in low kinetic Energy on the buckets. As the jet diameter rises, the turbine’s total speed lowers. So, the proposed model found that a minimum standoff distance of approximately 40 mm was maintained for each nozzle diameter to reduce the expansion of the jet. Also, it was observed with the Pelton turbine that the significant impact on efficiency was caused by jet misalignment on the turbine and vibrational and frictional losses, reducing the overall efficiency and power developed by the system. Compared to the Pelton turbine runner(PTR), the ability to handle the high flow rate of the Turgo turbine has shown increased hydraulic efficiency (ηh) with an increase in the nozzle diameter. A significant improvement in hydraulic efficiency (ηh) was achieved by increasing the overall speed ratio of the turbine under double-nozzle (2n) operation compared to single-nozzle (1n) operation. The maximum power developed from a 10 mm jet diameter, making the jet ratio 11.11 in the Pelton turbine runner (PTR) case. The nozzle angle (α) was crucial for testing the runners’ hydraulic performance. The normal incidence with a 90° nozzle angle was found more promising compared to deviated other jet angles, 92.5° and 95° in the case of PTR, and TTR is more efficient with a 95° nozzle angle as the jet incidence becomes smoother. RSM with central composite design (CCD) effectively optimizes TTR and PTR performance, reducing the need for repeated experiments and facilitating quick design decisions. The quadratic model developed by the RSM for the evaluation of hydraulic efficiency (ηh) and the most efficient runner was found to apply to a high degree of accuracy to quantify the hydraulic performance of the runners. The P-value for all the model parameters, such as nozzle angle, nozzle diameter, and number of nozzles at a standoff distance, was below 0.0001, indicating significant effects on the model and, ultimately, the turbine performance. A thorough statistical analysis of the model was conducted to verify its accuracy and validity. The optimized conditions for a vertically installed TTR included a 95° nozzle angle, 14 mm nozzle diameter, 40 mm distance from the nozzle tip to the bucket, and double nozzle operation, achieving 66.19% efficiency. The present study revealed that the TTR runner was more sensitive to changes in nozzle angle than the PTR. The optimality conditions of the developed RSM model are compared with the results of the experimental investigation to validate the design of geometric parameters. From the validation test, it is found that the error is minimal, which shows that only 0.54 % of actual and predicted values are compared and found with a degree

Conclusions

This study aimed to assess the performance of developed impulse turbines (PTR and TTR) running at optimal efficiency levels using response surface methodology (RSM)with central composite design (CCD). The experimental test was conducted to optimize the range of operating parameters, viz. jet incidence angle(90°-95°), nozzle diameter(10-14 mm), and number of nozzles(1 or 2) at a standoff distance( 40-60 mm) under low-head operation(10 m) for the range of global parameters. The hydraulic efficiency assessment of the Pelton and Turgo turbines was compared at optimum conditions, and the following conclusions were made. • It has been found from the literature studied and cited here that multiple research studies have been conducted in the past with horizontal axis low-head Turgo and Pelton turbines, and the vertical axis with jet deviation(α) is sidelined. Also, the effect of nozzle standoff distance (Nsod), which affects hydraulic efficiency (ηh) due to jet expansion, has not been identified or studied. • The Polylactic Acid (PLA) for 3D printed buckets with aluminum runner discs was a low-cost solution

of agreement. Thus, the validation process has verified the ultimate goal of the study. The hydraulic efficiency (ηh) achieved under optimized conditions in the present study is compared with past work, showing good efficiency improvement. The curve follows the trend line up to a 12 mm nozzle diameter, but with a further 2 mm stepped increase in nozzle diameter, the efficiency improves in the case of TTR with a 40 mm nozzle standoff distance.

A Turgo and Pelton turbine Runner with 100 mm PCD in a vertical axis configuration was designed and experimented with. The variation in flow, Nozzle diameter (jet diameter,dj), number of nozzles(n), nozzle angle (jet deviation,α), and nozzle standoff distance (Nsod) were kept as independent variables, keeping the head constant. The Response Surface Methodology (RSM) with a Central Composite Design (CCD) model was used for the optimization and has shown the effect of each parameter on hydraulic performance.

Abbrivation Anova

Analysis of variance Computational Fluid Dynamics Response Surface Methodology Central Composite Design Pitch Circle Diameter, mm Pelton Turbine Runner Turgo Turbine Runner Polylactic Acid Single nozzle Double nozzle Reynolds Averaged Navier-Stokes

Nomenclature

Q Volumetric flow rate/Discharge, m3/sec The inlet diameter of the nozzle or the inside Do diameter of the pipe, mm Nozzle(jet) diameter, mm dj N Runner speed, rpm H Available head, m Specific speed Ns g Gravitational constant, m/s2 Pu Unit power Power developed, Watt Pd Hydraulic power, Watt Ph Velocity of the jet, m/s Vjet u Peripheral velocity of runners, m/s Torque developed at runner shaft, N-mm. Td Nozzle standoff distance, mm Nsod W Dead weight, kg S Spring balance reading, kg

Greek Symbols ρ Density of the water, kg/m3 ηv Volumetric efficiency,% α Nozzle angle, degrees Mechanical efficiency,% ηm Hydraulic efficiency,% ηh Speed ratio/ Velocity ratio ϕs ω Angular speed, rad/sec The jet angle at the bucket exit, degrees β2 Speed or Velocity ratio λs Jet ratio ψj Subscripts h Refers to hydraulic s Refers to speed m Refers to mechanical 2 Refers to exit j Refers to jet sod Refers to the standoff distance v Refers to volumetric d Refers to the developed

Future Scope Of WORK

The work can be expanded to examine the impact of bucket spacing on performance for runners with a variable bucket number and a greater runner diameter. The bucket’s structural analysis can also be studied numerically under dynamic fluid action. The effect of different sustainable materials (compatible with 3-D printing technology) on hydraulic performance can also be explored for further investigation.

Acknowledgment

Thanks to my beloved students, Gaurav P. Bakhru and Darshan N. Modi, for supporting the experimentation and providing help for developing test setup and 3D printed turbine runners at Advance Fluid Mechanics and Fluid Power Laboratory, Sardar Vallabhbhai National Institute of Technology (SV NIT), Surat, Gujarat, India

Disclosure Statement

The authors gratefully acknowledge the TEQIP committee, SV NIT, Suart for funding this study through a core research grant. The sanction order number is TEQIP/ phd/2875.

Data Availability Statement

The authors confirm that the data that supports the findings of this study are available within the article. Raw data that support the finding of this study are available from the corresponding author, upon reasonable request.

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript.

Share and Cite