High Blockage Ratio Research Articles

Impact of the blockage ratio and void fraction of porous obstacle on gas explosion characteristics in semi-confined channel

This study conducted various explosion experiments under different porous obstacle conditions of blockage ratio (BR) and void fraction (Φf). The impact of porous obstacle on flame propagation velocity (v) and peak overpressure (Pop) were analyzed. The results indicate that an increase in the BR enhances explosion pressure near the blockage area for both porous and non-porous obstacles. However, it also increases the downstream pressure decline gradient. An increase in the Φf weakens the hindrance of porous obstacle on the flame propagation, allowing more flame to pass through the internal void channels of obstacles, thus delaying the downstream pressure decay. Compared to non-porous obstacles, gas explosions disturbed by porous obstacles with both high BR (BR＞75%) and high Φf (Φf＞0.55) exhibit a lower downstream pressure decline gradient and a longer positive pressure duration. As a result, the explosion can produce a broader range of destruction.

Research on the blockage effect in a shock tube

The shock tube is a crucial experimental apparatus in the field of explosive impact. Limited research has been conducted on the visualization of the internal flow field in shock tubes under blockage conditions, and there is a lack of comprehensive understanding of the mechanisms behind blockage effects. This paper presents experimental and numerical investigations into the propagation of shock waves inside a shock tube and their interaction with obstructive elements. Blockage effect experiments were conducted on a shock tube test platform, where pressure data were obtained through a pressure monitoring system. Additionally, schlieren imaging technology was employed to visualize the evolution of shock wave fronts. A two-dimensional numerical model of the shock tube was established using Fluent software, and the computed results exhibited excellent agreement with the experimental data, confirming the accuracy of the numerical model. The mechanism of the blockage effect was revealed through analysis of pressure-time curves and images depicting the evolution of shock wave fronts. Furthermore, adjustments to parameters on the validated numerical model allowed for analysis and comparison of different blockage ratios. The results indicate that the disturbance to the flow field caused by the blockage effect is primarily due to the reflection of shock waves between the front surface of the obstructive element and the shock tube wall. This reflection leads to differences in pressure curves compared to free-field conditions, and such differences increase with higher blockage ratios.

Study on the propagation characteristics of gas explosions disturbed by crushed rock in tunnels through gas-containing stratum

Gas explosions pose a serious risk to tunnel construction when through a gas-containing stratum. The crushed rock accumulated in tunnel could have a significant impact on explosion. To understand the mechanism of crushed rock influence on gas explosion, methane/air explosion experiments under the crushed rock with different blockage ratios and void ratios were carried out using an independently designed experimental system. The results show that the crushed rock can significantly affect the explosion intensity, and the various blockage ratios show a higher degree of influence than the void ratio. The crushed rock has the combined effect of accelerating and quenching on the flame, and there has an optimum blockage that dramatically accelerates the flame propagation. The needle-shaped, divergent and reversed flames appeared with high blockage ratio and void ratio conditions. The velocity ratio (ratio of the flame front velocities upstream and downstream of the crushed rock) has an exponential function relationship with the blockage ratio. Under certain void ratio conditions, the maximum explosion overpressure shows a parabolic trend with increasing blockage ratio. This study is helpful to guide the understanding of the explosion characteristics under practical tunnel conditions and the change law of flame structure with crushed rock obstruction.

Characteristics of smoke movement in subway evacuation corridor under different blockage ratios

This study employed FLUENT to analyse smoke movement and temperature distribution in an evacuation corridor with varying blockage ratios, focusing on the subway tunnel section of Fuzhou Metro Line 4. The simulation results revealed that under natural ventilation condition, the smoke spread area in the evacuation corridor is significantly greater for the high blockage ratio tunnel than for the low blockage ratio tunnel in the tunnel’s length direction, and the entire temperature distribution in the tunnel’s height direction is also high. Following the introduction of longitudinal ventilation, smoke spread in the evacuation corridor and the tunnel ceiling upstream of the fire source are effectively controlled, with smoke suppression movement in the evacuation corridor being significantly faster than that near the tunnel ceiling. As ventilation time increases, the back-layering length of smoke in the evacuation corridor gradually shortens. Within 150 s of ventilation, the critical safety distance below the safety temperature for a low blockage ratio is shorter than that for a high blockage ratio tunnel. In conclusion, longitudinal ventilation increases the cooling rate of high-temperature smoke in a high blockage ratio tunnel, but the influence of high ventilation velocity on evacuation cannot be ignored. Practical application This study provides recommendations for the evacuation plan and procedures under longitudinal ventilation. It is advisable to consider lowering the height of the evacuation corridor in the tunnel from the rail surface, thereby creating a more extensive safety space for personnel evacuation. Additionally, the implementation of prominent marks and voice prompts in the upstream area of the fire outbreak is crucial. This ensures that personnel are directed to evacuate from the upstream section during emergency situations.

The influence of surface roughness on postcritical flow over circular cylinders revisited

This work investigates the effect of surface roughness on cylinder flows in the postcritical regime and reexamines whether the roughness Reynolds number ( $Re_{k_s}$ ) primarily governs the aerodynamic behaviour. It has been motivated by limitations of many previous investigations, containing occasionally contradictory findings. In particular, many past studies were conducted with relatively high blockage ratios and low cylinder aspect ratios. Both of these factors appear to have non-negligible effects on flow behaviour, and particularly fluctuating quantities such as the standard deviation of the lift coefficient. This study employs a 5 % blockage ratio and a span-to-diameter ratio of 10. Cylinders of different relative surface roughness ratios ( $k_s/D$ ), ranging from $1.1\times 10^{-3}$ to $3\times 10^{-3}$ , were investigated at Reynolds numbers up to $6.8 \times 10^5$ and $Re_{k_s}$ up to 2200. It is found that the base pressure coefficient, drag coefficient, Strouhal number, spanwise correlation length of lift and the standard deviation of the lift coefficient are well described by $Re_{k_s}$ in postcritical flows. However, roughness does have an effect on the minimum surface pressure coefficient (near separation) that does not collapse with $Re_{k_s}$ . The universal Strouhal number proposed by Bearman (Annu. Rev. Fluid Mech., vol. 16, 1984, pp. 195–222) appears to be nearly constant over the range of $Re_{k_s}$ studied, spanning the subcritical through postcritical regimes. Frequencies in the separating shear layers are found to be an order of magnitude lower than the power law predictions for separating shear layers of smooth cylinders.

Experimental study and numerical simulation of the combustion characteristics of dust clouds in vertical pipelines underneath unilateral obstacles

To reveal the impact of unilateral obstacles on the combustion characteristics of dust clouds inside vertical pipelines. This paper uses high-speed photography to conduct research on the combustion of vertical dust clouds using a self-designed experimental platform. A numerical model is established using Fluent to numerically simulate the combustion process. The results show that obstacles can increase flame spread velocity inside the pipeline, leading to an increase in peak temperature. As the blockage ratio of the obstacles increases, the flame profile becomes increasingly distorted. The maximum flame spread velocity and temperature initially increase and then decrease, with the maximum flame spread velocity reaching further away from the pipeline outlet. At the same time, high blockage ratios can lead to the accumulation of dust concentration underneath obstacles, resulting in a continuous turbulent reaction. As the number of obstacles increases, the maximum flame spread velocity and temperature gradually increase, and the maximum flame propagation ratio is closer to the pipeline outlet. The experiment and the flame propagation procedure (as calculated by numerical simulation) are consistent. The discrepancy between the simulated results and the experimental results is < 15 %.

Numerical study on hydrogen heterogeneous reaction characteristic in a micro catalytic combustor with blunt body

A numerical investigation has been conducted to explore the effect of an inserted blunt body on the heterogeneous reaction (HTR) characteristics in a micro-catalytic combustor operating with premixed hydrogen/air. The two-dimensional numerical model incorporates a comprehensive heterogeneous reaction mechanism of hydrogen employed by experimental verification. The influences of blockage ratio at various inlet velocities have been investigated to obtain optimized design parameters of the combustor. The findings of this research highlight analysis of the positive influence of an inserted blunt body within the combustor, including enhancement of chemical reaction rate and hydrogen conversion ratio. Numerical results shows that the gaseous mixture between the blunt body and catalytic surface noticed a considerable velocity increase, leading to a greater adsorption–desorption of bulk species on the catalytic surface. At the same inlet velocity, the hydrogen conversion ratio gradually increases with higher blockage ratios. When the blockage ratio is less than or equal to 0.6, the average inner wall temperature is positively affected by the increased blockage ratio. However, the effect becomes negative at higher blockage ratios (0.8). The Pr (Prandtl number) number near the gas–solid interface adjacent to the blunt body initially decreases and then increases, while Nu/Nu0 (Nusselt number) and Pe (Peclet number) exhibit an initial increase followed by a decrease. The presence of the blunt body leads to a reduction in the cross-sectional area of the channel, causing an acceleration in fluid velocity near the blunt body and exerting an impact on the boundary layer near the gas–solid interface. This indicates that the addition of the blunt body reduces the boundary layer thickness and enhances the mass and heat transfer characteristics in the region. The study reveal that as the blockage ratio increases, the overall field synergy of the combustor initially increases and then decreases. The peak field synergy is attained at an optimal blocking ratio of 0.6. The findings of this study have important implications for the design of micro-scale combustors.

Blockage effect and ground effect on oscillating hydrofoil

Oscillating hydrofoils located in a channel or limited zone by two side walls will be affected by both the blockage effect and ground effect. To study the contribution of these two effects on the energy-extraction performance of hydrofoils, a two-dimensional numerical model was established based on the overset grid technology. The differences in the energy extraction of hydrofoil with different wall settings were compared, and the blockage effect and ground effect in the double-wall case were mainly studied. The results show that compared with the open flow field, the single-wall can only improve the hydrofoil energy extraction by 1.75%, while the double-wall with the same foil-wall spacing can greatly improve the oscillating hydrofoil efficiency by 19.34%. By linearly fitting the results at low blockage ratios and performing the subtraction process, the influence of blockage effect and ground effect can be separated preliminarily. These two effects have the same order of magnitude in improving the energy extraction of hydrofoils when the blockage ratio is high. In addition, the present study proposes to add the correction of the drag coefficient to remedy the shortcoming of the correction method proposed by Barnsley and Wellicome that cannot deal with the high blockage ratio cases, which means the influence of the ground effect is also corrected. Then the blockage effect and the ground effect can also be separated by the subtraction process. Based on the above analysis, it is found that the ground effect has little influence when the hydrofoil oscillates at high frequencies, while the influence of the blockage effect is mainly related to the blockage ratio rather than the oscillating frequency.

Effects of blockage ratio on the propagation characteristics of hydrogen-rich gas rotating detonation

The propagation characteristics of a hydrogen-rich gas/air rotating detonation wave (RDW) were investigated for different blockage ratios (BRs). Two rotating detonation chamber (RDC) widths were used in combination with different RDC exit widths to obtain different RDC BRs. The variations in the RDW propagation modes and wave velocities at different BRs and equivalence ratios (ERs) were studied and analyzed. The experimental results show that four types of RDW propagation modes can be obtained (single wave, single wave/counter-double waves hybrid mode, triple waves, and unstable triple waves) by changing the BRs and ERs. For BR &amp;gt; 0.64, the RDW exhibits a triple waves mode. The RDC width also affects the RDW propagation mode. The results show that at low BRs, the change in the RDW propagation mode owing to the injection pressure difference is the main influence mechanism. As the BR increases, the influence of the reflected shock wave from the exit of the RDC increases, which plays an important role in the generation of the triple waves mode. The stability of RDW propagation can be improved by appropriately increasing the blockage ratio in the RDC. The 26 mm RDC width at BR = 0 results in a maximum wave velocity of 1933.8 m/s. Moreover, the stability of the RDW propagation is poor at low and high BRs.

A state-of-the-art review of flows past confined circular cylinders

In this paper, we have reviewed the state-of-the-art of research on flow past a circular cylinder symmetrically placed between two parallel plates separated by a finite distance. Such flow, referred to as a confined flow or flow past a confined cylinder in this study, is characterized by the blockage ratio—the ratio of the cylinder diameter to the distance between the plates. Confined flows are common in engineering systems, but the interest in studying flows over confined cylinders was motivated by the need to correct unavoidable blockage effects in physical experiments for unconfined cylinders. A very early work on this topic was published in 1944. Since then, interest has gradually expanded to understanding the wake dynamics and hydrodynamic properties of confined cylinders at different blockage ratios. The emergence and further developments of the Computational Fluid Dynamics and Particle Image Velocimetry techniques have enabled researchers to unveil important and complex features of confined flows, such as the two-dimensional to three-dimensional flow transition, the analogy of the separated shear layers to mixing layers, different vortex shedding modes, and the asymmetry of confined flows at high blockage ratios. To date, there has been no systematic review dedicated to confined flows. The present review fills the gap and is aimed to provide a comprehensive account of relevant studies including a historical perspective of the studies, significant research findings, and most recent advancement of the knowledge. Further, we have also identified a number of research gaps for further investigations.

Analysis of the aerodynamic characteristics of the entire operation process of an ultra-high-speed elevator under the influence of high blockage ratio, hoistway, and car height parameters

Ultra-high-speed elevators are affected by various factors during operation, resulting in complex airflow disturbances and significant piston effects. To explore the aerodynamic characteristics and ventilation effects of the car at different stages of operation under multiple parameters, this paper first establishes a multi-parameter numerical model for the elevator system and verifies the numerical model through elevator experiments, and then analyzed the general variation characteristics of the pneumatic load during the car's acceleration, constant speed, and deceleration phases. On this basis, the influence of blockage ratio, hoistway and car height, and operating acceleration on multiple types of aerodynamic loads and hoistway ventilation was studied, with a special analysis of the viscous drag and pressure drag of the car. The results show that increasing the blockage ratio significantly increases the ventilation of the hoistway, with an increase in 1 and 0.7 factors in the acceleration and constant velocity stages, respectively. In the deceleration stage, the drag changes the most, with an increase in 3.1 factors, which hinders the ventilation of the hoistway. Meanwhile, the average lateral lift increased by 0.6 factors and the fluctuation increased, exacerbating the lateral vibration of the car. Viscous drag and pressure drag exhibit similar trends at each stage, but pressure drag is much higher than viscous drag. The height of the hoistway has a significant impact on the total drag of the car by increasing the pressure drag. In contrast, car height has the most significant effect on lateral lift and viscous drag.

Evolution of focused streams for viscoelastic flow in spiral microchannels

Particle migration dynamics in viscoelastic fluids in spiral channels have attracted interest in recent years due to potential applications in the 3D focusing and label-free sorting of particles and cells. Despite a number of recent studies, the underlying mechanism of Dean-coupled elasto-inertial migration in spiral microchannels is not fully understood. In this work, for the first time, we experimentally demonstrate the evolution of particle focusing behavior along a channel downstream length at a high blockage ratio. We found that flow rate, device curvature, and medium viscosity play important roles in particle lateral migration. Our results illustrate the full focusing pattern along the downstream channel length, with side-view imaging yielding observations on the vertical migration of focused streams. Ultimately, we anticipate that these results will offer a useful guide for elasto-inertial microfluidics device design to improve the efficiency of 3D focusing in cell sorting and cytometry applications.

Effect of Rib Blockage Ratio and Arrangements on Impingement Heat Transfer in Double-Wall Cooling

Abstract A numerical study was conducted on the multiple jet impingement heat transfer of the double-wall cooling with high blockage ratio ribs of various configurations. Three different blockage ratios (BR = 0.2, 0.3, and 0.5) and two rib arrangements relative to the effusion holes (l/Sx = 0.25 and 0.75) were thoroughly examined using the RANS method with the SST–KIC turbulence model, considering the Kato–Launder modification (K), intermittency (I), and crossflow (C) transition effects. The ratio of jet-to-target plate spacing to jet diameter (H/d) was fixed to be 1, and Reynolds numbers varied in the range of 4000–16,000. Furthermore, the computed data on the rib roughed wall were also compared with those on a flat plate for the double-wall cooling. The results demonstrate that the installation of the high blockage ribs significantly decreases the detrimental crossflow effect due to the blockage effect of the ribs and intensively disturbs the jet flow in flow passing over the ribs, thereby enhancing the heat transfer performance. For the impingement/effusion cooling, the arrangement of the rib downstream of the effusion holes (l/Sx = 0.25) shows more advantages, and the heat transfer level rises quickly as BR increases. The best thermal-hydraulic performance and heat transfer uniformity on the rib roughed target plate is both obtained at BR = 0.3, which can be increased by up to 10% and 8%, respectively, compared to those on the flat plate.

Effect of curvature radius and angle on aerodynamic characteristics of a sphere travelling in a branched tube system

Compressible flow through a branched duct and the motion of a sphere through a high blockage ratio pipe are two important and engaging topics throughout the years. The results of studies on these topics are of practical relevance to many fields such as the gas pipeline technology, air transport systems in gas turbines technology, and tube transportation, etc. However, studies on the motion of a sphere in a branched duct are scarce. Studies of the motion of a sphere in a near-vacuum tube could contribute to the development of a branched Hyperloop system in the future. In this study, we investigated the effect of the tube curvature radius and angle on the aerodynamic characteristics of a sphere during its motion in a branched tube. We examined, quantified, and compared the variation of the drag, side force, and pressure waves for the cases where a sphere enters a branch considering six curvature radii (from 500 to 3000 m), three angles (10°, 15°, and 20°), three speeds (100, 200, and 300 m s-1), and two initial pressures (1/1000 and 1 atm) in simulations. The results indicated that the drag and side force vary only in the intersection region (region where the straight tube and branched tube intersect); before and after the intersection region, they are similar. With an increase in the curvature radius, the rate of drag reduction (FD/max(FD)) decreases, while the changes in the angle do not affect variation of drag and side forces. Furthermore, we compared the motion of a sphere in straight and branched directions and found out that the flow in front and behind the sphere was similar for both directions.

Flame acceleration and DDT in a channel with fence-type obstacles: Effect of obstacle shape and arrangement

Experiments and numerical simulations were conducted to study the effects of obstacle shape and arrangement on the flame acceleration and deflagration-to-detonation transition (DDT) in an obstructed channel filled with a stoichiometric hydrogen–oxygen mixture. Two different shapes and arrangements of fence-type obstacles with the same blockage area were considered: continuous triangular and discrete rectangular obstacles. In the experiments, high-speed schlieren photography was used to record the flame acceleration and DDT process with a blockage ratio of 0.5. In the calculations with the different blockage ratios, a high-order numerical algorithm was used to solve the multidimensional, fully compressible, reactive Navier–Stokes equations coupled to a calibrated single-step chemical-diffusive model. The quantitative agreement between the calculations and experiments allows a detailed analysis of the DDT mechanism and the influence of obstacle shape/arrangement using the numerical results. The results show that the differences in the flame acceleration and distance to DDT between the triangular and rectangular obstacle arrays are closely related to the blockage ratio. For a low blockage ratio (br<0.5), flame accelerates faster and DDT occurs in a shorter time in the channel with the triangular obstacles because the inclined surfaces of the triangular obstacles allow stronger flame-vortex interactions and are more favorable to detonation survival once a detonation is initiated in the gap between obstacles. Nevertheless, for a high blockage ratio (br>0.5), the lateral triangle surfaces become steeper, and the advantages of triangular obstacles for promoting DDT become less effective. In addition, the triangles have a more significant weakening effect on the leading shock, while the rectangular obstacles allow the formation of Mach stems. These effects make the rectangular obstacles with a high blockage ratio more conducive to the occurrence of DDT than their triangular counterparts.

Influence of passive wake control on thermal-hydraulic performance of a cylinder confined in wavy channel under high blockage ratios

Influence of passive wake control on thermal-hydraulic performance of a cylinder confined in wavy channel under high blockage ratios

The rise and fall of banana puree: Non-Newtonian annular wave cycle in transonic self-pulsating flow

We reveal mechanisms driving pre-filming wave formation of the non-Newtonian banana puree inside a twin-fluid atomizer at a steam–puree mass ratio of 2.7%. Waves with a high blockage ratio form periodically at a frequency of 1000 Hz, where the collapse of one wave corresponds to the formation of another (i.e., no wave train). Wave formation and collapse occur at very regular intervals, while instabilities result in distinctly unique waves each cycle. The average wave angle and wavelength are 50° and 0.7 nozzle diameters, respectively. Kelvin–Helmholtz instability (KHI) dominates during wave formation, while pressure effects dominate during wave collapse. An annular injection of the puree into the steam channel provides a wave pool, allowing KHI to deform the surface; then, steam shear and acceleration from decreased flow area lift the newly formed wave. The onset of flow separation appears to occur as the waves' rounded geometry transitions to a more pointed shape. Steam compression caused by wave sheltering increases pressure and temperature on the windward side of the wave, forcing both pressure and temperature to cycle with wave frequency. Wave growth peaks at the nozzle exit, at which point the pressure build-up overcomes inertia and surface tension to collapse and disintegrate the wave. Truncation of wave life by pressure build-up and shear-induced puree viscosity reduction is a prominent feature of the system, and steam turbulence does not contribute significantly to wave formation. The wave birth-death process creates bulk system pulsation, which, in turn, affects wave formation.

Flow over a confined mounted fence at low and moderate Reynolds number: A numerical study

Direct numerical simulations of a flow over a wall mounted fence confined by two parallel walls were conducted at low and transitional Reynolds number (50⩽ReD⩽2000) for blockage ratios ranging from 0.25 (low blockage) to 0.9 (high blockage). A primary recirculation bubble forms downstream of the fence and the length of this recirculation region increased with Reynolds numbers. A secondary recirculation bubble appeared on the opposite wall to the mounted fence for the laminar cases with higher blockage ratios at sufficiently large Reynolds number. The separation and reattachment locations were documented and compared with numerical and experimental data. The length of the primary recirculation bubble in current simulations are consistent with the literature while the comparison of the secondary recirculation bubble with experimental data had limited agreement. This secondary recirculation bubble disappeared for the cases at transitional Reynolds number. Instead, the strong primary recirculation bubble induced a corner eddy at the rear of the fence. ‘Packets’ of cross stream velocity fluctuations were observed as the initially 2D, steady, laminar shear layer breakdowns to a 3D turbulent flow. The space–time diagram also showed ripple-like fluctuations of the shear layer further downstream of the fence with a single distinct peak observed in the streamwise and cross flow velocity fluctuations spectra. This peak in the spectra can be predicted by linear stability analysis of a mixing layer (Yasuo et al., 1986). In the near wake, scale-like features were observed while patches of fluctuations of a longer timescale were noted in the recirculation region.

Effects of cylinder cross-sectional geometry and blockage ratio on VIV-based mixing performance in two dimensional laminar channel flow

A novel self-sustained flow mixing methodology is numerically studied that takes advantage of the crosswise vortex induced vibrations (VIVs) of an elastically-suspended cylinder to enhance mass mixing of two coflowing miscible identical laminar streams of different concentrations within a two dimensional parallel-plate straight channel. The effects of mixer cross-sectional shape, channel blockage ratio, and reduced flow velocity on the main flow field and mixing performance characteristics are examined through extensive two dimensional CFD-based numerical simulations at low Reynolds and moderate Péclet numbers (Re=100,Pe=103). Five important canonical configurations (namely, circular, square, tilted square, tilted elliptical, and vertical elliptical) for three different blockage ratios (β=D/H=2/5, 1/4, 1/6) are considered. Numerical results indicate that the best overall mixing efficiency (over 90%) and mixing energy cost (about 8 units) are simultaneously obtained for the stationary vertical elliptical and tilted square cylinders set in the narrow channel (β=2/5), while the VIV-based mixing design does not lead to any appreciable improvements in the (already excellent) mixing performance parameters for these two specific configurations. Also, the greatest overall enhancements in the VIV-based mixing efficiencies in the order of preference are obtained for the square (up to 51%), circular (up to 39%), and tilted elliptical (up to 38%) cross sections in the lower VIV branch for the channel with highest blockage ratio (β=2/5), while the best general improvements in the mixing energy costs are achieved for the square and tilted elliptical cross sections. The overall validity of adopted computational methodology is rigorously verified against data available in the literature.

Modeling spherical turbines for in-pipe energy conversion

In-pipe hydrokinetic systems employing spherical turbines that operate in confined flows with high blockage ratio are a relatively new technology. The number of modeling and computational studies analyzing the performance of spherical turbines operating in confined area is quite limited. The main objective of this study is to model a novel in-pipe cross-flow turbine and perform numerical analyses. Accordingly, a five bladed spherical rotor was designed and numerical simulations were conducted for various inlet velocities (0.8–6.5 m/s), tip speed ratios (0.6–5.2) and blockage conditions (0.59–0.83). The relationships between geometric, dynamic parameters and power performance were discussed. The findings showed that increasing blockage ratio significantly improved the power performance by shifting the CP-λ curve to the right-upward direction. The output power was maximized by a factor of 2.5 where the pipe diameter is reduced from 1.3 to 1.1 times the turbine diameter. A linearly increasing relationship was achieved between power coefficient and blockage where the angle was proportional with λ. Optimum λ was obtained around 4.2 at high blockage where it was mostly between 1.5 and 2 in free flow turbines. This research is expected to contribute to spherical turbine studies for optimal power generation and energy efficiency in water transmission pipelines.