A Rortex-based method for evaluating hydraulic losses in pump-turbines: a case study of turbine mode under different load conditions

Multistage centrifugal pumps are highly efficient and compact in structure. Pump efficiency can be improved by an effective understanding of hydraulic behavior and energy loss, however, the traditional hydraulic loss evaluation method does not readily reveal the specific locations of energy loss in the pump. In this study, a guide ring was imposed in multistage pumps, and an entropy production theory was applied to investigate irreversible energy loss of a multistage pump with and without guide ring. Detailed distributions of energy losses in the pumps were calculated to determine the respective entropy production rates (EPRs). The EPR values as calculated are in close accordance with actual hydraulic loss values in the pumps. EPR values were higher in the multistage pump with the guide ring than the pump without a guide ring under part-load flow conditions (0.2Qd). However, the vortex flow in the pump was weakened (or eliminated) by the guide ring as flow rate increased; this reduced energy loss in the chambers. Flow passing the chamber was stabilized by the guide ring, which decreased shock and vortex loss in the chamber and guide vane. Under both designed flow condition and overload conditions, the EPR values of the guide ring-equipped multistage pump were lower than those without the guide ring. Furthermore, minimum efficiency index (MEI) values were also calculated for the two chamber structures; it was found that overall efficiency of pump with guide ring is better than that without.

Multi-stage pump as turbine (PAT) has a wider range of heads and application intervals compared to single-stage PAT. In our research, we have conducted experimental and numerical simulation studies on this issue. In this paper, based on experimental research, numerical simulation is applied to calculate the multi-stage PAT flow field. The flow characteristics of multi-stage PAT under different working conditions are studied using the entropy production theory. Finally, the Pearson correlation coefficient is used to evaluate the relationship between the hydraulic loss and entropy production of the impellers and guide vanes. The entropy production theory is used to determine the location where the multi-stage PAT energy loss occurs compared with the traditional pressure drop assessment method. The results show that the trend of the numerical simulation results is consistent with the experimental results. The energy loss in the multi-stage PAT is calculated combined with the impeller and guide vane which accounts for 69.1–73% of the total energy loss under all flow conditions. The total entropy production rate of each component under design flow conditions is listed in decreasing order: impeller, guide vane, front and back chamber, a balance disk, and inlet and outlet volute. The first stage component has a larger energy loss compared with the rest of the stages. The magnitude of energy loss is closely related to physical quantities such as flow field velocity and skin friction coefficient. Furthermore, the distribution of streamlines and vortex cores at the impellers reflects that flow domain stability increases from the first stage impeller to the fifth stage impeller. The correlation between entropy production and hydraulic loss was evaluated by the Pearson correlation coefficient. Therefore, using the entropy production theory can effectively identify the characteristics of the flow field and the location of energy losses. It provides a reference for the targeted optimization of multi-stage PAT.

This study investigated the irreversible energy losses in the different sections of propeller blades. To the best of our knowledge, this is the first study to consider the properties of a shear-thinning fluid in evaluating irreversible energy losses based on the entropy generation theory. The numerical simulation results were consistent with the experimental results. The flow energy losses and the total mechanical energy loss gradient of an anaerobic digestion (AD) system were determined. The results indicated that the total mechanical energy loss occurred in the propeller region and was primarily influenced by the operation speed. The effects of rheology were neglected, although rheology notably affects the equivalent-volume velocity field within specific power characteristics, leading to an insufficient mixing field in the AD system. The energy losses primarily occurred around the propeller region, primarily in sections 3–5 under different flow rates. Viscous diffusion and velocity fluctuation are the primary factors contributing to the entropy of the system, accounting for more than 98%. According to the wall separation and friction loss on the suction and pressure surfaces of the propellers, sections 3–5 accounted for 90% of the energy loss. Energy dissipation in the propeller was mostly constituted by turbulence entropy and direct entropy. The rotation speed was the key factor causing viscous diffusion. Although the rheology effect on hydraulic loss is limited at low concentrations, the hydraulic loss in the blade tip region due to high-concentration fluids is significantly affected by rheology.

Detailed aerodynamic data from the suction surface boundary layer on a turbine blade arranged in a linear subsonic cascade was acquired under high free stream turbulence conditions (∼ 5.2%) generated using a perforated plate placed upstream of the cascade. In addition, data was also obtained from a transonic turbine cascade utilizing the same blade profile but of much smaller chord at free stream turbulence levels of 3.5%. Velocity profiles from the laminar, transitional and turbulent boundary layers were measured at various locations along the airfoil suction surface for the incompressible regime at ReC of 76,000. For the compressible test cases, boundary layer velocity profiles were measured at two locations towards the aft section of the blade at ReC of 163,000 and MEx of 0.37 respectively. For both cases the boundary layer velocity profiles were acquired by traversing a single normal hot wire probe normal to the blade surface. In addition the extent of the transition region over the blade surface was determined for both compressible and incompressible regimes by the use of an array of heated thin film sensors over a range of Reynolds and exit Mach numbers. It was observed that an earlier transition ensued at high free stream turbulence conditions in comparison to a previous investigation at comparable ReC and lower turbulence level (0.8% Tu). In addition comparisons were made to existing incompressible data at ReC = 185,000 and 0.8% free stream turbulence intensity. One of the primary observations resulting from an earlier transition was a thicker turbulent boundary layer, but in addition it was also noted that shear strain rates in the laminar boundary layer were significantly higher than those obtained at the 0.8% turbulence intensity. Further analyses also elucidated the presence of fluctuating components of velocity in the laminar boundary layer and were attributed to the effects of the free stream turbulence. This leads to the notion of a hybrid boundary layer, possessing both laminar and turbulent characteristics. These findings have implications regarding the profile loss of the blade, that is the loss generated in blade boundary layers and wakes normally associated with phenomena such as viscous shear, Reynolds stress production, shock wave formation and heat transfer across temperature differences and can be quantified in terms of the amount of entropy generated. For the purposes of this study entropy creation is solely restricted to that arising due to fluid dynamic phenomena, thereby assuming an adiabatic and quasi-isothermal flow. The entropy generation rate per unit volume is obtained directly from the boundary layer velocity profile; further integration gives rise to the entropy generation rate over the boundary layer at a point or over the entire suction surface length. Even though the number of quantitative measurement points on the transonic cascade was limited due to the very thin boundary layer present, no effects attributable to compressibility were observed on the entropy generation rate at the Mach number in question. Increased free stream turbulence had a greater effect on the generated entropy due to increased viscous shear in the laminar boundary layer and increased Reynolds stress production. In contrast, free stream turbulence did not have any significant effect on the turbulent boundary layer in the context of this study, as it was observed that the amount of entropy generated in the turbulent boundary layer was approximately equivalent for both turbulence levels at comparable Reynolds number.

The power-trip of the pump under certain conditions leads to the runaway of the unit, causing dangerous transitional process in pumped storage power stations. This process is characterized by transient hydraulic features like flow separation and vortex structures, which increase hydraulic losses significantly and severely impact unit efficiency and stability. This paper aims to elucidate the mechanism of energy loss due to unstable flow during pump turbine runaway. It focuses on a high-head model pump turbine, examining the transient flow process from pump conditions to runaway conditions. It conducts quantitative analysis of energy loss using entropy production theory, besides, further clarifies the location and causes of hydraulic losses by integrating with internal flow analysis. The results show that a significant high-entropy production zone is captured in the pump braking condition, indicating extremely chaotic internal flow in this area during the runaway transition process. Additionally, throughout the transition process, turbulent entropy production initially increases, then decreases. Turbulent entropy production accounts for more than 80% of total entropy production, indicating that turbulent entropy production dominates throughout the entire transition process. The energy of the water is primarily dissipated within the runner during the runaway process. The maximum proportion is 87%, which is in the pump braking condition. Correlation analysis between flow and hydraulic losses reveals that vortex structure induced by flow separation under off-design conditions is the primary contributor to increased hydraulic losses.

Vibration is one of the main issues taken into consideration in the design and manufacture of the pump. The radial force and vibration of the impeller induced by fluid in a centrifugal pump were investigated at different flow rates by numerical simulation. The vibrations on the volute were measured by the experiment. The variation trend of the radial displacements of the impeller is consistent with that of the radial forces, and the variation in the radial displacement lags that of the radial force. The vibration energies on the impeller and the volute were analyzed based on root-mean-square (RMS) values in the frequency domain. The distributions of energy loss in the pumps were calculated to determine the total entropy generation (TEG) and entropy generation rate (EGR). The TEG values as calculated are in close accordance with hydraulic loss. The vibration is a result of the poor flow patterns and consequently results in increased energy losses in the pump.

Aerodynamic Entropy Generation Rate in a Boundary Layer With High Free Stream Turbulence

Computation of shock/boundary-layer interactions in bump channels with transport-type turbulence models

Loss reduction in the compressor corner region via blade cooling

In this paper, the hydraulic losses of a Kaplan turbine under optimal and rated operating conditions are investigated through the theory of entropy generation. The results show that hydraulic loss values calculated using pressure drop and entropy generation theory are similar. The hydraulic losses are mainly concentrated in runner and draft tube. However, when the operation condition of Kaplan turbines deviates from the optimal condition, the proportion of hydraulic loss in draft tube increases. The hydraulic loss in draft tube is mainly composed of entropy generation caused by turbulence fluctuation, which is the result of unstable flow induced by vortex rope. The hydraulic losses of other parts are mainly composed of entropy production caused by wall shear. The high entropy production of the runner concentrated on the shroud, hub, blade surface, and blade trailing edge, while entropy production caused by wall shear is concentrated on blade pressure surface and shroud near blades when the turbine strays from optimal operating condition.

Research on the mechanism of the effect of vortex on the hydraulic loss of pump as turbine units based on entropy production theory

Using the mechanorheological viscoelastic plastic model, the effect of impact velocity of a spherical body on rebound height after impact interaction was studied. With an increase in impact velocity, the energy losses of impact interaction increase. Under the elastic deformations, energy dissipation depends on the deformation rate and increases with increasing impact velocity. During plastic deformations, energy dissipation increases with increasing deformations. Plasticity of the material significantly reduces rebound height. The more ductile the material, the lower the rebound height due to large plastic deformations. In case of an elastic impact, a decrease in elasticity leads to a decrease in the rebound height, since the viscoelastic model becomes more viscous, and the viscous resistance to deformations increases compared to the elastic resistance. This increases energy losses and decreases the rebound height. For the elastic-plastic model, the relationship is reverse. A decrease in elasticity leads to an increase in the rebound height. This is due to the fact that an increase in elasticity of the material leads to an increase in its stiffness. Elastic deformation resistance increases. An increase in the force causes an increase in plastic deformations and an increase in energy losses. An increase in the viscous resistance to deformations leads to an increase in energy losses and a decrease in the rebound height. Thus, the rebound height depends on impact interaction velocity. To improve reliability of dynamic process simulation, it is necessary to take into account these factors when studying the operation of equipment in the conditions of impact interaction of structural elements.

The three-dimensional turbulent boundary layer developing on a rotor blade of an axial flow compressor was measured using a minature “x” configuration hot-wire probe. The measurements were carried out at nine radial locations on both surfaces of the blade at various chordwise locations. The data derived includes streamwise and radial mean velocities and turbulence intensities. The validity of conventional velocity profiles such as the “power law profile” for the streamwise profile, and Mager and Eichelbrenner’s for the radial profile, is examined. A modification to Mager’s crossflow profile is proposed. Away from the blade tip, the streamwise component of the blade boundary layer seems to be mainly influenced by the streamwise pressure gradient. Near the tip of the blade, the behavior of the blade boundary layer is affected by the tip leakage flow and the annulus wall boundary layer. The “tangential blockage” due to the blade boundary layer is derived from the data. The profile losses are found to be less than that of an equivalent cascade, except in the tip region of the blade.

Effects of an inlet swirl on pump performance and static pressure were investigated experimentally. When a swirling flow was introduced to a centrifugal pump, the pump head was increased/decreased depending on the direction of the inlet swirl, and efficiency deteriorated because of the increase in the hydraulic loss at he impeller inlet. The instantaneous pressures on the blade surface were measured by transducers mounted on the impeller, and the rapid change of static pressure caused by the interaction of the vortex core and the impeller blades was clarified. The static pressure change was found to be dominant near the leading edge of the blade, but decreased along the blade. Introducing a small quantity of air into the vortex core made it possible to visualize the behavior of the vortex core at the inlet of the impeller passages ; it was found that the behavior of the vortex core was quite different with the direction of the swirl.

The jet quenching parameter and energy loss of light and heavy quarks have been investigated in the framework of holographic quantum chromodynamics (QCD) models with a critical end point (CEP) at finite baryon chemical potential in Nf=2,2+1,2+1+1 systems. The properties of the jet quenching parameter and energy loss around phase boundary have been carefully studied. It is found that the dimensionless jet quenching parameter and the energy loss of light and heavy quarks exhibit evident features around the phase boundary. Specifically, all these quantities increase rapidly near the CEP phase transition temperature TCEP with fixed μCEP. Moreover, the velocity dependent behavior of heavy quark energy loss differs significantly from charged particle energy loss in quantum electrodynamics (QED) matter. For electromagnetic interaction, the energy loss of charged particle can be described by the Bethe-Bloch formula and the Lindhand-Scharff-Schiott theory at low and high velocities, respectively. However, the heavy quark energy loss at CEP is approximately proportional to velocity at low velocities and aligns with Bjorken’s results at high velocities, which indicates that the heavy quark energy loss is predominantly collisional at low velocities and gluon radiation dominant at high velocities. For light quark energy loss, the behavior of the energy loss per unit length and the total energy loss differs significantly. However, the total energy loss and stopping distance exhibit similar behavior. This implies that the stopping distance predominantly determines the total energy loss. Thus, even with increased energy loss per unit length at higher temperatures or chemical potentials, the total energy loss decreases due to the reduced stopping distance.