Isentropic Pressure Research Articles

Multi-objective optimization for impeller structure parameters of fuel cell air compressor using linear-based boosting model and reference vector guided evolutionary algorithm

As a pivotal part of cathode air supply system, centrifugal air compressors play a central position in ensuring efficient operations of onboard fuel cells. To improve the overall performance of compressors, comprehensive performance tests were conducted and an integrated simulation model was developed by using computational fluid dynamics (CFD) methods. On this basis, the prediction performance of Linear-based Boosting models was investigated, and multi-objective optimization of impeller structural parameters was carried out through the Reference Vector Guided Evolutionary Algorithm (RVEA). Simulation results indicate that the impeller of the original compressor exhibits significant entropy increase, insufficient gas compression and serious energy dissipation, highlighting considerable room for design optimization. The eXtreme Gradient Boosting (XGBoost) model with 29 estimators has superior generalization ability and prediction performance, making it the preferred Boosting model for the compressor. Multi-objective optimizations have strong universality and rationality, resulting in a well-distributed and diversified final non-dominated solution set. The isentropic efficiency and pressure ratio of the Max_σ solution are improved by 18.7% and 70.1%, while those of the Max_ηc solution are enhanced by 23.0% and 48.9%, respectively. After optimization, the gas experiences reduced shock loss, diminished entropy increase and enhanced flow stability. These findings can provide data support, theoretical basis and directional guidance for performance improvement of centrifugal air compressors.

Experimental Investigation on the Performance of the Scroll Expander under Various Driving Cycles

Energy storage is considered a crucial unit in utilizing renewable energy sources, and compressed air energy storage (CAES) provides a cost-effective solution. It offers the benefits of zero pollution, a long lifespan, low maintenance costs, and minimal environmental impact. In order to increase the possibilities of compressed air energy storage for vehicle power, the performance of the expander needs to be studied. First, a CAES unit test bench is established. Then, the volumetric flow rate, rotational speed, torque, and output power are examined. Additionally, the isentropic exhaust temperature, pressure, and gas consumption rate of the scroll expander are analyzed. Finally, analyzing the economic feasibility of the CAES unit entails running the unit under varied driving conditions. Results reveal that the pressure of the input expander is high, which will lead to greater torque, greater peak power, and a greater temperature drop, but the gas in the air tank will also run out quickly. The peak power of the scroll expander does not occur at the maximum volume flow rate, rotation speed, and torque. The basic investment of the CAES unit mainly depends on the peak output power.

Lie symmetry analysis for the Cargo–Leroux model with isentropic perturbation pressure equation of state

In this article, the well-known Cargo–Leroux model with isentropic perturbation equation of state is analyzed using the Lie symmetry method. By using invariant conditions of system of partial differential equations, six dimensional Lie algebra is obtained. The optimal system for system of partial differential equations is constructed using adjoint representation and the invariants of associated Lie algebras of the system. Further, with the help of one-dimensional optimal system invariant solutions are constructed. Also, physically significant solutions such as traveling wave solutions, specifically the kink-type solitons and peakon-type solitons are obtained by using traveling wave transformations and all the solutions are graphically demonstrated. Finally, the hyperbolic nature of system of partial differential equations is examined by studying the evolutionary behavior of a discontinuity wave.

Three-Dimensional Optimization of Blade Lean and Sweep for an Axial Compressor to Improve the Engine Performance

Nowadays, optimization methods have been considered as a practical tool to improve the performance of turbo-machines. For this purpose, the numerical study of the aerodynamic flow of the NASA Rotor-67 axial compressor has been investigated, and the results of this three-dimensional simulation show good agreement with experimental data. Then, the blade stacking line is changed using lean and sweep for Rotor-67 to improve the compressor performance. The third-order polynomial is selected to generate the lean and sweep changes from the hub to the shroud. The compressor flow field is solved by a Reynolds averaged Navier-Stokes solver. The genetic algorithm, coupled with the artificial neural networks, is implemented to find the optimum values for blade lean and sweep. Considering the three objective functions of pressure ratio, mass flow rate, and isentropic efficiency, the optimized rotor is obtained using the optimization algorithm. Two geometries are obtained using the optimization algorithm. The results of the optimized compressor include improving the isentropic efficiency, pressure ratio, and mass flow equal to 0.57%, 0.93%, and 1.8%, respectively. After compressor optimization, the effect of the changes in the compressor performance parameters is studied on a single spool turbojet engine. The engine is modeled by analyzing the Brayton thermodynamic cycle of the assumed turbojet engine under design point operating conditions. Results show that for the best test case, the engine with the optimized rotor, the thrust, and SFC are improved by 1.86% and 0.21%, respectively.

Robust optimization and uncertainty quantification of a micro axial compressor for unmanned aerial vehicles

Axial compressors are susceptible to uncertainties during their manufacturing and operation, resulting in reduced efficiency and performance dispersion. However, uncertainty quantification and robust design of compressors remains challenging due to the complexity of structure and internal flow. In this study, an automated framework for uncertainty quantification and robustness optimization of micro axial compressors is proposed. Ten geometrical uncertainties are propagated for the nominal design point and two off-design points, i.e., near stall and choke conditions, respectively. The main objective of this paper is to optimize the aerodynamic robustness performance at these operating points. The sparse grid-based probabilistic collocation method is used to propagate these uncertainties, and a multi-objective genetic algorithm is employed to perform robust optimization based on a novel constructed surrogate model.The results show that the optimal configuration achieves an improvement in aerodynamic robustness and mean performance across the entire characteristic map, with greater improvement at the design working point than at the off-design points. At the design working point, the mean isentropic efficiency and pressure ratio of the optimal configuration increase by 0.6% and 0.5%, respectively, while the standard deviation of isentropic efficiency, pressure ratio, and mass flow rate decreases by 32.4%, 41.2%, and 25.1%, respectively. This optimization framework proves to be both feasible and efficient and can be applied to aerodynamic robust optimization of turbomachinery. In the future, we will apply this framework to different aspects of the gas turbine life cycle to model and analyze uncertainties of larger orders of magnitude.

Design of Electric Supercharger Compressor and Its Performance Optimization

The performance of the centrifugal compressor, which is the main component of the electric supercharger, significantly impacts the engine’s dynamics, economy, emissions, and responsiveness. The purpose of this paper is to enhance the aerodynamic performance of the centrifugal compressor of the electric supercharger for the two-stroke engine by optimizing the design of its impeller and diffuser parameters. The paper employs the numerical simulation method and applies the Spalart–Allmaras turbulence model to solve the RANS equations to analyze the impact of impeller-related parameters on the centrifugal compressor’s performance. Subsequently, the paper optimizes the initial model parameters based on the simulation results and confirms its performance through an experiment. The findings indicate that enhancing the isentropic efficiency and pressure ratio of the compressor can be achieved by increasing the number of blades on the impeller, selecting an appropriate blade backward angle, and increasing the relative outlet width. After optimization, the compressor’s efficiency can achieve 0.842, the pressure ratio can reach 1.49 with a working margin of 22%, and the efficiency is enhanced by 1.4%, while the pressure ratio is increased by 1.8% compared to the pre-optimization state. Moreover, the optimized model is experimentally validated to meet the design requirements.

Robust aerodynamic optimization and design exploration of a wide-chord transonic fan under geometric and operational uncertainties

Axial compressors are inevitably affected by various uncertain factors in the process of manufacture and operation. These uncertainties obviously lead to reduced efficiency and large performance dispersion. However, researches on uncertainty quantification and robust design of compressors still faces severe difficulties due to the complexity of compressor structure and internal flow. This paper aims to present an automated and effective framework for uncertainty quantification and aerodynamic robustness optimization of axial compressor. The manufacturing error distribution is derived from the measurement data of machined fan blades, and the sparse grid-based polynomial chaos expansion method is used to propagate the uncertain factors and predict the probability density distribution of the fan performance. A novel surrogate model that combines a self-organizing mapping and a back-propagation neural network is constructed to explore and visualize the correlation between uncertainty parameters and performance responses. Robust aerodynamic design optimization is achieved based on the genetic algorithm. The results indicate that the coupled neural network model exhibits good accuracy for uncertain approximate modeling. Compared with the prototype fan, the optimized fan's mean isentropic efficiency and pressure ratio increase by 0.97% and 0.72%, respectively. The standard deviation of isentropic efficiency, pressure ratio, and mass flow rate decrease by 46.3%, 21.4%, and 15.2%, respectively. The present study provides a reference and exploration for uncertainty quantification and robust optimization of advanced refined multi-stage turbomachinery.

Influence of Blade-Flow Interactions on Flow Behaviours and Blade Loading of an Automotive Mixed-Flow Turbine

Mixed-flow turbine (MFT) is one type of turbines in automotive turbocharger. Multiple studies on turbine blades and flow interactions were done in this area but mainly focusing on structural responses and none on the fluid behaviours. The objectives of this paper are to compare and analyse the influence of blade-flow interactions on flow behaviours and blade loading at four MFT turbine operating conditions under steady state flow. Flow behaviours are indicated by appearances of secondary flows and blade loading is ratio of static pressure acting on turbine rotor blades over the total isentropic pressure at volute inlet. Blade loading represents capability of turbine blades to generate torque. Three validated simulations models using commercial software were developed, a non-coupled model and coupled models which consists of one-way and two-way coupled model. Non-coupled model assumes blades are rigid bodies and for coupled models, blades are deformable and share interfaces for interactions. Results show that there are differences in flow behaviours in non-coupled and coupled models that affect blade loading. Coupled models produce torque with range 1.33% to 0.60% lower than non-coupled model at most operating conditions. At 50% turbine design speed, average efficiency differences for non-coupled and coupled models to experiment data are 1.38% and 1.28% respectively. There is no significant difference in flow behaviours in one-way and two-way coupled models due to the stiffness of material of turbine blades is high but show minor differences in blade loading and torque.

Numerical study of effects of solid particle erosion on compressor and engine performance

Solid particle erosion (SPE) is a major source of damage to, and cause of failure of, turbomachinery, including centrifugal and axial compressors and gas turbines. There is considerable interest within the turbomachinery industry to develop the means to enhance durability and improve prediction of likely breakdowns of machinery operating in locations and conditions where ingestion of, for example, dust and sand grains is unavoidable during operation. The present study examines the implications of degradation of the compressor on gas turbine cycle performance, caused by operating in eroding environments, linking compressor aerodynamics with the thermodynamic cycle. The research engine employed in the study comprised a fan, bypass, and two stages of the low-pressure compressor (booster). A numerical simulation using Computational Fluid Dynamics (CFD) software was performed to predict the likely erosion patterns due to solid particles (SPs) impacting on the blades of the first two stages of an axial compressor. This study introduces a method that provides the freedom to apply roughness to a particular region of the blade following the SPE patterns identified as part of the CFD simulations so as to represent the effects of the erosion spots on the overall flow field. The localised roughness method employs a perturbation of the geometry of the blade in the regions corresponding to the location predicted by the SPE model. The intensity of the perturbation, which is governed by a “fraction factor” coded in a Matlab script, was calibrated by reference to a roughness case, applied over the entire blade surface, with equivalent sand-grain roughness (ks) of 60 μm. Turbomatch, the Cranfield in-house gas turbine performance simulation software, was employed to model the degradation of engine performance. The research confirmed that SPE is linked with significant decreases in engine performance parameters such as isentropic efficiency (ηis) and pressure ratio (PR). These quantities showed, for the SPE cases considered, a drop of 8.8% and 5.2%, respectively. These findings are useful to link local SPE events to global GTE cycle performance.

A New Entropy Function to Analyze Isentropic Processes of Ideal Gases with Variable Specific Heats.

A new entropy function s+ is defined in terms of the existing entropy function s° and temperature as s+ = s° − R lnT to facilitate the analysis of isentropic processes of ideal gases with variable specific heats. The function s+ also makes it possible to calculate the entropy changes of ideal gases during processes when volume information is available instead of pressure information and the variation of specific heats with temperature is to be accounted for. The introduction of the function s+ eliminates the need to use the dimensionless isentropic functions relative pressure Pr and relative specific volume vr of ideal gases and to tabulate their values. The Pr and vr data are often confused with pressure and specific volume, with an adverse effect on the study of the second law of thermodynamics. The new s+ function nicely complements the existing s° function in entropy change calculations: the former is conveniently used when volume information is given while the latter is used when pressure information is available. Therefore, the introduction of the new entropy function s+ is expected to make a significant contribution to the thermodynamics education and research by streamlining entropy analysis of ideal gases.

A Preliminary Design and Modeling Analysis of Two-Phase Volumetric Expanders for a Novel Reversible Organic Rankine-Based Cycle for Carnot Battery Technology

Carnot battery technology appears to be a promising solution to increase the development of power generation and offers a good solution for high-capacity, day-to-day energy storage. This technology may utilize the waste heat and store the electricity to recover it later. This article reports the preliminary analysis of a specially designed Carnot battery configuration employing a novel reversible Rankine-based thermodynamic cycle (RRTC). In this case, one volumetric expander is not only installed to generate power from a heat engine, but also to recover power during heat pump operating mode. The preliminary design and modeling results were obtained based on calculations taken from working fluid thermal properties of propane with some specific boundary conditions (i.e., secondary fluid hot temperature of 348.15 K, cooling temperature of 228.15 K, and waste heat temperature of 338.15 K). The results show that isentropic efficiency, pressure, and volumetric expansion ratio from both heat engine and heat pump operating modes are important parameters that must be taken into account when designing the two-phase expander for RRTC. The obtained results show that a designed two-phase volumetric expander in RRTC features a pressure ratio of 2.55 ± 1.15 and a volumetric ratio of 0.21 ± 0.105, and the Carnot battery may achieve the performance of 0.50–0.98.

Development of a one-dimensional code for the initial design of a micro gas turbine mixed flow compressor stage

Abstract The use of micro gas turbines (MGTs) for once-off and unique applications means that a rapid turnaround design process is required. The development of a MATLAB® application-based program for the initial design and performance analysis of radial and mixed flow compressors is discussed. The program code is based on one dimensional (1D) mean line flow and loss model theory. For verification, 18 test compressors were developed, covering a wide range of design velocities, mass flow rates and meridional exit angles. Predicted performance results were verified using Numeca/FINE™ Turbo software. Initial comparisons between 1D and Computational Fluid Dynamics (CFD) results did not match well. The 1D software over-predicted compressor performance and provided poor choke prediction. Consequently, empirical models to correct these deviations were derived and implemented into the 1D Application code. The updated 1D code provided a mean choke prediction difference of 1.59% compared to an initial 14.98% difference at the design point. Mean total-to-total isentropic efficiency and pressure ratio reduced to differences of 0.74 and 1.24% from values of 11.23 and 9.31% respectively.

Weak-strong uniqueness principle for compressible barotropic self-gravitating fluids

The aim of this work is to prove the weak–strong uniqueness principle for the compressible Navier–Stokes–Poisson system on an exterior domain, with an isentropic pressure of the type p(ϱ)=aϱγ and allowing the density to be close or equal to zero. In particular, the result will be first obtained for an adiabatic exponent γ∈[9/5,2] and afterwards, this range will be slightly enlarged via pressure estimates “up to the boundary”, deduced relaying on boundedness of a proper singular integral operator.

Construction of weak solutions to compressible Navier–Stokes equations with general inflow/outflow boundary conditions via a numerical approximation

The construction of weak solutions to compressible Navier–Stokes equations via a numerical method (including a rigorous proof of the convergence) is in a short supply, and so far, available only for one sole numerical scheme suggested in Karper (Numer Math, 125(3):441–510, 2013) for the no slip boundary conditions and the isentropic pressure with adiabatic coefficient \(\gamma >3\). Here we consider the same problem for the general non zero inflow–outflow boundary conditions, which is definitely more appropriate setting from the point of view of applications, but which is essentially more involved as far as the existence of weak solutions is concerned. There is a few recent proofs of existence of weak solutions in this setting, but none of them is performed via a numerical method. The goal of this paper is to fill this gap. The existence of weak solutions on the continuous level requires several tools of functional and harmonic analysis and differential geometry whose numerical counterparts are not known. Our main strategy therefore consists in rewriting of the numerical scheme in its variational form modulo remainders and to apply and/or to adapt to the new variational formulation the tools developed in the theoretical analysis. In addition to the result, which is new, the synergy between numerical and theoretical analysis is the main originality of the present paper.

Experimental investigations on high pressure ratio cryogenic turboexpanders for helium liquefier

Experimental investigations of two variants of a high pressure ratio cryogenic turboexpander, from a new series of turboexpanders for Bhabha Atomic Research Centre (BARC), are presented in the article. Both the variants are designed based on an earlier reported enhanced midstream method. The new turboexpanders are designed with larger turbine impeller-diffuser radial clearances and smaller turbine impeller L/D ratio as compared to previous series of BARC turboexpanders. The experimental investigations are carried out in BARC developed helium refrigerator CP1000 and helium liquefier LHP50. Different aspects of turboexpander performance, as defined by isentropic efficiency, pressure ratio and power developed in response to variation in parameters such as turboexpander flow and operational specific speeds, are presented in detail. The idea of using process turboexpanders for the mass flow measurements is also briefly studied using the results of the experiments. Experiment is also devised to compute heat-in-leak from turboexpander mountings and the results are used to critically analyse and provide corrections to the thermodynamic performance of the turboexpanders achieved during other experiments. From the two new variants of the turboexpanders investigated here, the better performing one is selected and mounted on LHP50 as TEX-2 for determining the maximum helium liquefaction capacity. LHP50 plant performance is then compared to the earlier reported liquefaction capacities with previous versions of BARC turboexpanders.

Flow unsteadiness and rotor-stator interaction in a two-stage axial turbine

This paper presents an in-depth investigation of the unsteady flows through two-stage high-pressure (hp) axial turbine with analyses of the rotor-stator interaction effects on the aerothermodynamic performance. The unsteady flow structures are characterized by the formation and convection of the tip leakage vortex and the hub corner vortices from the first stage blade-row through the second stage nozzle guide vanes (NGV) and blade-row. The modal decomposition of the circumferential distributions of static pressure depicts the modulation of the potential effect in the form of lobed structure propagating in both sides. Moreover, the blade pressure field shows that the first blade-row is exposed to a periodic overpressure induced by the first NGV while in the second blade-row the linear combination of both potential effects is dominant and results in a complex unsteady blade loading. FFT analyses of unsteady turbine performance for two-stage and part stages reveal that the total-to-total isentropic efficiency, torque-based efficiency and pressure ratio of the first stage depend strongly on the first blade-row passing frequency (BPF), whereas the total-to-total isentropic efficiency in second stage and two-stage turbine is related to the second blade-row BPF while the pressure ratio and the torque-based efficiency depend on the two rotors BPFs. Finally, the torque oscillations are mainly associated with the combination of frequencies of first stage NGV with that of second stage NGV. Furthermore, the obtained results show that Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations are essential in analyzing the complex wakes and vortical structures through the two-stage turbine components and may produce better estimation of the performance.

The influence of the trailing edge angle of the micro centrifugal impeller on the performance of the centrifugal compressor

In order to study the effect of the trailing edge sweep angle of the centrifugal impeller on the aerodynamic performance of the centrifugal compressor, 6 groups of centrifugal impellers with different bending angles and 5 groups of different inclination angles were designed to achieve different impeller blade trailing edge angle. The computational fluid dynamics (CFD) method was used to simulate and analyze the flow field of centrifugal compressors with different blade shapes under design conditions. The research results show that for transonic micro centrifugal compressors, changing the blade trailing edge sweep angle can improve the compressor’s isentropic efficiency and pressure ratio. The pressure ratio of the compressor shows a trend of increasing first and then decreasing with the increase of the blade bending angle. When the blade bending angle is 45°, the pressure ratio of the centrifugal compressor reaches a maximum of 1.69, and the isentropic efficiency is 67.3%. But changing the inclination angle of the blade trailing edge has little effect on the isentropic efficiency and pressure ratio. The sweep angle of blade trailing edge is an effective method to improve its isentropic efficiency and pressure ratio. This analysis method provides a reference for the rational selection of the blade trailing edge angle, and provides a reference for the design of micro centrifugal compressors under high Reynolds numbers.

Design Guidelines for Axial Turbines Operating With Non-Ideal Compressible Flows

Abstract The impact of non-ideal compressible flows on the fluid-dynamic design of axial turbine stages is examined. First, the classical similarity equation (CSE) is revised and extended to account for the effect of flow non-ideality. Then, the influence of the most relevant design parameters is investigated through the application of a dimensionless turbine stage model embedding a first-principles loss model. The results show that compressibility effects induced by the fluid molecular complexity and the stage volumetric flow ratio produce an offset in the efficiency trends and in the optimal stage layout. Furthermore, flow non-ideality can lead to either an increase or a decrease of stage efficiency up to 3–4% relative to turbines designed to operate in dilute gas state. This effect can be predicted at preliminary design phase through the evaluation of the isentropic pressure–volume exponent. Three-dimensional (3D) RANS simulations of selected test cases corroborate the trends predicted with the reduced-order turbine stage model. URANS computations provide equivalent trends, except for case study niMM1, featuring a non-monotonic variation of the generalized isentropic exponent. For such turbine stage, the efficiency is predicted to be higher than the one computed with any steady-state model based on the control volume approach.

Research on the Application of Partial Similarity for a 1-1/2 Axial Compressor

In this paper, a method based on the partial similarity principle is presented to improve the aerodynamic design with low cost and high accuracy for a 1-1/2 axial compressor. By means of this method, during the process of a similar design, the machine Mach number and flowrate coefficient are maintained. The flow similarity between the prototype and its large-scaled alternative was observed, according to a detailed analysis of flow fields of rotor and stator. As well, the relative discrepancies of isentropic efficiency and pressure ratio between two models are 1.25% and 0.4% at design point, respectively. Besides, their performance curves agreed very well in the whole operating range. Moreover, it was also found that the flow similarity between the two models can be maintained under unsteady working conditions. Thereafter, in order to investigate the impact of stability optimization method on the similarity principle, casing treatment with single circumferential groove was applied to these two models. The flow similarity was still maintained and the flowrate near the stall was reduced about 1.1% with negligible deterioration of the overall performance.

Implementation of Adaptive Neuro-fuzzy Model to Optimize Operational Process of Multiconfiguration Gas-Turbines

In this article, the adaptive neuro-fuzzy inference system (ANFIS) and multiconfiguration gas-turbines are used to predict the optimal gas-turbine operating parameters. The principle formulations of gas-turbine configurations with various operating conditions are introduced in detail. The effects of different parameters have been analyzed to select the optimum gas-turbine configuration. The adopted ANFIS model has five inputs, namely, isentropic turbine efficiency (Teff), isentropic compressor efficiency (Ceff), ambient temperature (T1), pressure ratio (rp), and turbine inlet temperature (TIT), as well as three outputs, fuel consumption, power output, and thermal efficiency. Both actual reported information, from Baiji Gas-Turbines of Iraq, and simulated data were utilized with the ANFIS model. The results show that, at an isentropic compressor efficiency of 100% and turbine inlet temperature of 1900 K, the peak thermal efficiency amounts to 63% and 375 MW of power resulted, which was the peak value of the power output. Furthermore, at an isentropic compressor efficiency of 100% and a pressure ratio of 30, a peak specific fuel consumption amount of 0.033 kg/kWh was obtained. The predicted results reveal that the proposed model determines the operating conditions that strongly influence the performance of the gas-turbine. In addition, the predicted results of the simulated regenerative gas-turbine (RGT) and ANFIS model were satisfactory compared to that of the foregoing Baiji Gas-Turbines.