Hydrogen Flow Research Articles

Analysis of operation modes of a counter ow column of chemical isotope exchange of hydrogen with water with independent flows of water and hydrogen

As a result of a theoretical analysis of the operation of a countercurrent column of chemical isotope exchange (CIE) of hydrogen with water in the mode with independent ows of hydrogen and water, it has been shown that there are temperature-dependent maximum values of the molar ratio of hydrogen and water ows at which the separating power of the column with respect to isotope mixtures protium-tritium and protium-deuterium are signi cantly reduced. Variants of the operation of the CIE column were experimentally studied under the condition that the condensate of water vapor is returned to the column from the outgoing steam-gas stream or without it. The results of the experiments agree with the theoretical analysis carried out.

Impact of hydrogen addition on diesel engine performance, emissions, combustion, and vibration characteristics using a Prosopis Juliflora methyl ester-decanol blend as pilot fuel

The research primarily focuses on investigating the impact of hydrogen induction on parameters of a compression ignition (CI) engine utilizing biodiesel blended with decanol, up to knock limit. The utilization of non-edible oil, exemplified by Prosopis Juliflora seed oil (JFO), presents inherent challenges due to its elevated viscosity, limited atomization, and suboptimal combustion attributes. However, the conversion of JFO into Prosopis Juliflora methyl ester (JFME) biodiesel substantially ameliorates its fuel characteristics, although it still exhibits relatively lower performance in comparison to conventional diesel fuel. To enhance the attributes of JFME blends, decanol is mixed with 20 % on volumetric basis (referred to as D20). Furthermore, the introduction of hydrogen into the engine's intake manifold is employed to bolster performance and curtail emissions. Different hydrogen flow rates, spanning from 2.5 to 10 litres per minute (lpm), are assessed in conjunction with the D20 biodiesel blend. The inclusion of hydrogen into D20 blends yields an enhancement in brake thermal efficiency (BTE), coupled with reductions in hydrocarbon (HC), carbon monoxide (CO), and smoke emissions. However, it should be noted that hydrogen's notable flame velocity and higher calorific value engender escalated combustion temperatures and an associated rise in Nitric oxide (NO) emission. The research also encompasses an evaluation of engine vibration during dual-fuel operation, revealing a proportional increase in engine vibration with heightened rates of hydrogen induction. In summation, the utilization of D20 in conjunction with hydrogen at a rate of 10 lpm emerges as a viable approach for operating diesel engines in a dual-fuel mode.

Multiphase Flow in Hydrogen Generation

This study examined the laminar-multiphase characteristics in hydrogen production processes by utilizing the simulation software, “COMSOL 5.3 multiphysics simulation software”. The study's objective enhanced the evaluation of the multiphase flow operations involved in hydrogen generation, and determined the key contributors to the multiphase flow in the production of hydrogen. The methodology of the study also involved the design and simulation of the multiphase flow operations involved in hydrogen production and showed the analysis of the flow properties, including pressure profile, velocity profile, concentration profile, and shear rate profile, thereby insights into the multiphase flow interactions. Additionally, the research results enabled an improved understanding of the multiphase flow interactions in hydrogen production and led to an improvement in the process operational conditions for the system. The inference of the study was based on the quantifiable results obtained from the simulation which provided a comprehensive analysis of the multiphase flow characteristics in hydrogen production. More importantly, the shear stress for water-hydrogen system and hydrogen were shown with the shear rate describing the gradient in velocity and the pressure profile, shear rate profile, and velocity profile were calculated for a 2D profile versus the arc length for each of these variables. Thereafter, the results of this research simulation demonstrated that high velocity profile for hydrogen flow was observed within the reactor; with the highest velocity observed in the reactor within the length of (0.5 – 6.5)m, hence indicating optimum length of the water-split reactor for maximum velocity flow. The results further indicated that the profile of water-hydrogen and hydrogen pressure becomes uniform at a distance of 1mm from the entrance and the maximum pressure flow for water-hydrogen and hydrogen fluids pressure are 17.8Pa and 238.27Pa which shows a sufficiently higher pressure of hydrogen.

Titanium Carbide Coating for Hafnium Hydride Neutron Control Rods: In Situ X-ray Diffraction Study

This article considers the possibility of using a magnetron-deposited coating for the protection of hafnium hydrides at high temperatures as a material for neutron control rods. We describe the role of TiC coating in the high-temperature behavior of hafnium hydrides in a vacuum. A 1 µm thick TiC coating was deposited through magnetron sputtering on the outer surface of disk HfHx samples, and then in situ X-ray diffraction (XRD) measurements of both the uncoated and TiC-coated HfHx samples were performed using synchrotron radiation (at a wavelength of 1.64 Å) during linear heating, the isothermal stage (700 and 900 °C), and cooling to room temperature. Quadrupole mass spectrometry was used to identify the hydrogen release from the uncoated and TiC-coated hafnium hydride samples during their heating. We found the decomposition of the HfH1.7 phase to HfH1.5 and Hf and following hafnium oxidation after the significant decrease in hydrogen flow in the uncoated HfHx samples. The TiC coating can be used as a protective layer for HfHx under certain conditions (up to 700 °C); however, the fast hydrogen release can occur in the case of a coating failure. This study shows the temperature range for the possible application of TiC coatings for the protection of hafnium hydride from hydrogen release.

High-efficient removal of Oxygen(O2) impurity from H2 flow on nickel-manganese Oxide: Regulating the exposed crystal plane, structure-activity relationship and determination of active sites

The presence of oxygen (O2) impurity in hydrogen produced by water electrolysis can pose safety hazards when hydrogen is used as a power source. Therefore, oxygen (O2) impurities must be removed from H2 flow to meet the strict purity requirements. In this work, nickel manganese oxide is applied to remove oxygen from H2 flow. It is synthesized via the co-precipitation method using different precipitants, manganese and nickel precursors. The results of the oxygen removal test show that NiMn-4 catalyst, prepared using oxalic acid, manganese acetate and nickel nitrate as the precursors, has the best performance in removing oxygen impurities from the hydrogen flow. The catalyst could retain an oxygen removal efficiency of nearly 70 % at the reaction temperature of 80 °C. Also, XRD, Raman spectra and HRTEM analysis results show that the crystal phase of NiMn-4 (Ni6MnO8) exhibits much stronger crystallinity than the other catalysts and has (400) and (222) planes of Ni6MnO8. H2/O2-TPD and H2-TPR analysis results indicate that NiMn-4 catalyst has much more adsorbed oxygen species, overflow hydrogen and hydrogen consumption at per specific surface area compared to the other catalysts. The XPS results of Ni2p and O1s imply that there is much higher valence of Ni (Ni3+).

The Effect of Rh/BAC Catalyst Preparation and Pretreatment Methods on Benzene Hydrogenation

The challenge of developing catalytic materials with improved performance relies on the support of metal particles on carbon surfaces. The results of benzene hydrogenation on Rh/BAC (birch activated carbon) prepared by different methods, including adsorption and impregnation, depending on the moisture capacity of the support, were presented. The volumes and diameters of the pores on the BAС surface were determined by BET method, SEM and chemical compositions were characterized. Benzene hydrogenation took place on various carbon-supported catalysts at a temperature of 60 °C and a hydrogen partial pressure of 40.0 MPa. Catalysts produced through the impregnation process were more effective than those produced via adsorption. Rhodium cations enter the micro pores and remain in their metallic form during the adsorption of chloride salt solutions. Hydrogen adsorption on them is facile, while access of benzene molecules is difficult. Prior reduction in the hydrogen flow is essential for full completion of the hydrogenation reaction on catalysts, as rhodium reduction and hydrogenation reaction occur simultaneously.

PEM Electrolyzer Digital Replica based on internal resistance determination applied to hydrogen energy storage

The rise of hydrogen as an energy storage means and its associated technologies have prompted the implementation of hydrogen generation systems based on electrolyzers. Electrolyzers exhibit complex behaviour and their implementation is not immediate, leading to the use of tools such as Digital Replicas (DR) for their study. This paper presents a DR for a Proton Exchange Membrane Electrolyzer (PEMEL) through the development of an Equivalent Circuit Model (ECM) that describes the static behaviour of the individual cells comprising it. This research is focused on contributing to hydrogen generation with the main objective of using this energy vector for energy storage applications. For this purpose, an installation consisting of a PEMEL and a set of auxiliary equipment required for its proper operation and for measuring key electrolyzer parameters such as current, voltage, hydrogen flow rate, temperature, etc. is implemented. Furthermore, a Data Acquisition System (DAQ) is available to collect process information for later analysis. The PEM cell model is obtained through an experimental process based on the determination of internal resistance to calculate the remaining key parameters. The successful functioning and suitability of the DR and developed model are reported through experimental data obtained from the PEMEL under operating conditions.

A region-based low-carbon operation analysis method for integrated electricity-hydrogen-gas systems

A region-based low-carbon operation analysis method for integrated electricity‑hydrogen-gas systems (IEHGSs) is proposed in this paper. The committed carbon emission operation region (CCE_OR) and the economic CCE_OR (ECCE_OR) are proposed to evaluate the low-carbon feasible space (LCFS) from the low-carbon, secure, and economic perspectives, which provides powerful tools for the low-carbon operation analyses of IEHGSs. Firstly, a coordinated mechanism of carbon flow and hydrogen flow is developed to excavate the low-carbon operation potential of IEHGSs. Then, based on the distributionally robust chance-constrained approach, the concepts and models of CCE_OR and ECCE_OR are defined and formulated considering uncertainties and hydrogen merits. Furthermore, a region model reformulation method is proposed to reformulate the uncertain and non-convex CCE_OR and ECCE_OR models into the deterministic and mixed-integer linear region models. The geometric properties of CCE_OR and ECCE_OR are both theoretically proven, which are the union set of finite convex and bounded polytopes. The united region solution methodology considering the geometric properties of CCE_OR and ECCE_OR is presented to effectively characterize CCE_OR and ECCE_OR. Finally, the numerical results on two test systems verify the effectiveness and applicability of the proposed methods. Simulation results indicate that the proposed methods can improve the LCFS, characterize visual coupling relationships between LCFS and observation variables, and provide comprehensive low-carbon operation information of operation points.

Synergetic effect of hydrogen supplementation with waste cooking oil biodiesel – An assessment of the emission, combustion and performance parameters of a compression ignition engine

This investigation aims at examine the effects of hydrogen gas at different flow rates in combination with biodiesel made from used cooking oil on the combustion, emissions, and performance parameters of an engine. In order to improve the thermal performance and combustion characteristics of the stationary engine and lower its emissions, hydrogen is injected through the main manifold at varying flow rates ranging from 3 to 9 LPM, and waste cooking oil biodiesel (WCO B20) is injected through the injector as the main fuel. Both of these fuels are used in conjunction with each other. Results of combustion characteristics revealed that the cylinder pressure enhanced by about 7.32 % using 9 LPM hydrogen flow through the main manifold compared to diesel fuel. Similarly, the HRR from the engine using 9 LPM hydrogen flow enhanced by about 9.43 and 13.76 % compared to diesel and WCO B20, respectively. A comparison is made between diesel fuel and with the proposed modified fuel on the engine's performance, which is assessed in terms of BTE and BSFC. For a range of different engine loads, several emission parameters including HC, NOx, CO, CO2, and smoke opacity are monitored and analyzed for the fuel that has been produced. The results showed that the BTE of the engine is higher in the case of WCO B20 with hydrogen fuel in the flow rate of 9 LPM by about 35.38 % at various engine loads in comparison with the other flow rates of hydrogen fuel, WCO B20 blend, and diesel fuel. Similarly, there is a significant decrease in the SFC by about 17.85 % of the fuel using hydrogen fuel at higher flow rates. The CO emissions with WCO B20 biodiesel blend and diesel fuel are higher, whereas there is a substantial reduction in the CO emission about 22.58 % using a higher concentration of hydrogen fuel along with the WCO B20 biodiesel blends. Similarly, the other emissions such as CO2, smoke and HC decrease about 5.38 %, 10.41 % and 5.38 % whereas the NOx formation increases about 7.67 % at peak loads due to a higher rate of combustion.

Research on an Active Hydrogen Maser Digital Circuit Control System Based on FPGA.

A hydrogen maser is a high-precision time measurement instrument with high frequency stability and low frequency drift, which is widely used in satellite navigation, ground time keeping, frequency measurement, and other fields. An active hydrogen maser (AHM) is better than the current space passive hydrogen maser (PHM) in orbit in terms of its frequency stability and drift rate, but it has the disadvantages of large volume and weight. To further reduce the volume and weight of the circuit, this paper demonstrates a digital circuit control system based on a field-programmable gate array (FPGA). It uses digital temperature control, digital detectors, digital down-conversion, digital phase-locked loops, and other digital methods for temperature control, cavity auto-tuning, and crystal phase locking, which improve the integration and flexibility of the circuit system. Meanwhile, a tuning method based on hydrogen flow is proposed, which effectively solves the problem of fluctuations in hydrogen maser resonance frequency with changes in the external environment. Our experimental results show that the designed digital circuit control system meets the requirements of an oven-controlled crystal oscillator (OCXO) loop and a cavity loop. Its frequency stability can reach 2.6×10-13/1 s and 1.4×10-15/10,000 s, which is close to the stability index of ground active hydrogen maser. This scheme has certain practical engineering value, and can be used in the design of hydrogen masers for next-generation space navigation satellites, deep space exploration, and space stations.

Numerical investigation on the influence of geometrical parameters on the temperature distribution in marine hydrogen storage tanks during filling

This paper established a two-dimensional axisymmetric model with a marine high-pressure hydrogen storage tank as the research object. Using numerical simulation, the effects of different aspect ratios, inlet diameters, and inlet pipe lengths on the temperature rise of the hydrogen storage tank during the filling process were studied. As the L/D ratio of the hydrogen storage tank increases, the momentum of the hydrogen gas reaching the bottom of the tank gradually decreases, making it easier to form localized high-temperature regions. For a hydrogen storage tank with an L/D of 6.0, the difference between the maximum and average temperature at the end of filling was 155.85 K. In contrast, the temperature difference of the tank with an L/D of 3.6 was only 32.81 K. In addition, the inlet pipe delivers the hydrogen deep into the tank and reduces the obstructing effect of the existing hydrogen in the tank on the newly filled hydrogen. For smaller L/D hydrogen storage tanks, the inlet pipe may backfire and create a high-temperature zone at the shoulder of the tank. In contrast, for larger L/D hydrogen storage tanks, a suitable length of inlet pipe can deliver the hydrogen deep into the tank. This will enhance the gas flow inside the tank, facilitating heat exchange and avoiding the formation of localized high-temperature areas at the bottom of the tank. However, excessively long inlet pipes can also lead to high-temperature areas on the shoulders. At a specific charge mass flow rate, the lower the inlet diameter, the higher the hydrogen flow rate. The larger flow rate helped promote uniform hydrogen mixing in the tank and made it challenging to form localized high-temperature regions.

Effect of unpaired electron number elements (Al, Cr, Mn) doping in Fe2O3 on ortho to para hydrogen conversion at 77 K

Para hydrogen (p-H2), as a low-energy spin isomer of hydrogen molecule, has an important significance in the storage and transportation of liquid hydrogen. The ortho hydrogen (o-H2) to p-H2 conversion catalyst accelerates the intrinsically slow o-H2 to p-H2 conversion and becomes an essential component of the hydrogen liquefaction process. In this paper, doped Fe2O3 with different hetero elements (X-FO, X = Al, Cr, Mn) are prepared by a simple co-precipitation method to explore the effect of different unpaired electron numbers in doping elements on catalytic performance. It is shown that the disorder in the internal crystal structure of X-FO caused by doping of hetero elements is the main reason for the increased performance of X-FO, as this leads directly to an increase in the internal magnetic disorder. The catalytic performance is enhanced with the increase in the number of unpaired electrons in doping elements. Mn-FO with high unpaired electron number exhibits optimal catalytic performance. When the hydrogen flow rate is 100 mL min−1, p-H2 content is 49.45 % after catalytic conversion at 77 K. In this paper, a simple method is adopted, which has advantages in terms of production process and cost, and provides experimental support for the large-scale production of catalysts.

Experimental exploration of hydrogen fuelled dual fuelled CRDI equipped diesel engine coupled with exhaust gas recirculation using ANN approach

The usage of diesel engines in the automobile and agricultural industries is growing daily. Therefore, this study aims to reduce the rate of exhaust emissions from water-cooled 4-stroke-single cylinder CRDI-equipped diesel engines by using hydrogen along with the exhaust gas recirculation (EGR) technique. The results proved that the dual-fuelled diesel engine enriched with 6 ms of hydrogen flow rate and 10% EGR promotes excellent engine characteristics. However, the reduced NOX emission was observed from 10% EGR application. Compared to pure diesel, the proposed dual fuel combination promotes 56.3%, 33%, 15.38%, 40% and almost 50% reduction in HC, CO, NOX, CO2 and smoke emissions. Similarly, the engine performances, such as brake thermal efficiency (BTE) and brake specific energy consumption (BSEC), have also been improvised. The maximum increment achieved for BTE is 7.6%, and the maximum reduction achieved for BSEC is 8.12%. Besides, the ANN model predicts the engine performance and emissions with a correlation coefficient of 0.964, 0.945, 0.98, 0.807, 0.979, 0.900, and 0.90 for BTE, BSEC, CO, CO2, NOX, HC and smoke respectively. A root mean square error (RMSE) of less than 1 was observed for the ANN prediction model, indicating that both the actual and predicted results agree better.

Experimental Control of a Methanol Catalytic Membrane Reformer

A simple proportional integral (PI) controller with scheduled gain has been developed and implemented in a catalytic membrane reactor (CMR) to obtain pure hydrogen from a methanol steam reforming process. The controller is designed to track the setpoint of the pure hydrogen flow rate in the permeate side of the CMR via the manipulation of the fuel inlet flow rate. Therefore, the controller actuator is the liquid pump that provides the mixture of methanol and water to the reactor. Within the CMR, the catalytic pellets of PdZn/ZnAl2O4/Al2O3 have been used to facilitate the methanol steam-reforming reaction under stoichiometric conditions (S/C = 1), and Pd–Ag metallic membranes have been employed to simultaneously separate the generated hydrogen. The PI controller design is based on a mathematical model constructed using transfer functions acquired from dynamic experiments conducted with the CMR. The controller has been successfully implemented, and experimental validation tests have been carried out at 450 °C and relative pressures of 6, 8, 10, and 12 bar.

Operational and design parameters evaluation to improve hydrogen production using a low-cost alkaline water electrolysis cell in direct combination with a photovoltaic cell

Hydrogen production from renewable sources such as photovoltaic solar energy can contribute to a more sustainable energy scenario worldwide. The present work aimed to evaluate hydrogen production via alkaline water electrolysis by finding the optimal operational conditions with electrodes, alkaline electrolyzers, and solar energy with a photovoltaic panel. Firstly, graphite, stainless steel 304, and Monel 400 electrodes were evaluated using a direct voltage source, resulting in maximum hydrogen flow rates of 4.86, 10.40, and 8.12 mL/min, respectively. Then, hydrogen generation was analyzed with electrolytes of KOH, NaOH, and LiOH in 1-10 mol/L concentrations. The highest hydrogen flow rates were found for KOH electrolytes, attributed to their higher electrical conductivity. Therefore, stainless steel electrodes and KOH electrolyte were evaluated with the photovoltaic panel. The optimized conditions were a KOH concentration of 6.18 mol/L and a solar radiation of 900 W/m2 for a hydrogen production of 71.83 mL/min. The hydrogen purity remained at 98.96 ± 0.10%.

Optimum Load Of a Proton Exchange Membrane Fuel Cells Based on Hydrogen Flow Control

In the future, proton exchange membrane fuel cells system (PEMFCs) hold promises for clean energy. However, there is a problem that causes the degradation in PEMFC system performance namely the voltage drops due to load fluctuations. The voltage drop is caused by the high load power demand. An important factor to improving PEMFCs performance is the availability of sufficient flow of hydrogen. In this paper optimisation of a PEMFCs load based on the hydrogen flow control is presented. In order to validate this project a model of the PEMFCs is simulated. Then verified by experimental testing using a 2 kW of the PEMFCs. The result shows the hydrogen flow control able to reduce the voltage drop of the PEMFCs during load variation and minimise hydrogen consumption.

A prediction of interfacial tension by using molecular dynamics simulation: A study on effects of cushion gas (CO2, N2 and CH4) for Underground Hydrogen Storage

Carbon Dioxide (CO2) emissions from fossil fuel consumption have caused global warming and remain challenging problems for mitigation. Underground Hydrogen Storage (UHS) provides clean fuel and replaces traditional fossil fuels to reduce emissions of CO2. Geological formations such as depleted oil/gas reservoirs, deep saline aquifers and shale formations have been recognized as potential targets to inject and store H2 into the subsurface formations for large-scale implementation of CCS and UHS. However, the presence of H2 with cushion gas at different fractions under different geo-storage conditions, which can influence Hydrogen's flow properties, was not investigated widely. Until now, studies of interfacial properties between water and a mixture of cushion gas (CO2, N2 or CH4) in the presence of H2 are very limited or unavailable data in experiments and simulations. In this study, many predictions by using molecular dynamics simulation were conducted to predict the interfacial tension (γ) for the systems of H2/CO2/H2O, H2/N2/H2O and H2/CH4/H2O at different pressures, temperatures, and fractions of cushion gases A comparison between the predicted γ results from the simulation and previous research were also made. The findings of this study indicated that γ of H2/CO2/H2O, H2/CH4/H2O, and H2/N2/H2O, as a function of pressure, temperature, and fraction of H2, decreased with increasing pressures and temperatures and increased with increasing H2% in the mixture. Additionally, an extending or new γ data in simulation for the CO2/H2/H2O, N2/H2/H2O and CH4/H2/H2O systems from this study were reported and support evaluating the stability and storage capacity of H2 combined with the cushion gas in geological formations. Furthermore, it can contribute to de-risking and proceeding safely and efficiently for the large-scale implementation of Underground Hydrogen Storage.

Dehydrogenation of Mg-Fe-Ni-H based hydrogen storage tank under different operating temperatures and hydrogen flow rates

Effects of setting temperatures (Tset = 310–350 °C) and hydrogen flow rates (H2-FR = 0.2–0.6 standard L/min, SLM) on kinetics and reaction mechanisms during dehydrogenation of Mg-Fe-Ni-H based tank are investigated. Mg2FeH6-Mg2NiH4 composite under 1:1 mol ratio (∼60 g) is packed in a small hydrogen storage tank with a packing volume of ∼96 mL. The experiment with high operating temperature, resulting in the enhanced decomposition rate requires fast H2-FR to reach the best dehydrogenation kinetics. In the case of de/rehydrogenation mechanisms, dehydrogenation under fast H2-FR leads to individual decomposition and reversibility of Mg2FeH6 and Mg2NiH4. The experiment under slow H2-FR hinders the decomposition of Mg2FeH6 and favors the formation of Mg2Fe(1-x)NixH6 via the reaction between Mg2FeH6 and Mg2Ni during dehydrogenation. The reversibility of Mg2Fe(1-x)NixH6 is accomplished by hydrogenation of Mg2Ni + Fe + Mg, benefiting the utilization of unreacted Fe upon cycling.

FCEV 충전 시스템 체크밸브의 수소 유입 극한 온도 조건에 따른 유동 성능 인자 분석

FCEV 충전 시스템 체크밸브의 수소 유입 극한 온도 조건에 따른 유동 성능 인자 분석

Mach number analysis of hydrogen flow in labyrinth passage under high pressure gradient

This work delves into a novel concept that harnesses the potential of labyrinth passages for hydrogen decompression, offering the advantage of dispersing the mainstream into multiple channels, thereby reducing hydrogen mass and energy. Compared to traditional hydrogen decompression devices, this approach demonstrates adaptability to high pressure gradients and boasts a simple structure. For the industry, the perennial challenge has been controlling energy loss and enhancing aerodynamic performance during hydrogen decompression. Hence, our primary focus lies in addressing the key challenges related to labyrinth passages in this field. Within this study, a detailed design of the labyrinth passage is proposed, and the correlation between Mach number and energy loss is studied. Additionally, an in-depth study is conducted on the effects of throttling parameters on Mach number in the labyrinth passage, aiming to achieve an optimized design. The results reveal a linear correlation between Mach number and energy loss. Furthermore, the research highlights that different throttling parameters have distinct impacts on energy loss. By utilizing the maximum average Mach number (Ma‾max) as a metric to evaluate different designs, we have determined the range (Ŕ) of factor values for series number (ni/n0), widths (wi/w0), expansion coefficients (ri/r0), interstage heights (hi/h0) and depths (di/d0) to be 0.687, 0.482, 0.228, 0.075, and 0.036, respectively. The range (Ŕ) directly signifies the influence that each factor has on the Mach number. As a result, it has been deduced that the parameter effects on controlling energy loss follow a descending order: series number (ni/n0), widths (wi/w0), expansion coefficients (ri/r0), interstage heights (hi/h0) and depths (di/d0). Moreover, for each factor, the preferred level ranking consistently remains as Ⅳ, Ⅲ, Ⅱ, and Ⅰ. Therefore, considering the need to control manufacturing costs, it is recommended to opt for a larger series number, expansion coefficient and a smaller width and interstage height.