One-dimensional Calculations Research Articles

A cooled turbine blade design and optimization method considering the cooling structure influence

This study introduces a multidisciplinary design methodology tailored for enhancing the performance of cooled turbine blades by amalgamating thermal and aerodynamic calculation modules. The approach is unique in terms of its integration of a multi-objective optimization platform, aimed at refining aerodynamic performance and gauging the heat transfer capabilities during the preliminary aerodynamic design phase. To accomplish this objective, a one-dimensional pipe-network calculation tool was incorporated into the thermal module to quickly evaluate the heat transfer performance of the blades under different conditions. This tool also provides more realistic film hole inlet boundary conditions essential for three-dimensional aerodynamic calculations. Implementing this platform in optimizing a high-pressure turbine blade revealed a Pareto-optimal front, comprising −η1 and η2 (representing optimization objectives for aerodynamic and heat transfer performance, respectively), showcasing a constrained relationship. Upon scrutinizing three optimization cases against the prototype, optimization case 1 demonstrates the most significant enhancements in aerodynamic performance, showing a 0.2015% improvement in aerodynamic efficiency relative to the prototype. Conversely, optimization case 3 displays a comparatively modest augmentation in aerodynamic performance but excels notably in heat transfer performance, showcasing a 7.61% reduction in the maximum temperature of the blade surface compared to the prototype. Through adept optimization strategies and meticulous variable selection, we maintained a relatively stable mainstream mass flow across the optimization cases (less than 0.05% variation). These findings underscore the efficacy of our multidisciplinary design approach for cooled turbine blades, promising efficiency improvements in current design practices and potential reductions in project duration.

Flux and estimated spectra from a low-intensity laser-driven X-ray source

Abstract Laser-driven X-rays as probes for high-energy-density physics spans an extremely large parameter space with laser intensities varying by 8 orders of magnitude. We have built and characterized a soft X-ray source driven by a modest intensity laser of 4 × 1013 W/cm2. Emitted X-rays were measured by diamond radiation detectors and a filtered soft X-ray camera. A material-dependence study on Al, Ti, stainless steel alloy 304, Fe, Cu and Sn targets indicated 5-μm-thick Cu foils produced the highest X-ray yield. X-ray emission in the laser direction and emission in the reverse direction depend strongly on the foil material and the thickness due to the opacity and hydrodynamic disassembly time. The time-varying X-ray signals are used to measure the material thinning rate and is found to be ∼1.5 μm/ns for the materials tested implying thermal temperature around 0.6 eV. The X-ray spectra from Cu targets peaks at ∼2 keV with no emission >4 keV and was estimated using images with eight different foil filters. One-dimensional hydrodynamic and spectral calculations using HELIOS-CR provide qualitative agreement with experimental results. Modest intensity lasers can be an excellent source for nanosecond bursts of soft X-rays.

Introduction to the FDTD method and its application to implicit locally one-dimensional calculations

Introduction to the FDTD method and its application to implicit locally one-dimensional calculations

Preliminary design and analysis of an afterburner module

In this study, design calculations and calculations of afterburner used in jet engines are presented by evaluating the results of analytical and computational analysis. Afterburner inlet values of 1050 K temperature, 300 kPa pressure and 3.6 kg/s mass flow rate are taken as the design conditions. Maximum length and diameter are 500 mm and 200 mm, respectively, for the sections to be designed as length constraints within the scope of the conceptual design. The two-ring vee-gutter has 1.33 cm in diameter and 4.25 cm high. Jet A fuel is assumed to be injected into the core flow (90 degrees) from the spray bars. The spray is mounted in line with the vee-gutter to optimize the mixing of the flow. Analyses are performed for 4 cm between the spray bar and the vee-gutter. For the study, the GE J79 engine was examined from the literature and taken as a basis for the aerodynamic transition section design. Within the scope of TEKNOFEST 2023 Jet Engine Design Competition, a preliminary design of an afterburner module that can produce 700 pounds of thrust and has a life capacity of 25 hours should be realized in line with the design requirements and constraints. In the light of geometric constraints, one-dimensional combustion calculations of the module are made, and the parts are modelled using the relevant SolidWorks CAD program and these modelled parts are then transferred to ANSYS™ environment and the results and analyses are verified. The afterburner module flow analysis software program ANSYS™ is used to analyse the afterburner operation in both cold operating ranges (i.e. without combustion) using compressible, viscous and standard k-epsilon turbulence model. As a result, the effect of afterburner length on combustion performance is found to be significant. As a result of the calculations, afterburner length is found as 28.14 cm. It is found that the combustion efficiency is 81.5% and the temperature can be increased from 1050 K to 2044 K. The total pressure loss is 14.96% as pressure drop due to the geometric parameters and heat addition. The blockage ratio calculated due to the use of vee-gutter geometry is the most important parameter in the pressure drop. It is found that the jet engine producing 670 lbs (2981 N) of thrust when the afterburner is not working whereas it can provide a significant amount of power increment at the expense of a 50% increase in specific fuel consumption when the afterburner is active as well as providing a 738 lbs (3238 N) with a 10.1% thrust increase. The reason of the enhancement is mainly coming from the mixing effect of the vee-gutter on the flow structure.

Research and Optimization on the Exhaust Flow Characteristics Based on Energy-Splitting Method of the Low-Speed Marine Diesel Engine

Abstract In this study, an optimization scheme for exhaust flow characteristics based on the energy-splitting method is proposed. The low-speed marine diesel engine adopts the exhaust energy-splitting method during the exhaust process. Based on this, a one-dimensional calculation model, a three-dimensional calculation model, and a three-dimensional model of the gas collection box are established. After splitting, the vortex structure in the same phase of the gas collection box has a larger scale, higher flowrate, more significant entropy increase, and more severe turbulence dissipation. The length and diameter of the high-grade gas collection box are optimized. The results show that after optimization, the flow energy dissipation brought by the vortex structure is reduced, and the outlet pressure and flow velocity of the gas collection box are increased.

Numerical modelling and analysis of current induced stresses in REBCO coil stacks

This study reports the effect of the radial, axial, and hoop electromagnetic stresses caused by the large current density and the self-field (screening current-induced magnetic field) on REBCO superconducting coil stacks. A two-dimensional numerical model is used to study the stress distribution of a superconducting coil stack under current. The electromagnetically homogenized coil stack is assumed to be composed of four equally spaced coils with rectangular cross-section. Initially, the verification of the model is done by comparing the analytical calculations (which were in good agreement) of stress distributions of a superconducting slab exposed to a variable magnetic field and in a superconducting strip exposed to a variable current. Then, the two-dimensional model is used to obtain the components of stress that occurred in the coil stack under sinusoidal varying currents. The stress component distributions are calculated at different time intervals, currents, frequencies, and coil distances. Besides, one-dimensional stress distributions are plotted to show how the stress distributions change while the current increases. The upper and lower coils have much higher magnetic stress than the inner coils. Results obtained from the one-dimensional stress distribution calculations show that the stress occurring in the radial direction is lower than the stress in the z-direction in the coil stack. The stress distributions do not show a significant change as the frequency of the applied current changes. The stresses in both the radial and axial directions decrease as the distance between coils increases. All results are presented, and the possible reasons are explained.

A 3D modeling method of layered acoustic material structures with finite dimensions

Modeling of layered acoustic structures to predict the sound absorption characteristics of complex materials is a widely used method in room acoustic practice. Commonly used modeling techniques-such as the transfer matrix method-typically assume locally reacting surfaces of infinite lateral dimensions and provide one-dimensional calculations only, offering limited accuracy, especially for resonant absorbers with finite dimensions. We present the direct, analytical modeling of sound propagation in extendedly reacting layered materials of finite dimensions allowing the estimation of the surface impedance or admittance distribution of layered structures, from which sound absorption properties can be calculated. The theoretical results are validated by measurements, performed on a small-sized resonant panel absorber. We present the implementation of the method in the soundy.ai application.

Calibration of a Near-Wall Differential Reynolds Stress Model Using the Updated Direct Numerical Simulation Data and Its Assessment

In the article, a differential Reynolds stress model is recalibrated using turbulent channel flow direct numerical simulation data in the range of friction Reynolds numbers 550–5200. The calibration aims to produce a RANS sublayer model for use within the hybrid RANS/LES framework. The model is designed to capture the average field of a thin near-wall part of a boundary layer as accurately as possible. An a posteriori procedure is employed in which one-dimensional channel flow calculations are performed for all variations of the model coefficients at each stage of the optimization procedure. The coefficients are initialized with their original values and then optimized by minimizing the appropriately chosen norm. An improved representation of the mean velocity profile and peak Reynolds stress values is demonstrated. Both models—baseline and recalibrated—are implemented in an in-house CFD code, and several simulations, including a channel flow, a flat plate boundary layer and a boundary layer separation from a rounded step, are performed. The latter benchmark flow is also simulated in hybrid RANS/LES mode. The updated model is compared to the original one, demonstrating improvements over the baseline model in the cases it was designed for.

METHOD OF CALCULATING THE UNSTATIONARY TEMPERATURE FIELD PARTS OF THE SPHERICAL FORM OF THE STRUCTURE FLIGHT APPARATUS OF UNMANNED AVIATION COMPLEXES

The design of unmanned aircraft vehicles during operation is exposed to significant temperature effects, which causes changes in the dielectric characteristics of radio technical elements and can lead to failures of on-board radio electronic equipment, as a result of which the task of determining the amount of temperature change in the compartments where the radio electronic equipment is located is performed. At the same time, some external elements of the aircraft vehicle can have complex structures with shapes close to spherical and different thicknesses in each cross-sectional structure.
 There is a need to develop a method for calculating the non-stationary temperature field with the purpose of finding out the real conditions in which all the elements of the aircraft structure work, which would help to determine how the temperature of the structure changes during any flight. At the same time, it is necessary to take into account the three dimensions of temperature gradients on spherical parts of structures of various shapes, namely nose part, rounded wing and others. In them, as a rule, each cross-section of the wall has its own thickness and, according to each cross-section, the temperature distribution along the thickness of the wall will correspond, that is, it is necessary to ensure the redistribution of temperature along the structural element, the calculation of which month. In addition, it is necessary to note that the wall of the aircraft can be multi-layered and the properties of its material can change along with the change in temperature. Considering the fact that it is impossible to take into account all the listed features by analytical methods, when choosing a calculation method, it will be advisable to stop at numerical methods.
 One of the most well-known numerical methods is the finite difference method with an implicit calculation scheme, which has an indisputable advantage for modeling - absolute stability with sufficient changes in time and coordinate steps. We will use the level of thermal conductivity in spherical coordinates in order to increase the accuracy of the calculation, for which solution, after finding out the boundary conditions, we will perform a one-dimensional calculation of the temperature by thickness in each mesh section of the structure, and also perform a calculation of the two-dimensional "heat flow" along the solid between the points, that are located on the same thickness, but have a temperature difference. Thus, when calculating the temperature field, the sphericity and multi-lay redness of the structural elements is taken into account, and the property of the material of the aircraft structure changes depending on the temperature.

Data-driven simulation of ammonia combustion using neural ordinary differential equations (NODE)

The direct use of detailed chemical kinetics in combustion simulations is limited by the extremely high computational costs. Recently, Owoyele and Pal (Energy and AI, 2022), proposed the neural ordinary differential equations (NODE) method to accelerate calculations of chemical kinetics and proved its effectiveness in zero-dimensional calculations of hydrogen combustion considering 9 species and 21 reactions. However, its performance for more realistic high-dimensional calculations and more complex kinetic systems remains unexplored. Therefore, this study further applies the method for more complex chemical kinetics of ammonia combustion, especially with optimizations in the data sampling, model training strategies, and model application methods that remedy the problems of versatility and application to more practical simulations. The newly developed NODE models are comprehensively validated in the zero-dimensional calculations of ammonia auto-ignition, one-dimensional calculations of laminar freely-propagating ammonia-premixed flames, and two-dimensional direct numerical simulation (DNS) of ammonia-premixed flames in a temporally evolving jet. Present NODE models focus on seven chemical species, namely NH3, O2, H2, OH, H2O, N2, and NO, and the results show that, compared with the results obtained by using detailed chemical kinetics, this method is able to reduce the computational costs of the zero-dimensional auto-ignition reaction to 1/24 while reproducing the ignition delay time for a wide range of initial temperatures and equivalence ratios with relatively good accuracy. Additionally, the method is able to reduce the computational costs of the one-dimensional freely propagating flame and two-dimensional jet flame to 1/4 and 1/38 respectively, while acceptable reproduction of the laminar flame speed and temporal evolution of the gas temperature and mass fractions of the interested species can be achieved.

STAJe−: A Supersonic Flight Program STAJe− 1 Payload Design and System Study

The STAJe− flight program is the latest implementation of a university-based supersonic and hypersonic flight-test program. In the first flight, which is the subject of this study, the focus is on evaluating the suitability of commercial off-the-shelf electronic hardware, additively manufactured internal payload structures, and a long-range communications technique in the challenging environment presented by flight at high supersonic Mach numbers. These items can significantly reduce the cost of a flight experiment, and thus lower the threshold for flight experimentation. The scientific objectives of this flight are to collect pressure and temperature data on the whole trajectory to compare to numerical models, to optically measure the temperature of composite fins mounted on the payload, and to eject the flight module from the rocket assembly and track its location for subsequent recovery. Design calculations for the tracking system are presented alongside experimental results from ground tests demonstrating the suitability of the system. Furthermore, a one-dimensional calculation of the external wall temperatures over the trajectory is presented, which shows that internal systems are sufficiently protected from the harsh environment. Although the materials are shown to be appropriate for the flight, a layer of cork will be added to parts of the payload to further reduce the chance of structural failure. In addition, it is shown that a pneumatic ejection system is suited to overcoming the drag forces on the front of the rocket to initiate separation.

Study and application of pollutant diffusion based on SPH method

In this paper, the meshless smooth particle hydrodynamics (SPH) method is used to simulate the transport process of pollutants in the environment by solving the convection-diffusion equation of pollutants under the Lagrangian framework. This method avoids various numerical problems caused by mesh distortion or mesh movement and the calculation of the derivative of the kernel function when approximating the second derivative kernel. In order to reduce the original virtual particle method of SPH to solve the boundary problem due to the large amount of particle searches will increase the amount of redundant calculation and other factors, selected with the finite difference method to solve the boundary. To verify the proposed Lagrangian particle model, numerical experiments were carried out. The one-dimensional calculation results are compared in detail with the results of different schemes in the finite difference method, and the L2, L∞ and relative errors are analyzed. The simulation results show that the SPH-based model requires fewer particles. In addition, the model is numerically analyzed under the condition of ensuring accuracy. The numerical solution is in good agreement with the analytical solution. The research results of this paper can provide a new solution and idea for environmental pollution early warning.

One-dimensional longitudinal space charge calculation based on integrated green function approach

For fast longitudinal electron beam dynamics study or optimization in an x-ray free electron laser (FEL) linear accelerator, the one-dimensional longitudinal space charge (1D LSC) impedance, assuming a round cylinder beam with uniform transverse distribution is extensively used in both analytical analysis and numerical simulation. In this paper, instead of employing the impedance model in the frequency domain, we directly calculate the longitudinal electric field by convolving the longitudinal beam density with the slice green function, i.e., the longitudinal electric field generated by a slice beam. For high-energy electron beam, the slice green function rapidly diminishes to zero within a distance significantly smaller than the bunch length. In order to resolve the sharp variation, we report on a fast and high-precision method by applying the integrated green function (IGF) approach to compute the 1D LSC field numerically with few grid points, therefore, providing us with an alternative approach to the impedance model.

Analysis of loss of cooling accidents in the spent fuel pools using system thermal hydraulics and computational fluid dynamic codes

The interest in the safety of on-site storage of Spent Fuel Assemblies (SFAs) has been increased after the accident on 11 March 2011, in Fukushima Daiichi Nuclear Power Plant. It is important to analyse the behaviour of not only integral effects in spent fuel pools, but also the local effects during heat removal from the SFAs. Usually, for the integral analysis the one-dimensional system computer codes were used. These codes allow to analyse whole pools and cover long time, with a relatively low cost of computational resources. The Computational Fluid Dynamic (CFD) codes could perform very detailed analysis, but this requires large computational resources. The strong side of CFD codes is the possibility to assess local effects which could occur.In the current work the analysis of heat transfer from the SFAs, placed in special baskets was performed using ANSYS FLUENT 17.2 and RELAP5 codes. The models of single basket with SFAs were developed using both codes. The comparison of calculations allowed to evaluate capabilities of both codes. It is shown, that using one-dimensional system thermal hydraulics code developed model allows to describe coolant mixing inside basket sections and received results fits well with CFD code calculation results. Based on gained experience, the loss of cooling accident in the spent fuel pools of Ignalina NPP was analysed using the model, developed by employing RELAP5 (one-dimensional system thermal hydraulics) code. The calculation results were used for safety evaluation of Ignalina NPP facilities.

Zadacha o neideal'nom teplovom kontakte

We consider the problem of determining the thermomechanical state of a fuel element in a nuclear reactor. A finite element algorithm for solving the thermal problem together with the problem of mechanical contact is described, and a model one-dimensional problem is studied to clarify the main features and a numerical algorithm for solving it. The leading term of the asymptotic expansion of the solution of this problem and a difference scheme for its solution, including iterative methods, are constructed. A cycle of test calculations is carried out to confirm the theoretical estimates. The comparison of calculations for real problems with theoretical predictions shows that the algorithm for solving a multidimensional nonlinear problem qualitatively corresponds to the behavior of one-dimensional calculations.

The kinetic Hamiltonian with position-dependent mass

In the present paper we examine in a systematic way the most relevant orderings of pure kinetic Hamiltonians for five different position-dependent mass (PDM) profiles: soliton-like, reciprocal quadratic and biquadratic, exponential and parabolic. As a result of the non-commutativity between momentum and position operators, a diversity of effective potentials is generated. We analyze the whole set and find unexpected coincidences as well as discrepancies among them. We obtain analytically the full-spectrum of energies and solutions in the twenty-five cases considered. It is shown how the simple ordinary constant-mass solutions are transformed into a variety of complex combinations of transcendental functions and arguments. We find that particles with a non-uniform mass density can present discrete energy spectra as well as continuous ones which can be bounded or not. These results are consistent with the fact that although the external potential is zero, PDM eigenfunctions are not actual free states but a sort of effective waves in a solid-state sample. This is precisely the origin of the position-dependent mass. In all the events we obtain exact complete spectral expressions. Our methodological procedure thus puts a wide diversity of Hamiltonian seeds on an equal footing in order to be compared. This allows choosing the better arrangement to model a specific solid or heterostructure once the spectrum of a given material is experimentally available. Finally, we perform a one-dimensional model calculation of a double heterostructure with a parabolic PDM particle in the interface region. Our study is also indicated for applications inside material structures with the addition of external potentials.

Coupling multi-fidelity xRAGE with machine learning for graded inner shell design optimization in double shell capsules

Bayesian optimization has shown promise for the design optimization of inertial confinement fusion targets. Specifically, in Vazirani et al. [Phys. Plasmas 28, 122709 (2021)], optimal designs for double shell capsules with graded inner shells were identified using one-dimensional xRAGE simulation yield calculations. While the machine learning models were able to accurately learn and predict one-dimensional simulation target performance, using simulations with higher fidelity would improve design optimization and better match with the expected experimental performance. However, higher fidelity physics modeling, i.e., two-dimensional xRAGE simulations, requires significantly larger computational time/cost, usually at least an order of magnitude, in comparison with one-dimensional simulations. This study presents a multi-fidelity Bayesian optimization, in which the machine learning model leverages low-fidelity (one-dimensional xRAGE) and high-fidelity (two-dimensional xRAGE) simulations to more accurately predict “pre-shot” target performance with respect to the expected experimental performance. By building a multi-fidelity Bayesian optimization framework coupled with xRAGE, the low-fidelity and high-fidelity simulations are able to inform one another, such that we have: (1) improved physics modeling in comparison with using low-fidelity simulations alone, (2) reduced computational time/cost in comparison with using high-fidelity simulations alone, and (3) more confidence in the expected performance of optimized targets during real-world experiments. In the future, we plan to use this robust multi-fidelity Bayesian optimization methodology to expedite the design of graded inner shells further and eventually full capsules as a part of the current double shell campaign at the National Ignition Facility.

Detonation behaviors in stoichiometric CH4-H2-O2 under different initial pressures conditions

In this study, the detonation behaviors (i.e., detonation limit, detonation overpressure, mean velocity, velocity deficit, and cell sizes) of CH4-H2-O2 mixtures in a small-bore tube at different initial pressures (ranging from 6 kPa to 300 kPa) were investigated. Mixtures with different proportions of H2 in the total fuel (0, 10%, 20%, 25%, 30%, 50%, 75%, 100%) were tested. Steady one-dimensional ZND calculations are used to obtain detonation parameters such as induction zone length, stability parameters, and cell sizes. Results indicate that increasing the hydrogen fraction decreases the detonation limit. The addition of hydrogen can reduce velocity deficit, especially near the detonation limit pressure. Velocity deficits were found to be within 3.5% when the initial pressure higher than 50 kPa. Higher initial pressure may result in the mean detonation velocity surpassing the theoretical CJ velocity. The detonation overpressure increases with the initial pressure and decreases with hydrogen fraction. The influence of initial pressure on cell sizes weakens as hydrogen fraction increases. Besides, the induction zone length and stability parameter decrease as hydrogen fraction increases Notably, the stability parameter of mixtures with different hydrogen fractions shows different trends as the initial pressure increases. A linear relationship between actual measured cell sizes and induction zone length is given as λ = 24.56Δi for hydrogen-methane-oxygen mixtures with the initial pressure range of 100 to 300 kPa. If experimental measurement error is considered, the prediction of the Ng model has reasonable accuracy.

Study on the ignition characteristics of CH4/H2/air mixtures in a micro flow reactor with a controlled temperature profile

The ignition characteristics of stoichiometric CH4/H2/air mixtures with different H2 dilution ratios were studied by using a micro flow reactor (MFR) with a controlled temperature profile. The weak flame positions of the mixtures were determined by the luminosity of CH∗, and the ignition temperatures (defined as the corresponding wall temperatures) were obtained. The ignition temperature of the mixture is smoothly decreased with a small amount of H2 addition, while the decrease of the ignition temperature is more rapid with increasing H2 dilution. One-dimensional computation with a detailed reaction mechanism was also conducted to study the ignition characteristics of the CH4/H2/air mixtures. The computational ignition temperature which is defined as the wall temperature at the peak of the heat release rate (HRR) peak is also obtained. Both the experimental and computational results show that the weak flame shifts to the lower temperature region with an increase of the H2 mole fraction. And the non-linear decrease of the ignition temperature of the CH4/H2/air weak flame versus increasing H2 dilution was also well reproduced by the numerical computation. The flame structures, primary exothermic and endothermic reactions of the CH4/H2/air weak flames were studied in detail. The importance of H and OH in the ignition process of the mixtures was analyzed, and the kinetic effects of H2 on the ignition of the mixture in the intermediate-temperature region (1000–1200 K) and high-temperature region (1200–1300 K) were elucidated. The analysis of the computational results reveals that the OH production routes in the intermediate-temperature region are substantially changed with different H2 dilutions, while the OH production routes at the peak of the heat release rate are not obviously influenced. In the end, the primary mechanism for the non-linear effects of H2 addition on the ignition temperatures of the CH4/H2 mixtures was clarified.

Distributed heat release effects on entropy generation by premixed, laminar flames

This article studies the generation of entropy disturbances by laminar premixed flames. The total entropy generation equals the integrated ratio of the local heat release rate and the local temperature, namely, [Formula: see text]. Due to this path dependency, evaluating this integral requires an understanding of how the heat release is distributed in the temperature space. Several studies evaluate the local entropy generation as [Formula: see text], where [Formula: see text] refers to the burned gas temperature, implicitly assuming all the heat release occurs at [Formula: see text]. Such an approximation is motivated by the high activation energy nature of combustion chemistry. This work evaluates this assumption by comparing it to results from one-dimensional premixed flame calculations for hydrogen, methane, and propane-air flames over a range of pressures, equivalence ratios, and preheat temperatures, quantified via the ratio [Formula: see text]. We show that this assumption is quite reasonable for methane and propane-air flames (with errors ranging from 5% to 25%) but deviates significantly from the exact results for hydrogen flames (where errors can be as high as 50%). In general, the peak heat release moves to lower temperatures as preheat temperature is increased. Noting that the temperature sensitivity of heat release is directly related to the activation energy, we use Law's approach to extract global activation energies and show that the deviations of [Formula: see text] from unity can be approximately correlated with [Formula: see text]. Finally, we show that significant improvements in entropy generation calculations can be obtained by estimating [Formula: see text] using [Formula: see text], where [Formula: see text] is the temperature at which the reaction rate peaks. This estimation leads to predictions of ∼5% within the exact value for the hydrocarbon cases but can still be in significant error for hydrogen at certain conditions.