Isentropic Assumption Research Articles

Investigating the laminar burning velocity of NH3/H2/air using the constant volume method: Experimental and numerical analysis

The fundamental combustion field of ammonia-hydrogen fuel is being extensively researched. However, studies on the laminar burning velocity (LBV) under high pressure with varying hydrogen concentration conditions are relatively scarce. This study innovatively used the constant volume method (CVM) to measure LBV of ammonia-hydrogen fuels with various hydrogen concentrations XH2 = 15%–30%, initial temperatures Ti = 298–428 K, initial pressures Pi = 1–3 bar, and equivalence ratios ϕ = 0.8–1.4. The LBV of the fuel mixture up to the temperature and pressure of 540 K and 7 bar under isentropic adiabatic assumption was determined with the CVM method. The results illustrate that the enhancing effect of hydrogen concentration on LBV is suppressed under high pressures, supporting the argument that the equivalence ratio associated with the maximum LBV is solely determined by the initial fuel composition. Chemical kinetics simulations were also analyzed including flame structure, sensitivity analysis, and reaction pathways. It indicated that the elementary reaction H + O2<=>O + OH predominantly governs the LBV of ammonia-hydrogen. An increase in hydrogen concentration intensifies this process by boosting the concentration of free radical hydrogen, albeit with a concomitant rise in NO emissions due to nitrogen-containing radical oxidation. Conversely, an increase in initial pressure diminishes NO emissions by strengthening the pathway from NO to NNH. The findings of this study enhance the LBV database of ammonia-hydrogen fuel at high pressures and high temperatures, and can further act as a reference for other experiments.

Probabilistic assessments of running ductile fractures in dense-phase and supercritical CO2 pipelines

Running ductile fracture (RDF) is a severe failure mode of high-pressure pipelines. Dense-phase and supercritical CO2 pipelines are particularly susceptible to RDF due to the unique characteristics of the depressurization process resulting from a fracture of the pipeline. The present study carries out probabilistic analyses of RDF in dense-phase and supercritical CO2 pipelines. The well-known Battelle two-curve method is employed to establish the limit state function for RDF by comparing the arrest pressure with the saturation pressure. The arrest pressure is computed using the Battelle through-wall crack model with the adjustment recently proposed in the literature. The saturation pressure is computed based on the one-dimensional isentropic decompression assumption and a rigorous equation of state. The first-order reliability method is employed to evaluate the probabilities of RDF in hypothetical CO2 pipelines designed per DVN-RP-F104 with representative pipe attributes and initial operating conditions by considering uncertainties in the relevant pipe geometric and material properties. The analysis results indicate that the probability of RDF can vary by several orders of magnitude depending on the pipe attributes and initial operating conditions. Furthermore, the results shed light on the key uncertainties associated with the pipe geometric and material properties that influence the probability of RDF.

Regenerative Cooling Comparison of LOX/LCH4 and LOX/LC3H8 Rocket Engines Using the One-Dimensional Regenerative Cooling Modelling Tool ODREC

Due to the extreme temperatures inside the combustion chambers of liquid propellant rocket engines, the walls of the combustion chamber and the nozzle are cooled by either the fuel or the oxidizer in what is known as regenerative cooling. This study presents an indigenous computational tool developed for the analysis of heat transfer in regenerative cooling of such rocket engines. The developed tool incorporates a one-dimensional (1-D) combustion analysis to calculate the thermophysical properties of the combustion gas. Basic engine properties were calculated and used to generate a thrust chamber profile based on a bell-shaped nozzle. The hot gas side was analyzed using 1-D isentropic flow assumptions, along with heat transfer correlations. The coolant side was evaluated using the hydraulic analysis in the axial direction and the heat transfer analysis in the radial direction. Thermophysical properties and the phase of the coolant were determined using the given property tables and the instantaneous state of the coolant. This flexible and computationally less demanding tool was used to analyze two small-scale engines utilizing liquid hydrocarbon fuels, which are used in modern rocket propulsion. The wall cooling analyses of a liquid oxygen (LOX)/liquid methane (LCH4) engine and a liquid oxygen (LOX)/liquid propane (LC3H8) engine are presented. Fuel and oxidizer were used separately as coolants for both engines, and both of them experienced phase change. Results reveal the advantage of the high mass flow rate of the oxidizer in cooling performance. In addition, the results of this study show that the cooling of the LOX/LC3H8 engine is somewhat more challenging compared to the LOX/LCH4 engine.

An improved artificial compressibility method for aeroacoustics at low Mach numbers

This work presents an improved artificial compressibility method that enables correct sound propagation behaviour in low Mach number flows. As an extension of incompressible approaches, it offers the advantage of low computational costs since compressible flow equations are simplified under the isentropic assumption, and the coupling of flow and sound is preserved. The non-uniform speed of sound is considered in this method, and eigenvalue analysis of the modified governing equations reveals that the propagation speed of pseudo waves restores to that of physical acoustic waves. The effect of Mach number on the dissipation and dispersion error is then studied using a two-dimentional monopole example with uniform background flow. The results suggest that the proposed method can provide a satisfactory prediction of sound propagation when the Mach number is below 0.3. Lastly, a direct noise computation of the aerofoil trailing-edge noise problem is performed to assess its capability to deal with the interaction between flow and sound. It shows that the present method can well capture the multiple-tone phenomenon.

Theoretical study of elastic effect of a cylindrical pipe wall on ultrasonic flow measurement

This paper addresses wave dynamics confined by an elastic fluid-filled pipeline with a uniform moving flow. The measurement deviation of an ultrasonic flow meter has been comprehensively analyzed with the flow profile ranging 0 m/s to 10 m/s. Governing equations of wave propagation are deduced based on isentropic process assumption in elastic solid and viscous fluid. Numerical analysis shows that acoustic modes in the elastic pipeline are different from those in a rigid-wall and a rod pipe. The wall thickness has obvious influence on the number of acoustic modes and phase velocity. Measurement deviations of elastic-wall pipeline are greatly different from those of rigid-wall pipeline. The wall thickness, wall material and acoustic frequency greatly affect the measurement deviation of each acoustic mode, showing that acoustic mode should be carefully selected in the implementation of an ultrasonic flow meter. Experimental validations are conducted to show the reasonability of theoretical analysis.

Third-order accurate 13-moment equations for non-continuum transport phenomenon

The derivation of analytical equations of non-continuum macroscopic transport phenomena is underpinned by approximate descriptions of the particle distribution function and is required due to the inability of the Navier–Stokes equations to describe flows at high Knudsen number (Kn ∼ 1). In this paper, we present a compact representation of the second-order correction to the Maxwellian distribution function and 13-moment transport equations that contain fewer terms compared to available moment-based representations. The intrinsic inviscid and isentropic assumptions of the second-order accurate distribution function are then relaxed to present a third-order accurate representation of the distribution function, using which corresponding third-order accurate moment transport equations are derived. Validation studies performed for Grad’s second problem and the force-driven plane Poiseuille flow problem at non-zero Knudsen numbers for Maxwell molecules highlight an improvement over results obtained by using the Navier–Stokes equations and Grad’s 13-moment (G13) equations. To establish the ability of the proposed equations to accurately capture the bulk behavior of the fluid, the results of Grad’s second problem have been validated against the analytical solution of the Boltzmann equation. For the planar Poiseuille flow problem, validations against the direct simulation Monte Carlo method data reveal that, in contrast to G13 equations, the proposed equations are capable of accurately capturing the Knudsen boundary layer.

Free-boundary plasma equilibria with toroidal plasma flows

Magnetohydrodynamic equilibrium schemes with toroidal plasma flows and scrape-off layer are developed for the ‘divertor-type’ and ‘limiter-type’ free boundaries in the tokamak cylindrical coordinate. With a toroidal plasma flow, the flux functions are considerably different under the isentropic and isothermal assumptions. The effects of the toroidal flow on the magnetic axis shift are investigated. In a high beta plasma, the magnetic shifts due to the toroidal flow are almost the same for both the isentropic and isothermal cases and are about 0.04a 0 (a 0 is the minor radius) for M 0 = 0.2 (the toroidal Alfvén Mach number on the magnetic axis). In addition, the X-point is slightly shifted upward by 0.0125a 0. But the magnetic axis and the X-point shift due to the toroidal flow may be neglected because M 0 is usually less than 0.05 in a real tokamak. The effects of the toroidal flow on the plasma parameters are also investigated. The high toroidal flow shifts the plasma outward due to the centrifugal effect. Temperature profiles are noticeable different because the plasma temperature is a flux function in the isothermal case.

Effect of wall heat transfer on the dynamics of premixed spherical expanding flames

Premixed laminar flame speed determination is a crucial point since its values are used for the sizing of every combustion systems. In order to measure this parameter, an isochoric combustion method can be used. It consists in measuring the pressure (and possibly other parameters) for a spherical expanding flame. This method allows to get flame speed data for a large scope of important pressures and temperatures supposing an isentropic compression. However, the entirety of the flame propagation process cannot be used to compute the flame speed as heat losses will start to appear as the flame come close the wall, making the isentropic compression assumption invalid. In order to precisely determine when significative heat losses occur, a criterion based on the evolution of the flame preheat zone thickness is described in this paper. The evaluation of this new method is performed using Direct Numerical Simulations for different mixtures (methane with various diluents) at different equivalence ratios and thermodynamic conditions. Finally, the criterion is compared to already existing methods, showing a relatively good accuracy to describe wall heat losses effect on the flame dynamics at high pressure.

Modeling of micro-channel critical flow with inlet sub-cooling: Metastable liquid and nucleation

Critical flows are relevant multiphase phenomena in many applications or scenarios for chemical processes. The paper aims to propose a reliable two-fluid model to accurately simulate the micro-channel critical flow. The fluid density of the metastable liquid is determined using an isentropic transformation assumption. The onset of flashing is evaluated by solving conservation equations coupled with a nucleation model. The available constitutive relations (interfacial force and interfacial heat transfer) are compared and evaluated depending on the analysis of the transfer process in two-phase flow regions to seek reasonable constitutive relations. The paper compares the proposed model and separated flow models using available constitutive relations, especially for the pressure profile. The proposed model shows superior performance in critical flow simulations. To further advance the understanding of the critical flow, the fluid flow and transport phenomena in a micro-channel are studied intensively, especially for the cooling of micro-channels.

Thermal Structure Strength Analysis of Nozzle of Solid Rocket Motor with the Coupled Algorithm

In order to achieve the thermal structural integrity analysis of the solid rocket motor nozzle accurately and efficiently, the multifield (flow-thermal-mechanical) coupled numerical investigation was carried out based on the mesh-based parallel code coupled interface. The numerical simulation process and finite element model of the coupled algorithm and engineering algorithm were obtained, while the physical model was simplified appropriately. The coupled interface parameters, internal flow field, temperature field, and stress field of the coupled algorithm were compared with the engineering algorithm results, and the effectiveness and accuracy of the numerical simulation were validated. The numerical investigations shown that both the temperature field and stress field obtained by the coupled algorithm were slightly lower than which obtained by the engineering algorithm. These were considered to be impacted by the Bartz empirical formula and the one-dimensional isentropic flow assumption. Further experimental investigations shown that the exterior surface temperature and strain of the nozzle throat obtained by the coupled algorithm were much closer to the experimental results, which further verified the accuracy of the coupled algorithm.

Compositional and entropy indirect noise generated in subsonic non-isentropic nozzles

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Sound generation by entropy perturbations passing through a sudden flow expansion

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A simple method to set the spray properties for flame spray pyrolysis production of nanoparticles

The most critical part of the flame spray pyrolysis (FSP) process is the nozzle, since it plays a key role in setting the spray properties. In this study, we developed an approach to adjust the nozzle throat gap size for a desired dispersion gas flow rate and upstream pressure, based on the external size and shape of a two phase external mixing nozzle. An equation was derived and validated by comparing the predicted gas flow rates with the data provided in a commercial nozzle supplier chart. Experiments were also conducted in our lab-scale FSP reactor to test the validity of the predictions. The approach developed here was found to closely predict the gap size necessary to pass the required dispersion gas flow at a desired pressure drop. Error in predictions was found to be less than 3% at an upstream pressure range of 3–10 bars. The isentropic flow assumption for perfect gases across the convergent-divergent nozzle was found to fail below 2 bars, consistent with the theory applied. By using the method here, the nozzle setting for a desired operation in an FSP process can be easily done, minimizing the time-consuming trial and error steps needed otherwise.

Isentropic analysis and numerical investigation on high-pressure hydrogen jets with real gas effects

The present work performs the isentropic analysis and numerical simulation of high-pressure hydrogen jets to study the hydrogen leakage. The exit parameters and the flow characteristics are studied with the ideal gas assumption and real gas effects. The jet exit parameters calculated by the real gas thermodynamic model are different from the results obtained by the ideal gas assumption at high initial pressure based on the isentropic analysis. The ideal gas and the real gas equation of state results in the differences of Mach disk parameters at high initial pressures. The ideal gas assumption underestimates the Mach disk distance by 8% and overestimates the Mach disk diameter by 15% at the initial pressure of 50 MPa. The exit mass flow rates computed from the isentropic expansion assumption agree well with the numerical simulations. The results show that it is reasonable to evaluate mass flow rates of high-pressure hydrogen jets by the isentropic expansion assumption.

A non-isentropic model of aluminized explosives involved with the reaction degree of aluminum powder for post-detonation burning behavior

The post-detonation burning effect of aluminum (Al) powder plays an important role during the expansion of detonation products (DPs) of aluminized explosives (AEs). Lithium fluoride (LiF) is an inert substitute for Al, and hence, a comparison of the performance of composite explosives based on cyclotrimethylenetrinitramine (RDX), such as RDX/Al and RDX/LiF, clearly illustrates its contribution to accelerating ability due to Al oxidation. A series of metal plate tests is conducted to measure the velocity history of a metal plate driven by RDX/Al and RDX/LiF through a photonic Doppler velocimetry system with 5%, 15%, and 25% Al or LiF contents. The detonation and expansion process of the AEs is generally divided into two stages: the detonation zone (DZ) and the post-detonation zone (PDZ). In the DZ, the Al powder remains inert, while it absorbs the detonation energy from pure explosives. Therefore, the equivalent inert dilution model is established and the equivalent inert dilution coefficient of the Al powder is introduced. In the PDZ, the Al powder reacts with DPs, and the Al oxidation reaction results with a change in entropy related to the reaction degree of the Al powder. Based on the local isentropic assumption, as well as the function of the reaction degree of the Al powder, a non-isentropic model is established. The method of the non-linear characteristic line is applied to theoretically calculate the metal plate velocity based on the non-isentropic model. In addition, the theoretical results show good agreement with the metal plate test results with an acceptable error (less than 10%), indicating that the non-isentropic model can be effectively applied to analyze the accelerating ability of the AEs.

Prediction of state property during hydrogen leaks from high-pressure hydrogen storage systems

In an actual hydrogen leakage process, heat exchange occurs between the gas in a high-pressure storage system and its surroundings. Therefore, the predictions of models that are established based on the isentropic process assumption have large errors. In this study, a high-pressure gas leakage process model including heat exchange (the HEC model) is established. It includes two parts; one is a high-pressure gas storage model without the isentropic process assumption, and the other is a leakage orifice model with the isentropic process assumption. Formulas for the pressure variation and temperature variation based on the mass and energy conservation equations, the Abel–Noble equation of state, and an enthalpy formula based on the Helmholtz free energy are used to establish the gas storage model. The leakage orifice model is built using a mass flow rate formula based on the van der Waals equation of state and Perry's flow coefficient formula. Finally, the proposed high-pressure gas leakage process model including heat exchange is compared with high-pressure hydrogen leakage process models with the isentropic process assumption based on the Abel–Noble and van der Waals equations of state. The results show that the proposed model can yield more promising results in predicting the gas leakage mass flow rate, gas pressure, and temperature inside hydrogen storage systems compared with previous models.

Assessment of Primary Energy Conversion of a Closed-Circuit OWC Wave Energy Converter

Tupperwave is a wave energy device based on the Oscillating-Water-Column (OWC) concept. Unlike a conventional OWC, which creates a bidirectional air flow across the self-rectifying turbine, the Tupperwave device uses rectifying valves to create a smooth unidirectional air flow, which is harnessed by a unidirectional turbine. This paper deals with the development and validation of time-domain numerical models from wave to pneumatic power for the Tupperwave device and the conventional OWC device using the same floating spar buoy structure. The numerical models are built using coupled hydrodynamic and thermodynamic equations. The isentropic assumption is used to describe the thermodynamic processes. A tank testing campaign of the two devices at 1/24th scale is described, and the results are used to validate the numerical models. The capacity of the innovative Tupperwave OWC concept to convert wave energy into useful pneumatic energy to the turbine is assessed and compared to the corresponding conventional OWC.

An unexpected balance between outer Rayleigh streaming sources

Acoustic streaming generated by a plane standing wave between two infinite plates or inside a cylindrical tube is considered, under the isentropic flow assumption. A two-dimensional analysis is performed in the linear case of slow streaming motion, based on analytical formal solutions of separate problems, each associated with a specific source term (Reynolds stress term). In order to obtain these analytical solutions, a necessary geometrical hypothesis is that $(R/L)^{2}\ll 1$, where $R$ and $L$ are the guide half-width (or radius) and length. The effect of the two source terms classically taken into account is quantified in order to derive the dependence of the maximum axial streaming velocity on the axis as a function of the ratio $R/\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$, where $\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D708}}$ is the acoustic boundary layer thickness. The effect of two other source terms that are usually neglected, is then analysed. It is found that one of these terms can generate a counter-rotating streaming flow. While negligible for very narrow guides, this term can become important for some values of the aspect ratio $L/R$.

Acousto-optically modulated quantum cascade laser for high-temperature reacting systems thermometry.

We demonstrate time-resolved temperature measurements in shock-heated mixtures of carbon monoxide over a temperature range of 1000-1800K for two pressure ranges, 2.0-2.9atm and 7.6-10.7atm, at rates up to 250kHz using a single acousto-optically modulated quantum cascade laser with mid-infrared output spanning from 1975 to 2260 cm-1. Measured temperatures were in excellent agreement with values determined by ideal shock relations, and the temperature profile after the passage of the reflected shock wave was found to be well-modeled by an isentropic compression assumption. Temperature measurements made with this setup are largely immune to effects of emissions and beam steering, making the diagnostic system well-suited for studying high-temperature gas-phase reactions of energetic materials such as octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine and hexahydro-1,3,5-trinitro-1,3,5-triazine.

Practical Approach for Absolute Density Field Measurement Using Background-Oriented Schlieren

A practical approach for deriving the absolute density field based on the background-oriented schlieren method in a high-speed flowfield was implemented. The flowfield of interest was a two-dimensional compressible flowfield created by two supersonic streams to simulate a linear aerospike nozzle operated under a supersonic in-flight condition. The linear aerospike nozzle had a two-dimensional cell nozzle with a design Mach number of 3.5, followed by a spike nozzle. The external flow simulating the in-flight condition was 2.0. The wall density distribution used as the wall boundary condition for Poisson’s equation to solve the density field was derived by a simplified isentropic assumption based on the measured wall pressure distribution, and its validity was evaluated by comparing with that predicted by numerical simulation. Unknown coefficients in Poisson’s equation were determined by comparing the wall density distribution with that predicted by the model. By comparing the derived density field based on the background-oriented schlieren method to that predicted by the model and numerical simulation, the absolute density field was derived within an error of 10% on the wall distribution. This practical approach using a simplified isentropic assumption based on measured pressure distribution thus provided density distribution with sufficient accuracy.