Transcritical State Research Articles

Modal and non-modal stability for Hagen–Poiseuille flow with non-ideal fluid

Modal and non-modal stability analyses are applied to Hagen–Poiseuille flow with a non-ideal fluid. The non-ideal fluid is defined as a fluid close to its vapor–liquid critical point. In this region, properties of the fluid deviate significantly from the assumptions of the ideal gas model. In this paper, the specific example of CO2 near the critical point is taken as a non-ideal fluid. We studied fluids at supercritical pressure and different wall temperatures so that the centerline temperatures can be lower, equal, and higher than the pseudo-critical temperature. Flow instability is characterized by the Reynolds number, and the product of the Prandtl and Eckert numbers. In modal stability analysis, we observe that there is no unstable mode in Hagen–Poiseuille flow with a non-ideal fluid. Regarding the growth rate, as the axial wavenumber increases, another mode becomes the least stable. The non-modal theory is employed to investigate the optimal response to harmonic external force and transient energy growth. The influence of axial and azimuthal wave numbers, Prandtl and Eckert numbers, and thermodynamic states are also taken into account. In this study, we identify an generalized inflection point in the transcritical base profile, causing the transcritical state to be the most unstable. In non-modal instability, we observe that the optimal response mainly occurs at time invariant axisymmetric disturbance. This suggests that the axisymmetric disturbance could potentially initiate the transition to turbulence.

Numerical study on thermal–hydraulic performance of hydrocarbon fuel under trans-critical states and supercritical CO2 in a zigzag printed circuit heat exchanger

The supercritical CO2 closed-Brayton-cycle (CBC) is a highly promising integrated scheme for cooling and power generation in hypersonic vehicles. However, the CO2-fuel printed circuit heat exchanger (PCHE) in the CBC faces extreme heat loads and fuel consumption constraints, leading to complex heat transfer phenomena including trans-critical processes and buoyancy effects. In this study, the coupled heat transfer process between the large-molecule hydrocarbon fuel and supercritical CO2 inside the zigzag-type PCHE is investigated using a numerical simulation, based on the practical constraints of the onboard CBC system. The results demonstrate that the distributions of eddy viscosity and specific heat within the boundary layer are significantly improved by the turbulence-enhancing effect of the zigzag channel, thus avoiding local heat transfer deterioration caused by trans-critical processes. Additionally, numerous small-scale vortex structures are found to increase the source term of turbulent kinetic energy generation, effectively suppressing the weakening effect of buoyancy on turbulence. Finally, an optimization study is conducted on the resistance of the zigzag channel starting from the power generation performance of the CBC system. The findings indicate a 71% reduction in pressure loss coupled with only a 7% reduction in volume heat transfer rate compared to the original configuration.

Experimental work for the performance of a printed circuit heat exchanger (PCHE) using nitrogen under trans-critical states

Experiments were carried out for the manufactured a printed circuit heat exchanger (PCHE) using nitrogen on the super-critical state. For the core of the PCHE, ‘N’ and reverse N, ‘RN’ shape microchannels were etched on stainless steel 316L plates, and total 120 plates were diffusion bonded. Then, for the PCHE evaluation in which the headers were welded, liquid nitrogen of below -170 °C and about 0.8 MPa was pressurized to about 3.42 ∼4.59 MPa, then was injected to the inlet on the cold side, and nitrogen gas of 72.7 ∼75.1 °C and about 0.6 ∼0.75 MPa was flowed through channels on the hot side. The flow rates were 2401 ∼3211 kg/h and 1592 ∼2357 kg/h on the hot and cold sides, respectively. In particular, the nitrogen on the cold side was pressurized by a pump, and state changes occurred over pseudo critical point. In order to evaluate performance of the PCHE with the super critical state nitrogen, the channels were simplified and discretized, then, effectiveness-number of transfer units (e-NTU) method was applied. Then, a new correlation expecting the thermal-hydraulic performance of PCHE was developed as Nu = 0.023Re0.78Pr0.4.

Pseudo-optimal discharge pressure analysis of transcritical CO2 electric vehicle heat pumps due to temperature glide

• A pseudo-optimal discharge pressure for electric vehicle heat pumps was proposed. • The principle of pseudo-optimal discharge pressure was explained. • Pseudo-optimal discharge pressure exists in subcritical and transcritical states. • The effects of conditions on pseudo-optimal discharge pressures were revealed. Performance improvement of electric vehicle heat pumps can enhance thermal comfort and reduce the power consumption of electric vehicles, hence stimulating their development. In this paper, the cyclic characteristics of an electric vehicle heat pump were studied under different operating modes and working conditions. Different from the optimal discharge pressure of conventional CO 2 systems which was determined by the variation gradient characteristics of the transcritical isotherm, the discharge pressure of electric vehicle heat pumps at the peak COP value was defined as a pseudo-optimal discharge pressure and was determined by the obvious temperature glide at the outlet of the gas cooler. This pseudo-optimal discharge pressure existed at both transcritical and subcritical states. The difference in the pseudo-optimal discharge pressure between the subcritical or transcritical states was first evaluated. Then an in-depth analysis of the influence of key parameters on the pseudo-optimal discharge pressure was studied to develop an accurate prediction method since the traditional prediction methods were not applicable. The results showed that pseudo-optimal discharge pressure increased with the ambient temperature, inlet air temperature, and supply air temperature. This study provides valuable information for the comprehensive performance optimization of an electric vehicle thermal management system.

Magnetic properties of Fe–Si–B thin films and their application as stress sensors

• As deposited sputtered thin films stress can be designed. • Amorphous FeSiB thin films have magnetic properties stress-dependent. • Permeabilities are larger for the tensile stress region than in the compressive stress region. • Stress is reducing the permeabilities of the thin films. • Amorphous FeSiB thin films can be candidates for Stress Impedance sensing systems. This study aimed to understand the magnetic behavior of amorphous Fe–Si–B thin films in the presence of residual stress. Residual stress appeared in the thin films during the sputtering process, which was controlled by changing the Ar flow rate during sputtering. Consequently, some thin films developed compressive stress and others developed tensile stress. The residual stress generated in the films ranged from –100 to 400 MPa. The magnetization curves of the samples were measured to extract their magnetic parameters, namely, the magnetic permeability, coercive field, and saturation magnetization. For the films of thickness 500 nm, the relative permeability was higher under tensile stress ( µ r ∼ 1000) than under compressive stress ( µ r ∼ 100). A transition between the high and low permeability values occurred for residual stress in the range 0–100 MPa. The relative permeability decreased from 1100 to 800 as the tensile stress increased from 0 to 400 MPa. In addition, the relative permeability decreased from 150 to 100 as the compressive stress increased from 0 to –100 MPa. Moreover, a transcritical state was observed in the samples under compressive stress. For the films of thickness 200 nm, the tensile stress lowered the relative permeability from 800 to 400; however, the compressive stress did not change the permeability significantly.

Synergistic mechanism of enhanced biocrude production during hydrothermal co-liquefaction of biomass model components: A molecular dynamics simulation

Hydrothermal co-liquefaction is a desirable technology for biocrude production from various biomass feedstocks, however, the insight into the mechanism of chemical reactions between biomass model components remains a huge challenge. To address this challenge, a detailed synergistic mechanism between model components was proposed based on molecular dynamics simulations for hydrothermal liquefaction (HTL) of cellulose, hemicellulose, lignin, lipid, and their mixtures. During the HTL process, the generation of aqueous phase products from cellulose and hemicellulose, polycyclic aromatic hydrocarbons from lignin, as well as undepolymerized macromolecules and carbon deposits from lipid hindered biocrude production from each component. As expected, synergistic interactions occurred between model components and enhanced biocrude produced from each component at a relatively mild HTL condition. Impressively, synergistic interactions were related to the transmission of reactive –OH groups between different biomolecules with the assistance of H2O molecules at transcritical states. By considering the interactions, a new and more versatile biocrude yield prediction model was developed based on biochemical compositions of feedstocks and reaction temperature. This work will provide new insight into potential interactions between biomass components and give a theoretical basis for feedstock “designing” in HTL of biomass wastes.

Experimental evaluation of a transcritical CO[formula omitted] refrigeration facility working with an internal heat exchanger and a thermoelectric subcooler: Performance assessment and comparative

The use of carbon dioxide in transcritical state has become one of the most used solutions to comply with the F-Gas directive and reduce greenhouse gases emissions from refrigeration systems at high ambient temperatures. For low-medium power units, the commonly used solutions to improve the efficiency such as the ejector, multiple compressor arrangements, mechanical subcooler, etc., add complexity and increase the cost of the refrigeration facility, which is not ideal for small units. In this low-medium power range, two technologies stand out to increase the performance of a carbon dioxide transcritical cycle: the internal heat exchanger and the thermoelectric subcooler. This study brings a complete research in which both solutions have been tested in the same experimental transcritical carbon dioxide refrigeration facility under the same working conditions. It focuses on the real performance of both systems and discusses the strengths and weaknesses of using an internal heat exchanger or a thermoelectric subcooler. The results show that the thermoelectric subcooler outperforms the internal heat exchanger in both the coefficient of performance and the cooling capacity while also being a more controllable and flexible solution.

Advanced Characterization of FeNi-Based Films for the Development of Magnetic Field Sensors with Tailored Functional Parameters.

Magnetometry and ferromagnetic resonance are used to quantitatively study magnetic anisotropy with an easy axis both in the film plane and perpendicular to it. In the study of single-layer and multilayer permalloy films, it is demonstrated that these methods make it possible not only to investigate the average field of perpendicular and in-plane anisotropy, but also to characterize their inhomogeneity. It is shown that the quantitative data from direct integral and local measurements of magnetic anisotropy are consistent with the direct and indirect estimates based on processing of the magnetization curves. The possibility of estimating the perpendicular magnetic anisotropy constant from the width of stripe domains in a film in the transcritical state is demonstrated. The average in-plane magnetic anisotropy field of permalloy films prepared by magnetron sputtering onto a Corning glass is almost unchanged with the thickness of a single-layer film. The inhomogeneity of the perpendicular anisotropy field for a 500 nm film is greater than that for a 100 nm film, and for a multilayer film with a total permalloy thickness of 500 nm, it is greater than that for a homogeneous film of the same thickness.

57Fe Mössbauer and magneto-optical Kerr effect (MOKE) study of transcritical state in permalloy (FexNi100-x) thin films

57Fe Mössbauer and magneto-optical Kerr effect (MOKE) study of transcritical state in permalloy (FexNi100-x) thin films

Large-eddy simulation of turbulent channel flow at transcritical states

We present well-resolved large-eddy simulations (LES) of a channel flow solving the fully compressible Navier–Stokes equations in conservative form. An adaptive look-up table method is used for thermodynamic and transport properties. A physically consistent subgrid-scale turbulence model is incorporated, that is based on the Adaptive Local Deconvolution Method (ALDM) for implicit LES. The wall temperatures are set to enclose the pseudo-boiling temperature at a supercritical pressure, leading to strong property variations within the channel geometry. The hot wall at the top and the cold wall at the bottom produce asymmetric mean velocity and temperature profiles which result in different momentum and thermal boundary layer thicknesses. Different turbulent Prandtl number formulations and their components are discussed in context of strong property variations.

Heat transfer characteristics of a natural circulation separate heat pipe under various operating conditions

In order to determine the heat transfer performance and the mechanisms of separate heat pipe (SHP) under various operating conditionscovering two-phase states and transcritical states, experimental investigation was carried out in this study. The effect of charging mass, cold bath temperature, heat load and height between evaporator and condenser on heat pipe was analyzed and the thermal resistance was calculated to characterize the heat transfer performance. Results showed that the increase of head load, the decrease of height difference and the increase of condenser temperature led to increases in thermal resistance. Appropriate charging mass was seen to be the most important factor in terms of optimum heat transfer performance, whereas too much or too little charging mass led to the subcooling or superheating in the evaporator, which was found to have a direct impact on heat transfer performance.

Experimental investigation on SCO2-water heat transfer characteristics in a printed circuit heat exchanger with straight channels

The supercritical CO2 Brayton cycle (SCO2-BC) is proposed to be used as the concept of fast cooled reactor (FCR), which is a typical application in the 4th generation reactors. The recuperator and cooler, which acted as important components in SCO2-BC, are required for long-term operation especially at the high pressure condition. However, the traditional shell-and-tube heat exchanger, which already has mature fabrication technology, is not appropriate in the developing miniaturized thermal system because of its low compactness. In the present paper, the compact printed circuit heat exchanger (PCHE) with straight ribs is manufactured by the photochemical etching technology and the diffusion bonding method independently. Then, the thermohydraulic performance of PCHE is tested on the SCO2-water experiment platform. Considering the difference of thermal properties of working fluid, the comparison of thermal and hydraulic performance between SCO2 and water in the tested PCHE is studied at the same mass flow rate, which shows that the SCO2 has better heat transfer capability than water fluid. Further, the heat transfer rate and pressure loss of PCHE are investigated at different SCO2 operating pressure, which indicates that the PCHE has better comprehensive performance when it operates at higher pressure condition. Meanwhile, the extreme operating condition due to the pseudo-critical point of CO2 working in the PCHE is analyzed comparing with the normal operating condition. The results show that the comprehensive performance of PCHE is significantly reduced nearly 17.6% when operates at the transcritical state. The heat transfer correlation of PCHE with straight ribs is fitted by experimental data in both the supercritical and transcritical states in order to simplifying design process.

Molecular Dynamics Study of Combustion Reactions in a Supercritical Environment. Part 1: Carbon Dioxide and Water Force Field Parameters Refitting and Critical Isotherms of Binary Mixtures

The oxy-fuel–carbon dioxide combustion process is expected to drastically increase the energy efficiency and enable easy carbon sequestration. In this technology, the combustion products (carbon dioxide and water) are used to control the temperature and nitrogen is excluded from the combustion chamber, so that nitrogen oxide pollutants do not form. Therefore, in oxy-combustion, carbon dioxide and water are present in large concentrations in their transcritical state and may play an important role in kinetics. The computational chemistry methods may assist in understanding these effects, and molecular dynamics with a reactive force field (ReaxFF) seems to be a suitable tool for such a study. Here, we investigate applicability of the ReaxFF to describe the critical phenomena in carbon dioxide and water and find that several non-bonding parameters need adjustment. We report the new parameter set, capable of reproducing the critical temperatures and pressures. The critical isotherms of CO2/H2O binary mixtures...

Large-eddy simulation of nitrogen injection at trans- and supercritical conditions

Large-eddy simulations (LESs) of cryogenic nitrogen injection into a warm environment at supercritical pressure are performed and real-gas thermodynamics models and subgrid-scale (SGS) turbulence models are evaluated. The comparison of different SGS models — the Smagorinsky model, the Vreman model, and the adaptive local deconvolution method — shows that the representation of turbulence on the resolved scales has a notable effect on the location of jet break-up, whereas the particular modeling of unresolved scales is less important for the overall mean flow field evolution. More important are the models for the fluid’s thermodynamic state. The injected fluid is either in a supercritical or in a transcritical state and undergoes a pseudo-boiling process during mixing. Such flows typically exhibit strong density gradients that delay the instability growth and can lead to a redistribution of turbulence kinetic energy from the radial to the axial flow direction. We evaluate novel volume-translation methods on the basis of the cubic Peng-Robinson equation of state in the framework of LES. At small extra computational cost, their application considerably improves the simulation results compared to the standard formulation. Furthermore, we found that the choice of inflow temperature is crucial for the reproduction of the experimental results and that heat addition within the injector can affect the mean flow field in comparison to results with an adiabatic injector.

Modeling and simulation of a GOX/kerosene subscale rocket combustion chamber with film cooling

Detailed knowledge on the heat transfer mechanisms is crucial for the design of reliable and efficient rocket engines. Due to the high heat loads of the combustion chamber walls and the corrosive hot gases, film cooling is often applied supplementary or even as a primary cooling technique. Nevertheless, the dominating processes determining the film effectiveness under the conditions representative for rocket combustors are still not fully understood. In context of the national research program Transregio SFB/TRR-40, TEKAN and TARES, the Institute for Flight Propulsion (LFA) of the Technische Universitat Munchen (TUM) and Airbus Defence and Space carry out experimental and numerical investigations on heat transfer and film cooling techniques at application-relevant combustion pressures and temperatures. In this paper, results from film cooling experiments and numerical simulations with liquid and transcritical kerosene films in a water-cooled GOX/kerosene rocket combustion chamber are presented. The tests have been performed at two different combustion chamber pressures and with two different throat diameters to study the influence of Reynolds and Mach number. In the numerical investigations, a major issue has been the modeling of kerosene films in sub- and transcritical state. For the modeling Airbus Defence and Space’s in-house tool, Rocflam-II has been applied. The main goal of Rocflam-II is to provide a tool package for the simulation of a wide range of rocket combustion devices, validated against experimental data. This includes the modeling of propellant injection, atomization, mixing, combustion, wall heat transfer, film modeling as well as the conjugate heat transfer into the chamber wall and the cooling channels.

The Reynolds number dependency of the steady and unsteady loading on a slightly rough circular cylinder: From subcritical up to high transcritical flow state

Simultaneous measurements of the spanwise-integrated unsteady aerodynamic forces and time-averaged local surface pressures on a 2D slightly rough circular cylinder were carried out over a wide range of Reynolds numbers in the high-pressure wind tunnel in Göttingen. The Reynolds numbers of 15×103≤Re≤12×106 spanned the known flow state regimes from subcritical up to high transcritical. The surface of the cylinder had a mean relative roughness of ks/D=1.2×10−3. The results demonstrated that especially in the critical flow regime the spanwise flow was strongly three-dimensional. In this regime two discontinuities at two closely spaced Reynolds numbers were observed, coupled with critical fluctuations in the lift force and the formation of a separation bubble at each side of the cylinder. The narrowing of the wake led to a sharp decrease of the drag coefficient and a steep increase of the values for the minimum pressure coefficients and the base pressure coefficient. In the upper transition state the boundary layer separation wandered upstream, resulting in an increase of the drag coefficient and a decrease of the base pressure coefficient and the Strouhal number. All measured flow field properties reached intermediate steady plateaus in the transcritical state for Re≥1.3×106. It was also shown that the surface roughness had a strong effect on the cylinder flow; in particular the disappearance of the supercritical regime and the subsequent strong recovery of the drag coefficient in the upper transition.

Structural Peculiarities and Magnetic Properties of FeNi Films and FeNi/Ti-Based Magnetic Nanostructures

Fe19Ni81 films and Fe19Ni81/Ti-based nanostructures were prepared by rf-sputtering. The thicknesses of FeNi samples were below and above the critical thickness of the transition into transcritical state which controls perpendicular magnetic anisotropy and there fore the low coercivity and magnetic softness. FeNi/Ti-based magnetic nanostructures were designed with focus on high-frequency applications. Their structure was studied by X-ray diffraction. The magnetic properties and magnetic domains were investigated by mag neto-optical Kerr effect and Bitter technique. The increase of the grain size was observed with an increase of the total thickness of the films. It was shown that [FeNi(50 nm)/Ti(6 nm)]7/FeNi(50 nm) nanostructures have the lowest coercivity and interesting struc tural features which can be responsible for the improvement of their magnetic properties.

Transcritical oxygen/transcritical or supercritical methane combustion

Injection of liquid fluid initially at subcritical temperature into an environment in which the temperature and pressure exceed the thermodynamic critical conditions is an important phenomenon in many high performance devices like liquid propellant rocket engines. This is found, for example, in the Space Shuttle main engines or in the Ariane 5 Vulcain engine both operating with liquid oxygen (LOx) and gaseous hydrogen (GH 2). This article is concerned with the less standard situation where both reactants are in a transcritical state. One case of current interest in propulsion, that of combustion of cryogenic oxygen and methane injected at high pressure, is investigated experimentally. A coaxial injector delivers oxygen at a temperature of 85 K and methane at 120 or 288 K. The pressure in the chamber takes values between 4.5 and 6 MPa. Emission images from excited state OH (A 2Σ, denoted OH*) and CH (A 2Δ, denoted CH*) are recorded and averaged. The Abel transform is used to determine the mean flame structure from these average images. Data indicate that the flame is stabilized in the vicinity of the injector. When both propellants are transcritical, the flame features two conical regions of light emission, one spreading close to the liquid oxygen boundary and the other located further away from the axis near the liquid methane boundary. The outer flame boundary is also conical with a relatively large expansion angle. This flame structure notably differs from that observed when one of the propellants is injected in a subcritical or transcritical state while the other is gaseous. An analysis of the relevant characteristic times suggests that under transcritical conditions the rate of combustion is mainly controlled by turbulent energy transfer to the propellants. This determines the mass fluxes from the dense regions to the lighter gaseous streams governing the rate of conversion into products.

Critical behaviour of a Timoshenko beam-half plane system under a moving load

In this contribution, attention is focused on the problem of a moving load on a Timoshenko beam-half plane system. Both the subcritical and the supercritical state will be analysed via a FE-simulation. The character of the response is explained by the analytical derivation and the elaboration of the eigen-value problem that follows from the characteristic wave equations together with the boundary conditions. It will be demonstrated that also transcritical states can occur. The total number of critical states and the values of the corresponding critical velocities are determined by the beam-half plane stiffness properties as well as the contact conditions.

Convection of tin in a Bridgman system I. Flow characterization by effective diffusivity measurements

An electrochemical titration method was used to investigate the dynamic states in a cylindrical layer of convecting tin. The liquid tin was contained in a cell, with curved boundaries made of quartz and flat boundaries made of a solid state electrolyte - yttria-stabilized zirconia (YSZ). The electrolyte acted as a window through which a trace amount of oxygen could be pumped in or out by the application of a constant voltage. The concentration at the YSZ interface was monitored by operating the electrochemical cell in the galvanic mode. Experimentally determined effective diffusivities of oxygen were compared with the molecular diffusivity. Dynamic states in the convective flow were thus inferred. Temperature measurements were simultaneously made in order to identify the onset of oscillations from a steady convective regime. The experiments were conducted for two different aspect ratios for various imposed temperature gradients and two different orientations with respect to gravity. Transcritical states were identified and comparison to two-dimensional numerical models were made.