Isobaric Mixing Research Articles

The effects of in-nozzle phase transition on injection characteristics of near- and supercritical kerosene jets

The escalating requirements for thermal management in advanced high-performance aviation engines necessitate the injection of aviation fuels under near- and supercritical conditions. The jet morphology both exterior and interior to the nozzle of aviation kerosene jets, injected from near-critical and supercritical states into a quasi-quiescent, near-atmospheric environment, was experimentally investigated, focusing on the effects of in-nozzle phase transitions. The in-nozzle flow behavior was characterized using shadowgraph imaging and pressure profile measurements, while downstream jet behavior was captured using both shadowgraph imaging and planar Mie scattering techniques. It is found that without observable in-nozzle phase transitions (OIPTs), the near-nozzle jet structure exhibits low sensitivity to injection temperature. However, under OIPT conditions, a reduction in injection temperature precipitates notable increases in jet expansion angle, jet diameter, and Mach disk diameter. Additionally, it initially provokes a downstream displacement of the Mach disk, subsequently reversing its direction upstream. Analysis using the surrogate fuel thermodynamic phase diagram indicates that without OIPT, jets injected from the supercritical and vapor states disintegrate similarly due to stages of isentropic expansion, compression, and isobaric mixing, leading to fuel condensation. Under OIPT conditions, crossing the Widom line or saturation line leads to an increase in the specific heat ratio of the fuel along the injection path and changes the near-nozzle shock structure from barrel-shaped to bowl-shaped, potentially triggering a compression shock wave in the ambient air. These findings are useful for the design and modification of supercritical fuel nozzles, fuel supply systems, and combustion chambers.

CCN Activation and Droplet Growth in Pi Chamber Simulations with Lagrangian Particle–Based Microphysics

Abstract Numerical simulations of turbulent moist Rayleigh–Bénard convection driving CCN activation and droplet growth in the laboratory Pi chamber are discussed. Supersaturation fluctuations come from isobaric mixing of warm and humid air rising from the lower boundary with colder air featuring lower water vapor concentrations descending from the upper boundary. Lagrangian particle–based microphysics is used to represent the growth of haze CCN and cloud droplets with kinetic, solute, and surface tension effects included. Dry CCN spectra in the range between 2- and 200-nm radii from field observations are considered. Increasing the total CCN concentration from pristine to polluted conditions results in an increase in the droplet concentration and reduction in the mean droplet radius and spectral width. These are in agreement with Pi chamber observations and numerical simulations, as well as with numerous past studies of CCN cloud-base activation in natural clouds. The key result is that a relatively small fraction of the available CCN is activated in the Pi chamber fluctuating supersaturations, from about a half in the pristine case to only a 10th in the polluted case. The activation fraction as a function of the dry CCN radius is similar in all simulations, close to zero at the CCN small end, increasing to a maximum at CCN radius around 50 nm, and decreasing to close to zero at the large CCN end. This is explained as too small supersaturations to activate small CCN as in natural clouds and insufficient time to allow large CCN reaching the critical radius. Significance Statement Impact of turbulence on the formation and growth of cloud droplets is an important cloud physics problem. Laboratory experiments in the Michigan Technological University cloud chamber provide key insights into this problem. Numerical simulations of cloud chamber processes discussed in this paper complement laboratory experiments by providing insights difficult or impossible to obtain in the laboratory. The study contrasts the formation and growth of cloud droplets in the laboratory cloud chamber with processes taking place in natural clouds. The differences documented in this paper pose questions concerning the impact of turbulence on the formation and growth of cloud droplets as a result of interactions of clouds with their environment.

Is the water vapor supersaturation distribution Gaussian?

AbstractWater vapor supersaturation in the atmosphere is produced in a variety of ways, including the lifting of a parcel or via isobaric mixing of parcels. However, irrespective of the mechanism of production, the water vapor supersaturation in the atmosphere has typically been modeled as a Gaussian distribution. In the current theoretical and numerical study, the nature of supersaturation produced by mixing processes is explored. The results from large eddy simulation and a Gaussian mixing model reveal the distribution of supersaturations produced by mixing to be negatively skewed. Further, the causes of skewness are explored using large eddy simulations (LES) and the Gaussian mixing model (GMM). The correlation in forcing of temperature and water vapor fields is recognized as playing a key role.

Physical processes analysis of contrails formation over the South Brazil Region

Contrails are clouds in the shape of condensation trails formed from hot air and particles exiting the engines of airplanes. These clouds form from the isobaric mixing of hot and humid air masses emitted by airplanes with cold ambient air. Their formation can alter the sky through cirrus clouds and the radiation balance. In this study, photographic images, satellite data and atmospheric reanalysis and radiosonde data were used to assess the occurrence of these events in the South Brazil region. The results showed that there were observed several cases of contrails in the region, mainly when the upper layer where the aircraft passed was colder and moister. Initially, several cases were selected from the observations and the Terra, Aqua and Suomi satellite images. Also, radiosonding data from Curitiba, Florianópolis and Porto Alegre were applied to the thermodynamic Appleman diagram to study the physical processes involved. The results showed that temperatures below -50 °C from cold advection and moister air at the cruising level of airplanes contribute to formation of more persistent contrails and cirrus clouds. Therefore, monitoring the environmental conditions may improve the prediction of contrails formation and better understanding the impacts on the radiation balance and climate.

Technical note: Equilibrium droplet size distributions in a turbulent cloud chamber with uniform supersaturation

Abstract. In a laboratory cloud chamber that is undergoing Rayleigh–Bénard convection, supersaturation is produced by isobaric mixing. When aerosols (cloud condensation nuclei) are injected into the chamber at a constant rate, and the rate of droplet activation is balanced by the rate of droplet loss, an equilibrium droplet size distribution (DSD) can be achieved. We derived analytic equilibrium DSDs and probability density functions (PDFs) of droplet radius and squared radius for conditions that could occur in such a turbulent cloud chamber when there is uniform supersaturation. We neglected the effects of droplet curvature and solute on the droplet growth rate. The loss rate due to fallout that we used assumes that (1) the droplets are well-mixed by turbulence, (2) when a droplet becomes sufficiently close to the lower boundary, the droplet's terminal velocity determines its probability of fallout per unit time, and (3) a droplet's terminal velocity follows Stokes' law (so it is proportional to its radius squared). Given the chamber height, the analytic PDF is determined by the mean supersaturation alone. From the expression for the PDF of the radius, we obtained analytic expressions for the first five moments of the radius, including moments for truncated DSDs. We used statistics from a set of measured DSDs to check for consistency with the analytic PDF. We found consistency between the theoretical and measured moments, but only when the truncation radius of the measured DSDs was taken into account. This consistency allows us to infer the mean supersaturations that would produce the measured PDFs in the absence of supersaturation fluctuations. We found that accounting for the truncation radius of the measured DSDs is particularly important when comparing the theoretical and measured relative dispersions of the droplet radius. We also included some additional quantities derived from the analytic DSD: droplet sedimentation flux, precipitation flux, and condensation rate.

Cleaner production of purified terephthalic and isophthalic acids through exergy analysis

The purified terephthalic and isophthalic acids production process was improved through the exergy analysis approach demonstrated in this work. The overall exergy losses and low-exergy-efficient units were first identified and presented using visualised exergetic flowsheets. Recommendations were then proposed to reduce losses based on the main cause(s) of irreversibility. Three out of the five constituent blocks contained the highest exergy losses. The oxidation block was the main player where it was suggested that using several reactors in series with gradually decreasing temperatures could lower losses. The product refining block had the second-largest irreversibilities, where improving coolers' performances were recommended. The crude terephthalic acid crystallisation block was the third-largest loss producer, where isothermal and isobaric mixing in the solvent dehydrator was suggested to reduce losses. The approach used in this work can be adapted to improve the energy footprint of other chemical processes.

Numerical research on coupling performance of inter-stage parameters for two-stage compression system with injection

Aimed at a two-stage compression system composed of two rotary compressors, a simulation model of the two-stage compression system with injection was constructed and validated by experiments. Based on the simulation and experiments, the coupling relation among the injection parameters, the formation process of the inter-stage parameters and the effects of the inter-stage injection on the two-stage compression process were analyzed. The simulation results show that the mass flowrate and specific enthalpy of the injection refrigerant are a pair of coupling parameters which are constrained by the subcooler. The specific enthalpy of the injection refrigerant first increases and then decreases gradually as the mass flowrate of the injection refrigerant increases. The intermediate injection parameters have a great influence on the inter-stage parameters. The specific enthalpy of the injection refrigerant determines the direction of the change in the state point, and the mass flowrate of the injection refrigerant determines the degree of the change in the state point of the system. From the dynamic point of view, when the mass flowrate of the injection refrigerant increases, the intermediate mixing process is stabilized to a new “isobaric mixing” process after a transition from a stable “isobaric mixing” process to a variable “isocratic mixing” process.

A Laboratory Facility to Study Gas–Aerosol–Cloud Interactions in a Turbulent Environment: The Π Chamber

Abstract A detailed understanding of interactions of aerosols, cloud droplets/ice crystals, and trace gases within the atmosphere is of prime importance for an accurate understanding of Earth’s weather and climate. One aspect that remains especially vexing is that clouds are ubiquitously turbulent, and therefore thermodynamic and compositional variables, such as water vapor supersaturation, fluctuate in space and time. With these problems in mind, a multiphase, turbulent reaction chamber—called the Π chamber because of the internal volume of 3.14 m3 with the cylindrical insert installed—has been developed. It is capable of pressures ranging from 1,000 to –60 hPa and can sustain temperatures of –55° to 55°C, thereby spanning much of the range of tropospheric clouds. To control the relative humidity in the chamber, it can be operated with a stable, unstable, or neutral temperature difference between the top and bottom surfaces, with or without expansion. A negative temperature difference induces turbulent Rayleigh–Bénard convection and associated supersaturation generation through isobaric mixing. Supporting instrumentation includes a suite of aerosol generation and characterization techniques; temperature, pressure, and humidity sensors; and a phase Doppler interferometer. Initial characterization experiments demonstrate the ability to sustain steady-state turbulent cloud conditions for times greater than 1 day, with droplet diameters typically in the range of 5–40 µm. Typical turbulence has root-mean-square velocity fluctuations on the order of 10 cm s–1 and kinetic energy dissipation rates of 1 × 10–3 W kg–1.

Evaluation of an alternative chlorine production process for energy saving toward sustainability

Exergetic‐based solutions are proposed in this work to reduce the energy footprint of an alternative chlorine production process. By presenting exergy analysis results in the form of visualized exergetic process flowsheets using a solution panel, this study does not only find the low‐exergy‐efficient unit operations, but also proposes ways to improve the exergy efficiency based on the major sources of irreversibility of individual unit operations. Based on the amount of exergy losses, the alternative chlorine production process is divided into three main functional blocks. The total internal and external exergy losses for the entire process are calculated as 14,523.5 and 286.1 kJ/kg, respectively. The electrolysis block shows the highest potential for improvements with the largest exergy loss (responsible for more than 96.0% of total losses; with 14,093.2 kJ/kg of internal losses and 146.5 kJ/kg of external losses). Isothermal mixing, lower reaction temperature, and reduced pressure drop are suggested as avenues for improvement. Exergy losses in the gas treatment block with total exergy losses of 411.7 kJ/kg (equivalent to 2.8% of total losses) are mainly due to the cooling column (241.9 kJ/kg), where modifications in column might be helpful as concentration and temperature gradients along the tower are sources of exergy loss. The highest exergy loss in the feed pretreatment block with the total exergy losses of 158.2 kJ/kg (i.e., 1.1% of total losses) belongs to the mixers (106 kJ/kg) where isothermal and also isobaric mixing is required. © 2016 American Institute of Chemical Engineers Environ Prog, 35: 1512–1520, 2016

Diagnosis of an alternative ammonia process technology to reduce exergy losses

Ammonia production through more efficient technologies can be achieved using exergy analysis. Ammonia production is one of the most important but also one of most energy consuming processes in the chemical industry. Based on a panel of solutions previously developed, this study helps to identify potential areas of improvement using an exergy analysis that covers all aspects of conventional ammonia synthesis and separation. The total internal and external exergy losses are calculated as 3,152 and 6,364kJ/kg, respectively. The process is then divided into five main functional blocks based on their exergy losses. The reforming block contains the largest exergy loss (3,098kJ/kg) and thus the largest potential for improvement including preheating cold feed through an economizer, developing technology towards isobaric mixing, and pressure drop reduction in the secondary reformer as the main contributors to the irreversibility (1,302kJ/kg) in this block. The second largest exergy loss resides in the ammonia synthesis block (3,075kJ/kg) where solutions such as reduced temperature rise across the compressor, proper compressor isolation, reducing undesired components such as argon in the reactor feed, and using lower temperatures for reactor outlet streams, are proposed to decrease the exergy losses. Throttling process in the syngas separator is the key contributing mechanism for the irreversibility (1,635kJ/kg exergy losses) in the gas upgrading block. The exergy losses in the residual ammonia removal block (833kJ/kg exergy losses) are mainly due to the stripper and the absorber column where a modified column design might be helpful. The highest exergy loss in the preheating block belongs to the compressors (518kJ/kg exergy losses) where a lower inlet temperature and better system isolation could help to reduce losses.

Effects of entrainment and mixing on droplet size distributions in warm cumulus clouds

AbstractA long‐standing problem in cloud physics is the broadening of the cloud droplet spectrum in warm cumulus clouds. To isolate the changes of the droplet size distribution (DSD) due to entrainment and turbulent mixing, we used the Explicit Mixing Parcel Model (EMPM). The EMPM explicitly represents spatial variability due to entrainment and turbulent mixing down to the smallest turbulence scales in a one‐dimensional domain. Several thousand individual droplets evolve by condensation or evaporation according to their local environments. We used EMPM results to characterize the evolution of the DSD due to entrainment and isobaric mixing for a wide range of conditions in a 20 m domain, including variations in entrained environmental air fraction, the turbulence dissipation rate, the size of the entrained blobs, and the relative humidity of the entrained air. We found that the broadening of the DSD due to entrainment and isobaric mixing for a specific value of the entrained air relative humidity depends only on the eddy mixing time scale and the LWC after mixing. Broadening increases substantially as the evaporation time scale decreases due to decreasing relative humidity of the entrained air. Our results also show that it is possible to parameterize the effects of entrainment and mixing on the droplet number concentration. The comprehensive results obtained for one set of values of entrained air relative humidity, droplet size, and droplet concentration should be extended to other values.

A New Mechanism of Droplet Size Distribution Broadening during Diffusional Growth

Abstract A new mechanism has been developed for size distribution broadening toward large droplet sizes. This mechanism may explain the rapid formation of large cloud droplets, which may subsequently trigger precipitation formation through the collision–coalescence process. The essence of the new mechanism consists of a sequence of mixing events between ascending and descending parcels. When adiabatically ascending and descending parcels having the same initial conditions at the cloud base arrive at the same level, they will have different droplet sizes and temperatures, as well as different supersaturations. Isobaric mixing between such parcels followed by further ascents and descents enables the enhanced growth of large droplets. The numerical simulation of this process suggests that the formation of large 30–40-μm droplets may occur within 20–30 min inside a shallow adiabatic stratiform layer. The dependencies of the rate of the droplet size distribution broadening on the intensity of the vertical fluctuations, their spatial amplitude, rate of mixing, droplet concentration, and other parameters are considered here. The effectiveness of this mechanism in different types of clouds is discussed.

Operation of a centrifugal pump and a liquid ejector with an isobaric mixing chamber

The influence of simultaneous operation of a centrifugal pump and an isobaric ejector on the pump’s cavitational stability is investigated.

Study of low-order numerical effects in the two-dimensional cloud-top mixing layer

Large-eddy simulation (LES) has been extensively used as a tool to understand how various processes contribute to the dynamics of the stratocumulus layer. These studies are complicated by the fact that many processes are tied to the dynamics of the stably stratified interface that caps the stratocumulus layer, and which is inadequately resolved by LES. Recent direct numerical simulations (DNS) of isobaric mixing due to buoyancy reversal in a cloud-top mixing layer show that molecular effects are in some instances important in setting the cloud-top entrainment rate, which in turn influences the global development of the layer. This suggests that traditional LES are fundamentally incapable of representing cloud-top processes that depend on buoyancy reversal and that numerical artefacts can affect significantly the results. In this study, we investigate a central aspect of this issue by developing a test case that embodies important features of the buoyancy-reversing cloud-top layer. So doing facilitates a one-to-one comparison of the numerical algorithms typical of LES and DNS codes in a well-established case. We focus on the numerical effects only by switching off the subgrid-scale model in the LES code and using instead a molecular viscosity. We systematically refine the numerical grid and quantify numerical errors, validate convergence and assess computational efficiency of the low-order LES code compared to the high-order DNS. We show that the high-order scheme solves the cloud-top problem computationally more efficiently. On that basis, we suggest that the use of higher-order schemes might be more attractive than further increasing resolution to improve the representation of stratocumulus in LES.

Gas ejector with isobaric mixing chamber

A method is proposed for calculating a gas ejector with a tapering isobaric mixing chamber. The efficiency of ejectors with isobaric and cylindrical mixing chambers is compared.

The evaporatively driven cloud-top mixing layer

Direct numerical simulations of the turbulent temporally evolving cloud-top mixing layer are used to investigate the role of evaporative cooling by isobaric mixing locally at the stratocumulus top. It is shown that the system develops a horizontal layered structure whose evolution is determined by molecular transport. A relatively thin inversion with a constant thickness h = κ/we is formed on top and travels upwards at a mean velocity we ≃ 0.1(κ |bs|χc2)1/3, where κ is the mixture-fraction diffusivity, bs < 0 is the buoyancy anomaly at saturation conditions χs and χc is the cross-over mixture fraction defining the interval of buoyancy reversing mixtures. A turbulent convection layer develops below and continuously broadens into the cloud (the lower saturated fluid). This turbulent layer approaches a self-preserving state that is characterized by the convection scales constructed from a constant reference buoyancy flux Bs = |bs|we/χs. Right underneath the inversion base, a transition or buffer zone is defined based on a strong local conversion of vertical to horizontal motion that leads to a cellular pattern and sheet-like plumes, as observed in cloud measurements and reported in other free-convection problems. The fluctuating saturation surface (instantaneous cloud top) is contained inside this intermediate region. Results show that the inversion is not broken due to the turbulent convection generated by the evaporative cooling, and the upward mean entrainment velocity we is negligibly small compared to the convection velocity scale w* of the turbulent layer and the corresponding growth rate into the cloud.

Laboratory and modeling studies of cloud–clear air interfacial mixing: anisotropy of small-scale turbulence due to evaporative cooling

Small-scale mixing between cloudy air and unsaturated clear air is investigated in numerical simulations and in a laboratory cloud chamber. Despite substantial differences in physical conditions and some differences in resolved scales of motion, results of both studies indicate that small-scale turbulence generated through cloud–clear air interfacial mixing is highly anisotropic. For velocity fluctuations, numerical simulations and cloud chamber observations demonstrate that the vertical velocity variance is up to a factor of two larger than the horizontal velocity variance. The Taylor microscales calculated separately for the horizontal and vertical directions also indicate anisotropy of turbulent eddies. This anisotropy is attributed to production of turbulent kinetic energy (TKE) by buoyancy forces due to evaporative cooling of cloud droplets at the cloud–clear air interface. Numerical simulations quantify the effects of buoyancy oscillations relative to the values expected from adiabatic and isobaric mixing, standardly assumed in cloud physics. The buoyancy oscillations result from microscale transport of liquid water due to the gravitational sedimentation of cloud droplets. In the particular modeling setup considered here, these oscillations contribute to about a fifth of the total TKE production.

Drop Growth Due to High Supersaturation Caused by Isobaric Mixing

A new conceptual model is proposed for enhanced cloud droplet growth during condensation. Rapid droplet growth may occur in zones of high supersaturation resulting from isobaric mixing of saturated volumes with different temperatures. Cloud volumes having a temperature different from the general cloud environment may form due to turbulent vertical motions in a temperature lapse rate that is not pseudoadiabatic. This mechanism is most effective in the vicinity of cloud-top inversions. It is also shown that the isobaric mixing of saturated and dry volumes with different temperatures may also lead to high supersaturations. The high supersaturations are associated with zones of molecular mixing, and they have a characteristic size of the order of millimeters with a characteristic lifetime near tenths of a second. Some small proportion of cloud droplets, over many supersaturation events, may grow large enough to grow effectively through collision–coalescence. This hypothesis of isobaric mixing may help explain freezing and warm drizzle formation.

Spreading width of the isobaric analog state and isospin mixing.

We study a relation between the spreading width of the isobaric analog state and the isospin mixing probability of the corresponding parent state by using the Feshbach projection method. The formula is applied for calculations of the spreading width of several heavy isotopes and compared with available experimental data. Contributions from isovector monopole states are found to be important to explain quantitatively the experimental spreading width. The isospin dependence of the calculated width of several isotopes is also found to be consistent with the experimental observations. \textcopyright{} 1996 The American Physical Society.

Calculation of supersonic separation flow in circular nozzles with abrupt expansion

A study is made of the interaction of a circular supersonic jet with a turbulent layer of the near-wake kind formed behind a circular step on the end part of a nozzle with abrupt expansion. The flow in the viscous layer is calculated by the integral method, and in the inviscid flow by a through-computation method using a monotonic implicit difference scheme of first order of accuracy. The interaction between the inviscid and turbulent flows is determined by the displacement thickness of the viscous layer. The initial conditions for the flow in the layer are determined from the integral conditions of its matching to the isobaric mixing flow in the base region behind the step. The computed interaction flows are determined as a function of the length of the end part and the counter pressure simultaneously or separately by the boundary condition that the pressure at the end of the end part be equal to the pressure of the external medium and by a singular solution of the equations passing through a saddle singular point — the throat of the wake. In a conical nozzle with profiled attachments of different lengths, calculations were made of separation flows with open and closed base regions and with allowance for secondary separation. The obtained solutions are multivalued in a certain range of lengths of the end part and values of the counter pressure. The solutions realized in reality are selected by analyzing the regimes of operation of the nozzles, and the calculated regions of hysteresis and associated low-frequency nonstationary separation flows are determined.