Transcritical Regime Research Articles

Mass transfer and combustion in transcritical non-premixed counterflows

The problem of transcritical mass transfer and combustion is considered in the counterflow geometry established at ambient pressures exceeding the critical pressure of the fluids but for an injection temperature (or injection temperatures) below critical. Real gas effects taking place under these conditions are treated with suitable models for thermodynamics and transport properties. A set of routines designated as ‘TransChem’ is constructed to extend the standard ‘Chemkin’ package to the transcritical regime. Three configurations are investigated. In the first case a low temperature oxygen stream impinges on a high temperature supercritical stream of the same substance and the ambient pressure exceeds the critical pressure. The structure of this flow is determined numerically and the mass transfer taking place between the dense oxygen and the hot stream is evaluated. It is shown that this rate can be correlated in terms of a transfer number which depends on the hot and cold temperatures and on the critical temperature. The mass transfer rate is also found to evolve like the square root of the strain rate. In the second case a flame is formed in the counterflow of a stream of cold oxygen injected at a temperature which is below critical and impinges on a supercritical stream of methane. In this flow, the flame is established in the light gas region adjacent to a sharp density gradient. The flame structure is close to that found in a gaseous situation except for the very large density change on the oxygen side which fixes the oxygen mass transfer rate to the flame. In the third case, the two streams are transcritical with temperatures below the respective critical values. The flow features two sharp gradients on the oxygen and methane sides and the flame is established between these two layers in the low density gaseous region.

Synthetic Aperture Radar observations of resonantly generated internal solitary waves at Race Point Channel (Cape Cod)

Synthetic Aperture Radar images revealed the two‐dimensional propagation characteristics of short‐period internal solitary waves in Race Point Channel in Massachusetts Bay. The images and in situ measurements of the flow in the channel are used to infer the likely generation mechanism of the waves. The solitary waves are generated during the ebb phase of the tide within the channel. On some occasions, two trains of internal waves are generated presumably at the same location but at slightly different phases of the ebb tide. The main characteristics of the (two‐layer) flow are described based on the criticality of the Froude number. It is suggested that these two individual packets of waves result from flow passage through resonance (where the Froude number is one). One packet is generated as the flow passes through the transcritical regime during the acceleration phase of the (ebb) tidal current, and another packet is generated during the deceleration phase. Both packets propagate upstream when the tide slacks, but with slightly different propagation directions.

The role of the contact geometry in wheel–rail impact due to wheel flats: Part II

A classification of wheel flats according to the different stages of their growth is given, along with the characteristic features of the dynamic wheel–rail interaction for each category. Mathematical expressions and frequency spectra of the corresponding wheel mass trajectories are derived. Difference is made between the subcritical and the transcritical speed regime. A criterion is derived for contact loss for worn flats. Simulations show that the dynamic wheel–rail interaction is governed by the track stiffness for low train speeds or long flat lengths; for high speeds and/or short flat lengths the interaction is governed by the inertial properties of the wheel and the rail. For a given flat geometry, nonlinearities in the relationship between the impact magnitude and the train speed occur in the stiffness-dominated speed domain, whereas this relationship is approximately linear in the inertia-governed domain. In the latter domain, the impact magnitude is found to be linearly dependent upon the maximum trajectorial curvature or inversely linearly dependent on the minimum circumferential wheel tread curvature. The above relationships are valid for the subcritical speed regime, in which no contact loss occurs. Different contributions from the literature are compared with respect to the established relationship between impact magnitude and speed. Significant differences are found, due to insufficiently defined parameters and conditions. Conditions are derived for a consistent application of the so-called equivalent rail indentation in experiments with wheel flats, and the indirect strain registration method for measuring dynamic wheel–rail contact forces is reviewed.

Counterflow diffusion flames of general fluids: Oxygen/hydrogen mixtures

A comprehensive framework has been established for studying laminar counterflow diffusion flames for general fluids over the entire regime of thermodynamic states. The model incorporates a unified treatment of fundamental thermodynamic and transport theories into an existing flow solver DMCF to treat detailed chemical kinetic mechanisms and multispecies transport. The resultant scheme can thus be applied to fluids in any state. Both subcritical and supercritical conditions are considered. As a specific example, diluted and undiluted H 2/O 2 flames are investigated at pressures of 1–25 MPa and oxygen inlet temperatures of 100 and 300 K. The effects of pressure p and strain rate ϵ s on the heat release rate q ˙ s , extinction limit, and flame structure are examined. In addition, the impact of cross-diffusion terms, such as the Soret and Dufour effects, on the flame behavior is assessed. Results indicate that the flame thickness δ f and heat release rate correlate well with the square root of the pressure multiplied by the strain rate as δ f ∼ 1 / p ϵ s and q ˙ s ∼ p ϵ s , respectively. The strain rate at the extinction limit exhibits a quasi-linear dependence on p. Significant real-fluid effects take place in the transcritical regimes, as evidenced by the steep property variations in the local flowfield. However, their net influence on the flame properties appears to be limited due to the ideal-gas behavior of fluids in the high-temperature zone.

Subcritical to supercritical mixing

Liquid jet injection into a quiescent gaseous environment has been experimentally and analytically studied covering subcritical to supercritical conditions. The focus was placed on the influence that the surrounding gas pressure and temperature have on the jet breakup. Under subcritical conditions, the surrounding gas inertia and surface tension forces controlled this process with ligament formation from which the material broke off and the drops, later, formed. Decreasing surface tension influenced the jet surface behavior under transcritical conditions: Ligament formation was significantly reduced under these conditions with only occasional drop formation. Further increasing the pressure and temperature led to supercritical breakup modes. This manifested through a smoothening of the liquid-gas interface. Ligament formation was not observed under supercritical conditions; this indicated that surface tension did not play any role in the supercritical jet breakup. The experimental technique, using planar laser induced fluorescence, revealed important core jet structures previously undetected. A linear jet stability analysis was, then, performed to gain physical insight into the jet breakup mechanisms. The results showed good correlation with experimental results under subcritical mixing but failed to predict the transcritical and supercritical regimes.

The role of the contact geometry in wheel–rail impact due to wheel flats

A thorough investigation of wheel–rail impact due to wheel flats is presented, together with a quantitative characterization of the main mechanisms and parameters. A criterion for the speed with respect to contact loss between wheel and rail is derived. In the subcritical speed regime, the magnitude of the impact force is shown to be directly related to the geometry of the flat, whereas in the transcritical speed regime a fictitious or effective flat depth exists, which decreases with the second order of the speed. In this domain, the position of impact shifts towards the end of the flat with increasing speed. The impact force increases with the second order of the speed in the subcritical speed regime and approximately the first order of the speed in the transcritical speed regime. The magnitude of the impact force is inversely proportional to the minimum circumferential curvature of the wheel tread defect in the subcritical speed regime, and to the effective minimum curvature in the transcritical case. The variation with the flat depth is less; the impact varies with the square root of the flat depth. The presented theory is in accordance with measurements reported in the literature and explains characteristic features in them.

Transcritical rotating flow over topography

The flow of a one-and-a-half layer fluid over a three-dimensional obstacle of non-dimensional height M, relative to the lower layer depth, is investigated in the presence of rotation, the magnitude of which is measured by a non-dimensional parameter B (inverse Burger number). The transcritical regime in which the Froude number F, the ratio of the flow speed to the interfacial gravity wave speed, is close to unity is considered in the shallow-water (small-aspect-ratio) limit. For weakly rotating flow over a small isolated obstacle (M → 0) a similarity theory is developed in which the behaviour is shown to depend on the parameters Γ = (F−1)M−2/3 and ν = B1/2M−1/3. The flow pattern in this regime is determined by a nonlinear equation in which Γ and ν appear explicitly, termed here the ‘rotating transcritical small-disturbance equation’ (rTSD equation, following the analogy with compressible gasdynamics). The rTSD equation is forced by ‘equivalent aerofoil’ boundary conditions specific to each obstacle. Several qualitatively new flow behaviours are exhibited, and the parameter reduction afforded by the theory allows a (Γ, ν) regime diagram describing these behaviours to be constructed numerically. One important result is that, in a supercritical oncoming flow in the presence of sufficient rotation (ν ≳ 2), hydraulic jumps can appear downstream of the obstacle even in the absence of an upstream jump. Rotation is found to have the general effect of increasing the amplitude of any existing downstream hydraulic jumps and reducing the lateral extent and amplitude of upstream jumps. Numerical results are compared with results from a shock-capturing shallow-water model, and the (Γ, ν) regime diagram is found to give good qualitative and quantitative predictions of flow patterns at finite obstacle height (at least for M ≲ 0.4). Results are compared and contrasted with those for a two-dimensional obstacle or ridge, for which rotation also causes hydraulic jumps to form downstream of the obstacle and acts to attenuate upstream jumps.

POINTWISE AND UPWIND DISCRETIZATIONS OF SOURCE TERMS IN OPEN-CHANNEL FLOOD ROUTING

Upwind algorithms are becoming progressively popular for river flood routing due to their capability of resolving trans-critical flow regimes. For consistency, these algorithms suggest natural upwind discretization of the source term, which may be essential for natural channels with irregular geometry. Yet applications of these upwind algorithms to natural river flows are rare, and in such applications the traditional and simpler pointwise, rather than upwind discretization of the source term is used. Within the framework of a first-order upwind algorithm, this paper presents a comparison of upwind and pointwise discretizations of the source term. Numerical simulations were carried out for a selected irregular channel comprising a pool-riffle sequence in the River Lune, England with observed data. It is shown that the impact of pointwise discretization, compared to the upwind, is appreciable mainly in flow zones with the Froude number closer to or larger than unity. The discrepancy due to pointwise and upwind discretizations of the source term is negligible in flow depth and hence in water surface elevation, but well manifested in mean velocity and derived flow quantities. Also the occurrence of flow reversal and equalisation over the pool-riffle sequence in response to increasing discharges is demonstrated.

A Series-Solution Method for Free-Boundary Problems Arising from Flow Over Topography

An analytical series method is presented for steady, two-dimensional, irrotational flow of a single layer of constant-density fluid over topography. This problem is formulated as a Laplacian free-boundary problem with fully nonlinear boundary conditions. The method is an iterative scheme that allows the calculation of analytical series solutions for supercritical, transcritical and subcritical flow regimes over arbitrary topography. By an appropriate choice of the free-boundary representation, exponential convergence of the series solution is achieved. With this accuracy, the issue of apparent dual transcritical/subcritical solutions previously obtained by boundary-integral-equation methods (BIEM) is resolved. Results are compared with solutions previously obtained using BIEM, and solutions are presented for flow over asymmetric and arbitrarily shaped obstacles.

Planar laser-induced fluorescence of OH in high-pressure cryogenic LOx/GH 2 jet flames

This article deals with the application of OH planar laser-induced fluorescence (PLIF) to the study of high-pressure cryogenic flames ( p = 6.3 MPa ) . It is shown that this optical diagnostic provides good-quality data and can be used to examine the flame structure in the injector near-field. High-pressure conditions require a careful choice of excitation wavelength based on a detailed analysis of the absorption coefficient dependence on pressure and temperature. It is particularly important to consider line-broadening and central-frequency-shifting effects induced by high-pressure operation. PLIF is used to examine jet flames formed by a single coaxial injector fed by liquid oxygen and gaseous hydrogen (LOx/GH 2) in subcritical and transcritical regimes. In the latter case, the liquid oxygen temperature is below its critical value while its pressure is above critical ( T LOx = 85 K < T c ( O 2 ) = 150 K , p LOx = 6.3 MPa > p c ( O 2 ) = 5.04 MPa ). Such transcritical conditions prevail in many high-performance devices such as liquid-propellant rocket engines. A detailed understanding of this type of combustion is necessary to the development of improved and more reliable propulsion systems. PLIF provides images that may be considered to represent instantaneous distributions of OH radicals and may be used to infer the structure and position of the flame. An optical multichannel analyzer is also used in the experiments to ensure that the detected signals have the expected spectral features. Fluorescence spectra are also compared with emission spectra synthesized with Lifbase in terms of line positions and broadening. Mean flame positions deduced from PLIF images are shown to nearly match those deduced from the Abel transformed average OH * light-emission distributions. The difference is related to a biased estimate of the flame position resulting from the Abel transformed emission data. PLIF is also used to examine the flame edge. It is known from a previous analysis of the flame-holding mechanism that the low-speed wake established just behind the oxygen injector lip and generated by the two propellants must be thicker than the flame-edge thickness to ensure stable anchoring. PLIF images indicate that the flame thickness is on the order of the wake transverse size. When the thickness exceeds this transverse dimension it is found that the flame becomes sensitive to the high-speed hydrogen stream. Finally, the instantaneous PLIF images of OH included in this article may serve as a guide to current efforts directed at the large-eddy simulation of transcritical combustion.

Transport and dynamics of liquid oxygen droplets in supercritical hydrogen streams

The transport and dynamics of an isolated liquid oxygen (LOX) droplet in a supercritical hydrogen stream has been numerically studied based on the complete conservation equations in axisymmetric coordinates. The approach employs a unified treatment of general fluid thermodynamics and transport, and accommodates rapid variations of fluid properties in the transcritical regime. Surface tension of the droplet is ignored in consistency with the supercritical thermodynamic condition. The analysis allows for a systematic investigation into droplet behaviour over broad ranges of fluid thermodynamic states and ambient flow conditions. Detailed flow structures and transport phenomena are examined to reveal various key mechanisms underlying droplet vaporization in a supercritical forced convective environment. In addition, correlations of droplet lifetime and drag coefficient are established in terms of fluid properties, pressure, and free-stream Reynolds number.

On the sensitivity of dynamo action to the system’s magnetic diffusivity

An experiment at the Karlsruhe dynamo test facility has shown that the intensity of the dynamo magnetic field decreases significantly with increasing temperature of the test fluid, liquid sodium, while keeping the other control parameters constant. This is explained by the increasing magnetic diffusivity with increasing temperatures utilizing results from a weakly nonlinear analysis of Tilgner and Busse [“Saturation mechanism in a model of the Karlsruhe dynamo,” in Dynamo and Dynamics, a Mathematical Challenge, NATO Science Series, II. Mathematics, Physics and Chemistry, Vol. 26, edited by P. Chossat, D. Armbruster, and I. Oprea (Kluwer, Dordrecht, 2001)] for the transcritical regime of the Karlsruhe dynamo experiment. The observations are also interpreted by dimensional reasoning utilizing previous experimental results.

Mutual interference on transition of wake of circular cylinder

An experimental investigation was carried out in the very near wake of a circular cylinder over the Reynolds number range of 260&amp;lt;Re&amp;lt;1.8×103. The aspect ratio of the cylinder was 4. The present study concerns the regular shedding mode of the wake, in which the large-scale primary vortex sheet and the small-scale individual and pairing secondary vortices are present. Based on a new conditionally sampling technique, there is mutual interference between the high-energy small-scale secondary vortices and the development of large-scale primary vortex sheet and of the strain field of primary vortex sheet on individual secondary vortices. The pairing vortices, however, do not significantly affect the large-scale vortices. In the transition regimes within this low Reynolds number range, in which transition of two-dimensional large-scale primary vortices to three dimensionality occurs, the disturbances of the individual and pairing secondary vortices excite the separated shear layer at the most amplified mode. Coupled with mutual interference, they play an important role in the transition. Correlation with the available and additional results in the upper transition regime and in the supercritical and transcritical regimes suggests the same mechanism of transition. The mutual interference of different types of vortices in the very near wake is the key factor for transition.

A unified treatment of general fluid thermodynamics and its application to a preconditioning scheme

A unified treatment of general fluid thermodynamics is developed to handle fluid flows over their entire thermodynamic states. The analysis is based on the concepts of partial-mass and partial-density properties, and accommodates thermodynamic non-idealities and transport anomalies in the transcritical regime. The resultant routine is incorporated into a preconditioning scheme. All the thermophysical properties and numerical Jacobian matrices are derived directly from fundamental thermodynamic theories, rendering a robust algorithm valid for fluid flows at all speeds and at all thermodynamic states. As a specific example, a modified Soave–Redlich–Kwong equation of state is employed to obtain the fluid p– V– T properties. Several test cases concerning supercritical droplet vaporization in both quiescent and convective environments are presented to demonstrate the effectiveness of the present algorithm.

Transcritical vaporization of a liquid fuel droplet in a supercritical ambient

The transcritical vaporization of a fuel drop placed in supercritical ambient is reported. A detailed model based on the numerical solution of the time-dependent conservation equations for both liquid and gas phase is employed. The equations are solved using an arbitrary Lagrangian-Eulerian procedure, which allows a dynamically adaptive mesh to analyze interfacial time-history effects, and a comprehensive thermodynamic model that accounts for the variation of thermotransport properties and the gas-phase nonidealities in the transcritical regime. The transcritical vaporization behavior is shown to be characterized by two parameters. One is the minimum pressure ( P min ) required for the drop surface to reach the critical mixing state, and the other is the time ratio parameter ( t r ), which is the ratio of the time to attain critical mixing state to the drop lifetime. For pressures below P min , the droplet undergoes subcritical vaporization ( t r =1), characterized by a distinct liquid-gas interface whose regression rate is determined by the gas-phase mass diffusivity and the difference between fuel vapor concentrations at the surface and in the ambient. For pressures above P min , the droplet undergoes transcritical vaporization, i.e., it attains the critical mixing state sometime during its lifetime. The instant at which the critical mixing state is reached determines t r . The subsequent surface regression or "supercritical vaporization" rate is given by the inward velocity of the critical surface, which is determined by the gas-phase thermal diffusivity and the difference between critical mixing temperature and liquid temperature in the droplet interior. While both the subcritical and supercritical vaporization rates are enhanced as the pressure is increased, the latter is consistently higher than the former. The effects of ambient temperature and initial drop size on P min and t r are quantified. The parameter P min shows a strong dependence on ambient temperature ( T ∞ ), decreasing rapidly as T ∞ increases, but a weak dependence on drop size. The parameter t r is strongly sensitive to ambient temperature, pressure, and droplet size. It decreases as ambient temperature and pressure are increased, and as drop size is decreased.

RE technology update

Dimples on the golf ball have significant effect on its aerodynamic properties as well as the flight trajectory. The aerodynamic of golf ball is still not fully understood in spite of a significant number of published data in the open literature. Most studies were conducted using the wind tunnel testing and Computational Fluid Dynamics (CFD) simulation. This paper examines the aerodynamic effect of dimple depth on golf balls. 3D printing technology was used to manufacture 11 balls with varied dimple depth. RMIT Aero Wind Tunnel was used to measure the drag forces over a range of wind speeds. It was found that the drag coefficient of golf ball varied significantly due to varied dimple geometry. The results indicate that the increase of the dimple depth ratio or surface roughness of the golf ball can shift the transition to a lower Reynolds number and increase the drag coefficient in transcritical regime. The results also established a positive linear correlation between relative roughness and drag coefficient.

INVESTIGATION OF BREAKUP OF TURBULENT CRYOGENIC VARIABLE-DENSITY JETS

This article summarizes recent results of research on the breakup of turbulent liquid jets. The research focuses on observations of atomization phenomena of cryogenic variable-density jets at various back pressures and injection velocities. The experiments used liquid nitrogen (LN2) as simulation fluid for single-component and LN2/He for binary-component injection studies. The theoreticl assessments show that for binary and multicomponent systems a transcritical region exists where surface tension is present even at pressures above the critical pressure as long as the critical mixing temperature is not exceeded. An important finding is that when approaching the critical point (transcritical regime), capillary forces decrease and a principal change of the atomization mechanism indicated by the change of jet contour length scales and ligaments sizes takes place. A discussion of the transcritical jet breakup regime with regard to classical regimes is presented.

Across-wind aerodynamic parameters of tall chimneys with circular cross section—a new empirical model

The prediction of across-wind response of circular cylinders remains a challenging task, despite extensive research efforts. An attempt has been made to correlate the rms lift coefficient due only to vortex shedding, C′ L,VS both in wind tunnel and full-scale conditions by separating the local rms lift coefficient, C′ L, into two components, one due to the lateral turbulence and the other due to the vortex shedding. Based on the literature, and also using test results measured by the authors, it is found that the final value of C′ L,V, as discussed in the paper, show a mean value of 0.089 with a coefficient of variation of 18%, independent of Reynolds number regime. The above value plus 1.66 times the standard deviation gives a value of 0.115 which is in excellent agreement with the value of C′ L,VS=0.12 recommended for design of chimneys under open terrain conditions, as per the Indian Standard Code of Practice: IS: 4998 Part-2, 1992. Further it is shown that the Griffin universal Strouhal number, G attains a mean value of 0.065 with a coefficient of variation (cov) of 8%, independent of sub-critical and trans-critical Reynolds number regime.

Mesoscale Simulation of Supercritical, Subcritical, and Transcritical Flow along Coastal Topography

Abstract A mesoscale atmospheric model is used to address the characteristics of stratified flow bounded by a side wall along a varying coastline. Initial Froude number values are varied through alteration of marine inversion strength, permitting examination of supercritical, subcritical, and transcritical flow regimes encountering several coastal configurations. Consistent with shallow water models, sharp drops in boundary layer depth and flow acceleration occur in flow rounding convex bends; however, significant flow response occurs in the stratified layer aloft, which is unexplained by conventional shallow water theory. The strongest flow acceleration occurs in the transcritical case while, regardless of inversion strength, the deformation of the isentropes aloft shows general structural similarity. Advection of horizontal momentum is an important component of the horizontal force balance. A simulation having several coastline bends exhibits a detached, oblique hydraulic jump upwind of a concave bend t...

Vortex interaction in the formation region of a grooved circular cylinder

Based on the conditional sampling technique, the present study in the formation region of the flow over a partially grooved circular cylinder of smooth half and groove half of θ g=+90° over a Reynolds number range of 7.7×10 3–1.3×10 5 establishes the presence of the Gerrard–Bloor secondary vortices in the subcritical, critical, supercritical and transcritical regimes of a smooth cylinder. Quantitatively, there is evidence of mutual interaction of the primary vortex sheet and the secondary vortices. Due to the presence of the secondary vortices, the development of the primary vortex sheet is affected, depending on the energy of the small-scale vortices. The effect of the primary vortex sheet is to enhance the development of the secondary vortices under its strain field. The degree of mutual interaction depends on the energy of the secondary vortices. The present findings on the small-scale streamwise wake vortices on the groove half also indicate similar phenomena.