Fundamental Derivative Of Gas Dynamics Research Articles

Dense gas effect on small-scale structures of compressible isotropic turbulence

The small-scale statistics and local flow topology of compressible homogeneous isotropic turbulence of dense gas are numerically investigated with the turbulent Mach number and Taylor Reynolds number, respectively, nearly equaling 1.0 and 153.0. The initial state of the flow field is in the inversion zone, where the fundamental derivative of gas dynamics is negative. After reaching the stationary state, the flow field includes three different gas regions: a Bethe–Zel'dovich–Thompson (BZT) region, a classical dense gas (CDG) region, and a usual gas region. In the present study, the effects of different gas regions on the statistical properties of the enstrophy production term are investigated. Based on Helmholtz decomposition, it is found that the enstrophy production mainly comes from its solenoidal component. The dense gas effect reduces the production of enstrophy in the compression region and weakens the loss of enstrophy in the expansion region. Furthermore, the properties of flow topology based on the three invariants of the velocity gradient tensor are studied. The expansion region is mainly occupied by the BZT and CDG regions. In the expansion region, the dense gas effect significantly reduces the expansive vortex structure and weakens the contribution of this structure to the enstrophy loss.

Amplification of Operational Uncertainty Induced by Nonideal Flows in Supersonic Turbine Cascades

Abstract In high-temperature transcritical organic Rankine cycles (ORCs), the expansion process may take place in the neighborhood of the thermodynamic critical point. In this region, many organic fluids feature a value of the fundamental derivative of gas dynamics Γ that is less than unity. As a consequence, severe nonideal gas-dynamic effects can be possibly observed. Examples of these nonideal effects are the nonmonotonic variation of the Mach number along an isentropic expansion, oblique shocks featuring an increase of the Mach number, and a significant dependence of the flow field on the upstream total state. To tackle this latter nonideal effect, an uncertainty-quantification strategy combined with Reynolds-averaged flow simulations is devised to evaluate the turbine performance in presence of operational uncertainty. The results clearly indicate that a highly nonideal expansion process leads to an amplification of the operational uncertainty. Specifically, given an uncertainty in the order of 1% in cycle nominal conditions, the mass flow rate and cascade losses vary ±4% and ±0.75 percentage points, respectively. These variations are four and six times larger than those prompted by an ideal-like expansion process. The flow delivered to the first rotating cascade is severely altered as well, leading to local variations in the rotor incidence angle up to 10 deg. A decomposition of variance contributions reveals that the uncertainty in the upstream total temperature is mainly responsible for these variations. Finally, the understanding of the physical mechanism behind these changes allows us to generalize the present findings to other organic-fluid flows.

Analysis of turbulence characteristics in a temporal dense gas compressible mixing layer using direct numerical simulation

This study investigates the effects of a Bethe–Zel’dovich–Thompson (BZT) dense gas (FC-70) on the development of a turbulent compressible mixing layer at a convective Mach number . Three-dimensional direct numerical simulations are performed with both FC-70 and air. The initial thermodynamic state for FC-70 lies inside the inversion region where the fundamental derivative of gas dynamics ( ) becomes negative. The complex Martin–Hou thermodynamic equation of state is used to reproduce thermodynamic peculiarities of the BZT dense gas (DG). The unstable growth phase in the mixing layer development shows an increase of -turbulent stress tensors in DG compared to perfect gas (PG). The following self-similar period has been carefully defined from the time evolution of the integrated streamwise production and transport terms. During the self-similar stage, DG and PG mixing layers at display close values of the momentum thickness growth rate, which seems similarly affected by the well-known compressibility-related reduction for PG. The same mechanisms are at stake, related to the reduction of pressure–strain terms. Turbulent kinetic energy (TKE) spectra show a slower decrease of TKE at small scales for DG compared with PG. The filtered kinetic energy equation balance developed by Aluie (Physica D, vol. 247 (1), 2013, pp. 54–65) is applied for the first time to a compressible mixing layer. The equation is reshaped to better account for TKE transport across the mixing layer. This new formulation brings out the role played by , the pressure strengths power. A detailed comparison of the contributions to the filtered TKE equation is provided for both PG and DG mixing layers.

Shock interactions in two-dimensional steady flows of Bethe–Zel’dovich–Thompson fluids

The morphology of nodes generated by the interaction of discontinuities in steady two-dimensional inviscid flows is examined. The fluids considered are Bethe–Zel’dovich–Thompson (BZT) fluids, which feature negative values of the fundamental derivative of gas dynamics in the vapour phase. The operating conditions correspond to the non-classical gas-dynamic regime where expansion shocks, compression fans and composite waves are admissible in addition to the classical compression shocks and expansion fans. Interactions caused by the crossing, overtaking and splitting of compression/expansion shocks, along with the refraction of these through a contact discontinuity, are analysed here. The well-established method of wave curves is applied to non-classical wave curves, revealing a variety of interaction patterns that are simply not admissible in classical gas dynamics. It is shown that shock waves can be reflected, transmitted and refracted as Prandtl–Meyer fans or composite waves. Based on numerical evidence, the splitting (and consequently the Mach reflection) of an expansion shock seems to be disallowed. Theoretical considerations on the admissibility of such configurations are also provided. The present analysis is relevant to applications potentially involving supersonic flows of BZT fluids, e.g. organic Rankine cycle power systems, and can also be used in front-tracking algorithms for general equations of state.

Weak shock reflection in channel flows for dense gases

The canonical problem of transonic dense gas flows past two-dimensional compression/expansion ramps has recently been investigated by Kluwick & Cox (J. Fluid Mech., vol. 848, 2018, pp. 756–787). Their results are for unconfined flows and have to be supplemented with solutions of another canonical problem dealing with the reflection of disturbances from an opposing wall to finally provide a realistic picture of flows in confined geometries of practical importance. Shock reflection in dense gases for transonic flows is the problem addressed in this paper. Analytical results are presented in terms of similarity parameters associated with the fundamental derivative of gas dynamics$(\unicode[STIX]{x1D6E4})$, its derivative with respect to the density at constant entropy$(\unicode[STIX]{x1D6EC})$and the Mach number$(M)$of the upstream flow. The richer complexity of flows scenarios possible beyond classical shock reflection is demonstrated. For example: incident shocks close to normal incidence on a reflecting boundary can lead to a compound shock–wave fan reflected flow or a pure wave fan flow as well as classical flow where a compressive reflected shock attached to the reflecting boundary is observed. With incident shock angles sufficiently away from normal incidence regular reflection becomes impossible and so-called irregular reflection occurs involving a detached reflection point where an incident shock, reflected shock and a Mach stem shock which remains connected to the boundary all intersect. This triple point intersection which also includes a wave fan is known as Guderley reflection. This classical result is demonstrated to carry over to the case of dense gases. It is then finally shown that the Mach stem formed may disintegrate into a compound shock–wave fan structure generating an additional secondary upstream shock. The aim of the present study is to provide insight into flows realised, for example, in wind tunnel experiments where evidence for non-classical gas dynamic effects such as rarefaction shocks is looked for. These have been predicted theoretically by the seminal work of Thompson (Phys. Fluids, vol. 14 (9), 1971, pp. 1843–1849) but have withstood experimental detection in shock tubes so far, due to, among others, difficulties to establish purely one-dimensional flows.

Preliminary Design Method for Dense-Gas Supersonic Axial Turbine Stages

A fast preliminary design methodology for supersonic organic Rankine cycle (ORC) stator and rotor axial turbine blades with low degree of reaction is presented. First, the stator and rotor blade mean-line profiles are designed by using the two-dimensional (2D) method of characteristics (MOC), extended to gases governed by general equations of state (EOS). We focus more specifically on working fluids with medium to high molecular complexity, operating at thermodynamic conditions such that the fundamental derivative of gas dynamics Γ is lower than one in a significant portion of the flow field. For rotor blades, MOC is combined with a free-vortex method to achieve a smooth deflection of the supersonic incoming flow. A numerical approach is developed for solving the unique incidence problem in the case of gases governed by general EOS. Both stator and rotor blade geometries designed according to the inviscid MOC model are subsequently corrected to account for the development of viscous boundary layers by solving the compressible integral boundary layer equations extended to dense gases. The resulting blade designs are assessed by means of computational fluid dynamics (CFD) simulations based on a high-order finite volume solver equipped with advanced thermodynamic and transport-property models. Properly accounting for dense gas and viscous effects at an early design stage is found to improve the expected performance of ORC turbine rows significantly and delivers valuable baseline profiles for any further optimization.

Steady small-disturbance transonic dense gas flow past two-dimensional compression/expansion ramps

The behaviour of steady transonic dense gas flow is essentially governed by two non-dimensional parameters characterising the magnitude and sign of the fundamental derivative of gas dynamics ($\unicode[STIX]{x1D6E4}$) and its derivative with respect to the density at constant entropy ($\unicode[STIX]{x1D6EC}$) in the small-disturbance limit. The resulting response to external forcing is surprisingly rich and studied in detail for the canonical problem of two-dimensional flow past compression/expansion ramps.

Steady transonic dense gas flow past two‐dimensional compression/expansion ramps

AbstractThe dynamic behaviour of compressible fluids depends crucially on the curvature of isentropes in the pressure/specific volume diagram. Most conveniently this curvature is expressed in form of a non‐dimensional quantity Γ now commonly referred to as the fundamental derivative of gasdynamics, Thompson [5]. Bethe‐Zel'dovich‐Thompson (BZT) fluids have the distinguishing property that they exhibit embedded regions in the general neighbourhood of the thermodynamic critical point where Γ is negative in contrast to classical gases of low molecular complexity including perfect gases where Γ is strictly positive.The behaviour of steady transonic flows of such fluids is essentially governed by two non‐dimensional parameters: (Γ) and its derivative with respect to the density at constant entropy (Λ), Cramer and Fry [2], Kluwick [4]. The resulting response to external forcing is surprisingly rich in nonclassical phenomena such as rarefaction shocks, sonic shocks, split shocks, etc. and is studied in detail for the canonical problem of two‐dimensional flow past compression/expansion ramps. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Small-scale dynamics of dense gas compressible homogeneous isotropic turbulence

The present paper investigates the influence of dense gases governed by complex equations of state on the dynamics of homogeneous isotropic turbulence. In particular, we investigate how differences due to the complex thermodynamic behaviour and transport properties affect the small-scale structures, viscous dissipation and enstrophy generation. To this end, we carry out direct numerical simulations of the compressible Navier–Stokes equations supplemented by advanced dense gas constitutive models. The dense gas considered in the study is a heavy fluorocarbon (PP11) that is shown to exhibit an inversion zone (i.e. a region where the fundamental derivative of gas dynamics $\unicode[STIX]{x1D6E4}$ is negative) in its vapour phase, for pressures and temperatures of the order of magnitude of the critical ones. Simulations are carried out at various initial turbulent Mach numbers and for two different initial thermodynamic states, one immediately outside and the other inside the inversion zone. After investigating the influence of dense gas effects on the time evolution of mean turbulence properties, we focus on the statistical properties of turbulent structures. For that purpose we carry out an analysis in the plane of the second and third invariant of the deviatoric strain-rate tensor. The analysis shows a weakening of compressive structures and an enhancement of expanding ones. Strong expansion regions are found to be mostly populated by non-focal convergence structures typical of strong compression regions, in contrast with the perfect gas that is dominated by eddy-like structures. Additionally, the contribution of non-focal expanding structures to the dilatational dissipation is comparable to that of compressed structures. This is due to the occurrence of steep expansion fronts and possibly of expansion shocklets which contribute to enstrophy generation in strong expansion regions and that counterbalance enstrophy destruction by means of the eddy-like structures.

Assessment of grid adaptation criteria for steady, two-dimensional, inviscid flows in non-ideal compressible fluids

Two-dimensional simulations are carried out to assess standard grid adaptation criteria, widely used for ideal flows, for steady inviscid flows in the proximity of the liquid-vapor saturation curve, where non-ideal compressible-fluid behavior is expected. A van der Waals fluid description of the thermodynamic properties is assumed to account for non-ideal effects at least qualitatively. Nitrogen under-expanded nozzle jets are chosen as the reference flow to assess different adaptation criteria. Isotropic and anisotropic error estimators based on the derivatives of flow variables prove to be suitable to capture the rarefaction, the reflected shock and the constant-pressure jet boundary. Both density and Mach-based estimators are found to be very suitable to drive grid adaptation in the non-ideal compressible-fluid regime, which is characterized by large fluid compressibility. Then, similar adaptation criteria are used to simulate under-expanded nozzle jets of the siloxane MDM, a high molecular complexity fluid for which the van der Waals model predicts the existence of a thermodynamic region where the fundamental derivative of gasdynamics has values less than one. In this region, Mach number estimators prove to be more effective because of the non-ideal dependence of the speed of sound on the density and the temperature.

Non-Ideal Compressible Fluid Dynamics: A Challenge for Theory

The possibility that compression as well as rarefaction shocks may form in single phase vapours was envisaged first by Bethe (1942). However calculations based on the Van der Waals equation of state indicated that the latter type of shock is possible only if the specific heat at constant volume cv divided by the universal gas constant R is larger than about 17.5 which he considered too large to be satisfied by real fluids. This conclusion was contested by Thompson (1971) who showed that the type of shock capable of forming in arbitrary fluids is determined by the sign of the thermodynamic quantityto which he referred to as fundamental derivative of gas dynamics. Here v, p, s and c denote the specific volume, the pressure, the entropy and the speed of sound. Thompson and co-workers also showed that the required condition for the existence of rarefaction shocks, that Γ may take on negative values, is indeed satisfied for a number of hydrocarbon and fluorocarbon vapours. This finding spawned a burst of theoretical studies elaborating on the unusual and often counterintuitive behaviour of shocks with rarefaction shocks present. These produced both results of theoretical character but also results suggesting the practical importance of Non-Ideal Compressible Fluid Dynamics in general. The present paper addresses some of the challenges encountered in connection with the theoretical treatment of the associated flow behaviour. Weakly nonlinear acoustic waves of finite amplitude serve as a starting point. Here mixed rather than strictly positive nonlinearity generates a wealth of phenomena not possible in perfect gases. Examples of steady flows where these non-classical effects play a decisive role (and which may be useful also for future experimental work) are quasi one-dimensional nozzle flows and transonic two-dimensional flows past corners. The study of viscous effects concentrates on laminar flows of boundary layer type. Here non-classical phenomena are caused by the uncommon smallness of the Eckert number but also by the unconventional Mach number dependence on p in the external inviscid flow region.

1st International Seminar on Non-Ideal Compressible-Fluid Dynamics for Propulsion & Power

1st International Seminar on Non-Ideal Compressible-Fluid Dynamics for Propulsion & Power

Non-classical gas dynamics of vapour mixtures

AbstractThe non-classical gas dynamics of binary mixtures of organic fluids in the vapour phase is investigated for the first time. A predictive thermodynamic model is used to compute the relevant mixture properties, including its critical point coordinates and the local value of the fundamental derivative of gas dynamics $\Gamma $. The considered model is the improved Peng–Robinson Stryjek–Vera cubic equation of state, complemented by the Wong–Sandler mixing rules. A finite thermodynamic region is found where the nonlinearity parameter $\Gamma $ is negative and therefore non-classical gas dynamics phenomena are admissible. A non-monotone dependence of $\Gamma $ on the mixture composition is observed in the case of binary mixtures of siloxane and perfluorocarbon fluids, with the minimum value of $\Gamma $ in the mixture being always larger than that of its more complex component. The observed dependence indicates that non-ideal mixing has a strong influence on the gas dynamics behaviour, either classical or non-classical, of the mixture. Numerical experiments of the supersonic expansion of a mixture flow around a sharp corner show the transition from the classical configuration, exhibiting an isentropic rarefaction fan centred at the expansion corner, to non-classical ones, including mixed expansion waves and rarefaction shock waves, if the mixture composition is changed.

On the fundamental derivative of gas dynamics in the vapor–liquid critical region of single-component typical fluids

This document describes the results of an investigation on the variation of the so-called fundamental derivative of gas dynamics, Γ, in the vapor–liquid critical region of well-measured substances, namely methane, carbon dioxide and water, for which accurate, scaled fundamental equations are available. The results demonstrate that for a pure fluid in the single-phase thermodynamic regime, Γ diverges to +∞ independent of the direction of approach of the vapor–liquid critical point. Furthermore, in the two-phase thermodynamic regime, Γ diverges to −∞ independent of the direction of approach of the vapor–liquid critical point. These two qualitative results, as well as the value of the exponent giving the power-law dependence of Γ along the critical isochore as a function of |T−TC|/T (T is the temperature and “C” indicates its critical point value), namely ≈−0.89, are similar for all pure, non-ionized fluids belonging to the class of 3-dimensional Ising-like systems, i.e., systems governed by short-range forces.

Pure saturated gases with predicted negative fundamental derivative of gas dynamics

The fundamental derivative of gas dynamics is a purely thermodynamic property associated with the analysis of detonation processes and shock waves. A fluid with negative value of this derivative, called a BZT (Bethe, Zel’dovich, and Thompson) fluid, would present rarefaction shock waves. Also, close to conditions in which in the fundamental derivative of gas dynamics is equal to zero, entropy losses are small, potentially leading to improved efficiency in turbomachinery. The experimental evidence that BZT fluids exist is disputed, but published calculations based on equations of state (EOS) predict their existence. Here, calculations with more than 1800 pure substances using the original Peng–Robinson EOS, in its modified form known as PR78, and the Patel–Teja–Valderrama EOS have initially identified 185 organic substances with negative or near-zero, positive minimum value of the fundamental derivative of gas dynamics. The effect of uncertainties in critical properties and acentric factors on the predicted fundamental derivative of gas dynamics has also been evaluated.

Shock regularization in dense gases by viscous–inviscid interactions

Transonic high-Reynolds-number flows through channels which are so narrow that the classical boundary-layer approach fails locally are considered in the presence of a weak stationary normal shock. As a consequence, the properties of the inviscid core and the viscosity-dominated boundary-layer region can no longer be determined in subsequent steps but have to be calculated simultaneously in a small interaction region. Under the requirement that the core-region flow should be considered to be one-dimensional to the leading order the resulting problem of shock–boundary-layer interaction is formulated by the means of matched asymptotic expansions for laminar flows of dense gases (Bethe–Zel'dovich–Thompson, or BZT, fluids). Such fluids have the distinguishing feature that the fundamental derivative of gas dynamics can become negative or even change sign under the thermodynamic conditions to be considered. The regularizing properties of the mechanism of viscous–inviscid interactions on the different anomalous shock forms possible in the flow of dense gases with mixed nonlinearity, namely rarefaction, sonic, double-sonic and split shocks, will be discussed. To this end we show the consistency of the resulting internal-shock profiles because of strong shock–boundary-layer interaction with a generalized shock admissibility criterion formulated for the case of purely inviscid flows. Representative solutions for the internal-shock structures are presented, and the importance of such flow phenomena in technical applications in the near future are shortly discussed by considering estimates of the actual dimensions of the interaction region for a specific representative situation in which the BZT fluid PP10 (C13F22) has been selected.

Erratum to "On the computation of the fundamental derivative of gas dynamics using equations of state"

The value of the fundamental derivative of gas dynamics, Γ, is a quantitative measure of the variation of the speed of sound with respect to density in isentropic transformations, such as those occurring, for example, in gas-dynamic nozzles. The accurate computation of its value, which is a constant for a perfect gas, is key to the understanding of real-gas flows occurring in a thermodynamic region where the polytropic ideal gas law does not hold. The fundamental derivative of gas dynamics is a secondary thermodynamic property and so far, no experiments have been conducted with the aim of measuring its value. Several studies document the estimation of Γ for fluids composed of complex molecules using mainly simple thermodynamic equations of state, e.g., that of Van der Waals. A review of these studies has revealed that the calculated values of Γ are affected by large uncertainties; these uncertainties are due to the functional form of the adopted equations and because of uncertainties in the available fluid property data on which these equations were fitted. In this work, the fundamental derivative of gas dynamics of molecularly simple fluids is computed with the aid of, among other models, modern reference equations of state. The accuracy of these computations has been assessed. Reference thermodynamic models however, are not available for molecularly complex fluids; some of these molecularly complex fluids are the substances of interest in studies on the so-called nonclassical gas dynamics. Therefore, results of the computation of Γ for few, molecularly simple hydrocarbons, like methane, ethane, etc., are used as a benchmark against which the performance of simpler equations of state, can be assessed. For the selected substances, the Peng-Robinson, Stryjek-Vera modified, cubic equation of state yields good results for Γ-predictions, while the modern multiparameter technical equations of state, e.g., the one in the Span-Wagner functional form, are preferable, provided that enough accurate thermodynamic data are available. Another notable result of this study, is that Γ for a fluid composed of complex molecules is less affected by the inaccuracy of C 1 ,-information (C 1 , is the isochoric heat capacity), if compared to the estimation of Γ for simple molecules. Inspection of the results of the calculation of Γ in the proximity of the critical point confirms that analytical equations of state fail to predict the correct physical behavior, even if they include terms which allow for the correct estimation of thermodynamic properties.

On the computation of the fundamental derivative of gas dynamics using equations of state

The value of the fundamental derivative of gas dynamics, Γ , is a quantitative measure of the variation of the speed of sound with respect to density in isentropic transformations, such as those occurring, for example, in gas-dynamic nozzles. The accurate computation of its value, which is a constant for a perfect gas, is key to the understanding of real-gas flows occurring in a thermodynamic region where the polytropic ideal gas law does not hold. The fundamental derivative of gas dynamics is a secondary thermodynamic property and so far, no experiments have been conducted with the aim of measuring its value. Several studies document the estimation of Γ for fluids composed of complex molecules using mainly simple thermodynamic equations of state, e.g., that of Van der Waals. A review of these studies has revealed that the calculated values of Γ are affected by large uncertainties; these uncertainties are due to the functional form of the adopted equations and because of uncertainties in the available fluid property data on which these equations were fitted. In this work, the fundamental derivative of gas dynamics of molecularly simple fluids is computed with the aid of, among other models, modern reference equations of state. The accuracy of these computations has been assessed. Reference thermodynamic models however, are not available for molecularly complex fluids; some of these molecularly complex fluids are the substances of interest in studies on the so-called nonclassical gas dynamics. Therefore, results of the computation of Γ for few, molecularly simple hydrocarbons, like methane, ethane, etc., are used as a benchmark against which the performance of simpler equations of state, can be assessed. For the selected substances, the Peng–Robinson, Stryjek–Vera modified, cubic equation of state yields good results for Γ -predictions, while the modern multiparameter technical equations of state, e.g., the one in the Span–Wagner functional form, are preferable, provided that enough accurate thermodynamic data are available. Another notable result of this study, is that Γ for a fluid composed of complex molecules is less affected by the inaccuracy of C v -information ( C v is the isochoric heat capacity), if compared to the estimation of Γ for simple molecules. Inspection of the results of the calculation of Γ in the proximity of the critical point confirms that analytical equations of state fail to predict the correct physical behavior, even if they include terms which allow for the correct estimation of thermodynamic properties.

Transonic flows of dense gases over finite wings

Transonic inviscid flows of dense gases of the Bethe–Zel’dovich–Thompson (BZT) type over finite wings are numerically investigated. BZT gases are fluids of the retrograde type (i.e., that superheat when expanded), which exhibit a region of negative values of the fundamental derivative of gas dynamics Γ. As a consequence, they display, in the transonic and supersonic regime, nonclassical gas dynamic behaviors, such as rarefaction shock waves and mixed shock/fan waves. The peculiar properties of BZT fluids have received increased interest in recent years because of their possible application in energy-conversion cycles. The present research aims at providing insight about the transonic aerodynamics of BZT fluids past finite wings, roughly representative of isolated turbine blades with infinite tip leakage. This represents an important step toward the design of advanced turbine blades by using organic working fluids. An investigation of the flow patterns and aerodynamic performance for several choices of the...

Dense Gas Thermodynamic Properties of Single and Multicomponent Fluids for Fluid Dynamics Simulations

The use of dense gases in many technological fields requires modern fluid dynamic solvers capable of treating the thermodynamic regions where the ideal gas approximation does not apply. Moreover, in some high molecular fluids, nonclassical fluid dynamic effects appearing in those regions could be exploited to obtain more efficient processes. This work presents the procedures for obtaining nonconventional thermodynamic properties needed by up to date computer flow solvers. Complex equations of state for pure fluids and mixtures are treated. Validation of sound speed estimates and calculations of the fundamental derivative of gas dynamics Γ are shown for several fluids and particularly for Siloxanes, a class of fluids that can be used as working media in high-temperature organic Rankine cycles. Some of these fluids have negative Γ regions if thermodynamic properties are calculated with the implemented modified Peng-Robinson thermodynamic model. Results of flow simulations of one-dimensional channel and two-dimensional turbine cascades will be presented in upcoming publications.