Investigation of the optimum longitudinal mixing regime in an isothermal chemical flow reactor

A one-dimensional isothermal flow reactor with longitudinal mixing is examined. The known asymptotic results are analyzed and used as a basis for formulating the conditions and initial values of the parameters for a numerical investigation by the parameter mapping method. The object of the investigation is to construct the exact boundaries of the regions of variation of the characteristic parameters in which the maximum extent of reaction is achieved in one of the limiting (Pe=0 and Pe=) or intermediate (0相似文献   

Operating regimes of a chemical reactor with longitudinal and transverse mixing in the case of large Péclet numbers

A two-dimensional model of a chemical reactor with longitudinal and transverse mixing is investigated in the case of large Péclet numbers calculated from the effective thermal conductivity in the transverse direction. For this model the existence of at least one steady-state regime has been demonstrated [1], sufficient criteria of its uniqueness have been determined, an asymptotic expansion of the solution has been constructed in the case of small Péclet numbers, and the critical ignition and quenching parameters have been found. In this paper the other limiting case of the model, in which heat is propagated in the transverse direction much more slowly than it is transported by the flow along the reactor (large Péclet numbers), is analyzed in detail. An asymptotic expansion of the solution which closely coincides with the data of numerical calculations is constructed. The critical quenching and ignition conditions of the process are determined.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 120–127, January–February, 1987.     

Consecutive chemical reactions in a turbular reactor with turbulent flow

Homogeneous consecutive chemical reactions in turbulent flow system is analyzed in this paper. Arbitrary chemical reaction order is considered. The governing nonlinear material balance equations are solved numerically on a digital computer. It is seen from the preliminary numerical results that high Reynolds and Schmidt numbers significantly increase both reaction velocities.Nomenclature c _i concentration of i species, g. mole/cm³ - C _i dimensionless concentration of i species, c _i /c _A0 - c _A0 inlet concentration of A, g. mole/cm³ - D _i molecular diffusivity of i species, cm²/sec. - f Fanning friction factor - k ₁ first reaction rate coefficient, (g. mole/cm³)^1–m /sec. - k ₂ second reaction rate coefficient, (g. mole/cm³)^1–n /sec. - K ₁ dimensionless first reaction rate coefficient, k ₁ r ₀ ² c _A0 ^–1 /D _A - K ₂ dimensionless second reaction rate coefficient, k ₂ r ₀ ² c _A0 ^–1 /D _A - m order of the first chemical reaction - n order of the second chemical reaction - r radial distance, cm - r ₀ reactor radius, cm - R dimensionless radial distance, r/r ₀ - Re Reynolds number, r ₀ / - Sc Schmidt number, D/ - u local velocity, cm - bulk velocity, cm - U dimensionless local velocity, u/ - X, Y dimensionless concentrations of A and B, c _i /c _A 0 - xxx0058;, xxx0059; dimensionless bulk concentrations of A and B - z axial distance, cm - Z dimensionless axial distance, zD _A /r ₀ ² - ratio of eddy mass diffusivity to eddy viscosity, / - eddy mass diffusivity, cm²/sec. - kinematic viscosity, cm²/sec.     

The low Reynolds number turbulent flow and mixing in a confined impinging jet reactor

Turbulent mixing takes an important role in chemical engineering, especially when the chemical reaction is fast compared to the mixing time. In this context a detailed knowledge of the flow field, the distribution of turbulent kinetic energy (TKE) and its dissipation rate is important, as these quantities are used for many mixing models. For this reason we conduct a direct numerical simulation (DNS) of a confined impinging jet reactor (CIJR) at Re = 500 and Sc = 1. The data is compared with particle image velocimetry (PIV) measurements and the basic flow features match between simulation and experiment. The DNS data is analysed and it is shown that the flow is dominated by a stable vortex in the main mixing duct. High intensities of turbulent kinetic energy and dissipation are found in the impingement zone which decrease rapidly towards the exit of the CIJR. In the whole CIJR the turbulence is not in equilibrium. The strong mixing in the impingement zone leads to a rapid development of a monomodal PDF. Due to the special properties of the flow field, a bimodal PDF is generated in cross-sections downstream the impingement zone, that slowly relaxes under relaminarising conditions. The time required for meso-mixing is dominating the overall mixing performance.     

Consecutive chemical reactions in an annular reactor with non-newtonian flow

The purpose of this paper is to analyze the homogeneous consecutive chemical reactions carried out in an annular reactor with non-Newtonian laminar flow. The fluids are assumed to be characterized by a Ostwald-de Waele (powerlaw) model and the reaction kinetics is considered of general order. Effects of flow pseudoplasticity, dimensionless reaction rate constants, order of reaction kinetics and ratio of inner to outer radii of reactor on the reactor performances are examined in detail.Nomenclature c _A concentration of reactant A, g.mole/cm³ - c _B concentration of reactant B, g.mole/cm³ - c _A0 inlet concentration of reactant A, g.mole/cm³ - C ₁ dimensionless concentration of A, c _A/c _A0 - C ₂ dimensionless concentration of B, c _B/c _A0 - C ₁ dimensionless bulk concentration of A - C ₂ dimensionless bulk concentration of B - D _A molecular diffusivity of A, cm²/sec - D _B molecular diffusivity of B, cm²/sec - k _A first reaction rate constant, (g.mole/cm³)^1–m /sec - k _B second reaction rate constant, (g.mole/cm³)^1–n /sec - K ₁ dimensionless first reaction rate constant, k _A r ₀ ² c _A0 ^m–1 /D _A - K ₂ dimensionless second reaction rate constant, k _B r ₀ ² c _A0 ^n–1 /D _B - K apparent viscosity, dyne(sec) ^m /cm² - m order of reaction kinetics - n order of reaction kinetics - P pressure, dyne/cm² - r radial coordinate, cm - r _i radius of inner tube, cm - r _max radius at maximum velocity, cm - r _o radius of outer tube, cm - R dimensionless radial coordinate, r/r _o - s reciprocal of rheological parameter for power-law model - u local velocity, cm/sec - u _max maximum velocity, cm/sec - u bulk velocity, cm/sec - U dimensionless velocity, u/u - z axial coordinate, cm - Z dimensionless axial coordinate, zD _A/r ₀ ² /u - ratio of molecular diffusivity, D _B/D _A - ratio of inner to outer radius of reactor, r _i/r _o - ratio of radius at maximum velocity to outer radius, r _max/r _o     

Influence of transport processes on steady regimes of a chemical flow reactor with reaction of the type a → b,a+b→2c

An approximate analytic solution is obtained to the problem of the concentration distribution in a one-dimensional chemical flow reactor for a reaction of the type A B, A + B 2C in the approximation of a weak reaction. The method of small perturbations up to terms of third order is used. A study is made of the influence of the intensity of longitudinal mixing on the degree of transformation, the selectivity, and the yield. It is found that the optimal level of longitudinal mixing in the weak reaction approxmation is determined by a dimensionless parameter that is a combination of the dimensionless rates of the chemical reactions. The dependence of the optimal Péclet number on this parameter is found. Characteristic regions are determined on the plane of the determining parameters in which the interaction of the physical and chemical processes in the reactor leads to different results, which must be taken into account when choosing the type and the parameters of a chemical reactor.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 106–113, November–December, 1982.     

The stability of steady regimes in an isothermal chemical flow reactor

One of the fundamental problems in the theory of chemical reactors is the determination of the number of steady regimes and their stability. The problem of the number of steady regimes has been considered in many studies, for example, in [1–4]. The stability of a steady regime is usually established from an analysis of the behavior of small perturbations. The corresponding linear boundary-value problem for perturbations has been studied mainly in the limiting cases of ideal mixing and ideal displacement. When account was taken of longitudinal mixing, the only criteria obtained were ones which imposed fairly severe restrictions on the parameters [5]. In the present study numerical analysis is used in order to investigate the stability of steady concentration distributions in an isothermal chemical flow reactor with longitudinal mixing in the case of a single chemical reaction. The eigenvalues were obtained for the Sturm-Liouville problem, which fully characterize the stability for several laws of variation of the chemical reaction rate as a function of the concentration. A knowledge of the eigenvalues is essential, for example, in order to construct the stabilization system proposed in [6] for the unsteady regime.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 179–182, March–April, 1985.     

Experimental realization of unstable regimes of ethanol oxidation into acetaldehyde on a copper-oxide catalyst in a chemical flow reactor

Unstable regimes of operation of a chemical reactor have been stabilized in an experiment by means of a control system with feedback. It has been shown that the concentration limits of the region of multiplicity of reactor steady states do not in general coincide with the concentration limits that can be obtained without the use of stabilizing systems.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 8–13, March–April, 1984.     

Particle mixing in a sheared granular flow

Mixing experiments were performed in a shear cell device using differently colored but otherwise identical glass spheres, with five different bottom wall velocities. The motions of the granular materials were recorded by a high-speed camera, so the development of mixing boundaries could be analyzed from the images. By continually tracking the movements of particles, the velocity, fluctuations and the granular temperatures were measured. The self-diffusion coefficients were determined from the histories of particles movements. The mixing layer thicknesses were compared with the calculations from a simple diffusion equation using the data of self-diffusion coefficients obtained from the current measurements. The calculations and experimental results showed good agreements, demonstrating that the mixing process of granular materials occurred through the diffusion mechanism.     

Wall effects on close-to-equilibrium flow in a tubular reactor

The deviation from local homogeneous chemical equilibrium flow due to non-catalytic heterogeneous reactions in a tubular reactor is analysed by an asymptotic expansion for large Damköhler numbers. Close to the reacting surface a boundary layer is shown to exist where the effects of the homogeneous and the heterogeneous reaction have an influence of the same order of magnitude. The extension of this boundary layer into the equilibrium flow is proportional to the inverse of the square root of the Damköhler number. The boundary layer equation is derived and solved for a particular example.     

Influence of jet exit conditions on mixing and statistics of flow fine structures

Mixing in a coaxial jet mixer was investigated at variable initial conditions simultaneously using PIV and PLIF methods. Velocity and concentration fields were measured at two spatial resolutions: across the mixer and in a small area at its axis resolving Kolmogorov's scale. Jet exit conditions were modeled by varying flow rate (3⋅10³ ≤ Red ≤ 1.78⋅10⁴) and by applying vortex generators (tabs) at the jet exit. The study was executed within a transition flow region. Nevertheless, it is possible to claim that in the self-similarity flow region mean flow parameters do not depend on the initial conditions but turbulence does. The influence of the initial conditions is manifested in turbulent characteristics measured at a high spatial resolution and in the size of fine structures of the studied flows.     

On the longitudinal heat flux in a Couette flow

The problem of shear motion of a gas (Couette flow) is studied. Two infinite parallel plates with temperatures T₁ and T₂ separated by the distance L each move in their own plane with velocities u₀ and -u₀, respectively. It is assumed that there is a monatomic gas between the plates. In such a formulation, the Couette problem has been considered earlier by many authors. A difference in the present paper is that it investigates the behavior of the heat flux directed along the plates. It has been found that the presence of this heat flux has a strong influence on the direction of energy transfer that is established in a Couette flow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 162–166, May–June, 1980.We are grateful to O. S. Ryzhov and A. T. Onufriev for discussions which led to the writing of the present paper.     

Experimental study on the two-phase flow pattern and transformation characteristics of a flow mixing nozzle under a moderate flow rate

Meccanica - A flow mixing nozzle can produce satisfactory atomization for heavy oil. However, the study of the internal flow pattern of this nozzle, along with the spray morphology and its...     

High-intensity turbulence measurements in a Taylor-Couette flow reactor

Turbulence-intensity measurements were made in a Taylor-Couette flow reactor consisting of two counter-rotating concentric cylinders designed for the purpose of studying turbulent premixed-flame propagation. In the annulus separating the two cylinders, a nearly homogeneous turbulent flow is generated. The intensities of turbulent velocity fluctuations in the annulus in both axial and circumferential directions were measured by using laser-Doppler velocimetry for a wide range of cylinder rotation rates, corresponding to low through high (120 cm/s) intensities relative to typical laminar flame speeds for lean methane-air mixtures. The experimental measurements indicate a linear relation between turbulence intensities and average cylinder surface speed and demonstrate the usefulness of the Taylor-Couette apparatus for studies of premixed-flame propagation in high-intensity turbulent flow.     

Steady states of a continuous-flow adiabatic chemical reactor

Flow reactors are widely used in the chemical industry for purposes of catalytic reactions [1,2]. Calculation of reactors of this type, even in one-dimemional approximation, is complicated and possible only with the use of numerical methods [1, 3]. Such calculations make it possible to find the steady-state distribution of temperature and concentration in the chemical reactor if one exists; in general, however, there may be other steady-state regimes which may be preferable from the standpoint of obtaining a different degree of conversion of the starting product, operating stability, etc.In this connection special interest attaches to the question of the existence and number of steady-state solutions of the system of equations describing the reactor process.This problem was previously considered in [4–7]. Thus, in [4, 5] it was pointed out that in certain special cases more than one steady-state regime may exist. In [6, 7] the question of sufficient conditions of uniqueness was investigated. In [7] it was shown that the steady-state regime is unique in the ease of short reactors or a dilute mixture of reactants. In [8] the problem of the existence and uniqueness of the steady-state regime was examined for a chain reaction model with direct application of the general theorems of functional analysis.The present paper includes an analysis of a very simple mathematical model of an adiabatic chemical reactor in which an exothermic or endothermie reaction takes place. It is established that in the case of an endothermic process a unique steady-state regime always exists. In the exothermic case the problem of the steady-state regime also always has a solution which, however, may be nonunique; the possibility of the existence of several steady-state regimes, associated with the form of the temperature dependence of the heat release rate, is substantiated.The authors thank G. I. Barenblatt, A. I. Leonov, L. M. Pis'men, and Yu. I. Kharkats for discussing and commenting on the work.