Thermal dynamics of a distributed parameter nonadiabatic humidification process

Stewart, Richard R.; Bruley, Duane F.

doi:10.1002/aic.690130437

Cited by 2 publications

(1 citation statement)

References 2 publications

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“…The following four systems of simultaneous equations were derived after finite diff erencing Equations (13), (14), (15), and (16) and including boundary conditions at the centerline, gas-liquid interface and the wall. The gas and liquid phase subscripts g and I are omitted.…”

Section: Systems Of Simultaneous Equationsmentioning

confidence: 99%

Process dynamics of distributed parameter counterflow systems in laminar flow

Stewart

Bruley

1969

AIChE Journal

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Many studies dealing with the process dynamics of distributed parameter counterflow systems have been reported in the literature. Nearly all of the investigators have considered counterflow systems whose dynamic performance can be described mathematically by a partial differential equation having only two independent variables. For example, in previous studies of double pipe heat exchanger dynamics (11, 12) an accurate mathematical description of the system was obtained with time and axial position as the independent variables. As a result of these and other studies, methods of extracting the theoretical process dynamics from mathematical models of distributed parameter counterflow systems having time and a single space dimension as independent variables are well known.Several papers dealing with steady state solutions of countercurrent laminar flow problems have been reported. Nunge and Gill (10) presented a separation of variables solution for a laminar counterflow double-pipe heat exchanger at steady state. Their solution required a convergent series in both positive and negative eigenvalues in order to satisfy the split boundary conditions. The negative set of eigenvalues occurs because one of the fluid velocities is negative with respect to a fixed coordinate system. The split boundary conditions occur because the axial position boundary conditions are usually known at the fluid inlets which are at opposite ends of the system. The eigenvalues for this steady state case were evaluated numerically using an iterative integration procedure.In the present study of an unsteady state case, Laplace transformed energy balance equations result which are similar in form to the energy balance equations for the steady state case, for example, Equations ( 3 ) and (6) herein. However, these transformed equations for the unsteady state case contain an additional term which includes the Laplace transform variable, s, as a parameter. Because the steady state solution of Nunge and Gill involved a numerical integration step to determine the eigenvalues and because the complex parameter, s, complicates the unsteady state equations, the direct transfer function substitution method (2, 3) and the use of a completely numerical solution was chosen for the unsteady state equations.Completely numerical solutions for the steady ,state case have been reported, also by Nunge and Gill (9). Their numerical procedure was a modification of the work of King (6). The present study extends the method of King, as modified by Nunge and Gill, to the unsteady state case.The present study is concerned with mathematical modeling and theoretical calculation of process dynamics for distributed parameter counterflow systems which require two space variables and time for an accurate mathematical description. Most distributed parameter counterflow heat and mass transfer systems having radially dependent velocity, temperature, and/or concentration profiles fall into this category.A wetted wall column using air and water in countercurrent laminar flow was s...

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Section: Systems Of Simultaneous Equationsmentioning

confidence: 99%

Process dynamics of distributed parameter counterflow systems in laminar flow

Stewart

Bruley

1969

AIChE Journal

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Distributed‐Parameter dynamics by correlation analysis

Ledbetter

Bruley

1972

AIChE Journal

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1. Brown, D. E.;and K. Pitt, paper presented at CHEMECA, 2. Calderbank, P. H., Trans. Inst. Chem. Engrs., 36, 443 3. Chen, H. T., and S . Middleman, AlChE J., 13, 989 (1967). 4. Collins, S. B., Ph.D. thesis, Oregon St., Univ., Corvallis (1967). 5. Doulah, M. S., and J. D. Thornton, paper presented atThe experimental dynamic response of a distributed-parameter, simultaneous heat and mass transfer system was investigated using correlation analysis. The system was a wetted-wall column operating as a nonadiabatic humidifier with both liquid and gas phases in turbulent flow.The experimental frequency response results were compared t o the values predicted by an existing mathematical model. The investigation also included a study of the effect of employing forcing functions having nonideal power spectra. Analog-simulated, first-order systems were tested to verify the computational procedure and to support the conclusions for the humidification system. System dynamic identifications, acceptable for most engineering purposes, were obtained from forcing signals having power spectra which differed significantly from ideality. For the reduction technique employed, o time-domain record of approximately 2,500 pairs of inputoutput data points was found to suffice for a satisfactory analysis. The correlation technique yielded reliable results over approximately the same range of frequencies as reported for previous pulse test studies based on a comparable forcing procedure. However, the results showed an upper frequency limit below that previously achieved by direct frequency forcing of the same system. A simple thermodynamic expression determining the infinite dilution ternary activity coefficients from the dew point isobar is presented. A flow method measuring the dew point temperature for ternary and binary isobaric systems is proposed. An analysis determining the infinite dilution ternary activity coefficients for ethanol-isopropyl alcohol-water system a t 1 atm. is illustrated.Knowledge of the infinite dilution ternary activity coefficients in the liquid phase is important for the design of distillation equipment, especially for the proper choice of solvent in distillation operation.There have been several studies for experimentally determining the activity coefficients at infinite dilution. For binary systems the useful procedure, which is based on readily obtained data such as total pressure-concentration curve ( Pz), bubble point-concentration curve (2'x) and dew point-concentration curve ( Ty, or Py), has been proposed by Carlson and Colburn (5), Redlich and Kister ( 1 3 ) , Gautreaux and Coates ( 7 ) , and Ellis and Jonah (6), and recently examined by Slocum and Dodge (15), and Kojima et al. (9, 11). K. Kojima is

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Thermal dynamics of a distributed parameter nonadiabatic humidification process

Cited by 2 publications

References 2 publications

Process dynamics of distributed parameter counterflow systems in laminar flow

Process dynamics of distributed parameter counterflow systems in laminar flow

Distributed‐Parameter dynamics by correlation analysis

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