Differential-Discrete Mathematical Model of the Recuperative Counter-Flow Heat Exchanger

2008 ◽  
Author(s):  
G. Simeunovic´ ◽  
P. Zi´tek ◽  
D. Lj. Debeljkovic´
Keyword(s):  
Mathematical Model ◽  
Heat Exchanger ◽  
Differential Equations ◽  
Power Plants ◽  
Initial Conditions ◽  
Time Lag ◽  
Experimental Investigations ◽  
Counter Flow ◽  
Real Process ◽  
Flow Heat

The heat exchangers are always constructive elements of nuclear power plants and their dynamics is very important since they introduce a significant time lag in control actions. That’s why their dynamics cannot be ignored. On the basis of the accepted and critically clarified assumptions, a linearized mathematical model of the recuperative counter flow heat exchanger has been derived, taking into account the wall dynamics. The model is based on the fundamental law of energy conservation, covers all heat accumulation storages in the process, and leads to the set of partial differential equations, which solution is not possible in closed form. In order to overcome the solution difficulties, the procedure of differential discrete modelling is applied, leading to the set of ordinary differential equations of a rather high order. These equations are transformed into the state space form suitable for the Matlab environment. The experimental investigations were made, putting some different typical input variables. Specifying the input temperatures and output variables, under the constant initial conditions, the step transient responses have been simulated and presented in graphic form for the particular positions in the heat exchanger in order to compare these results with the experimental data collected from the real process.

scholarly journals An Approximate Transfer Function Model for a Double-Pipe Counter-Flow Heat Exchanger

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4174
Author(s):  
Krzysztof Bartecki
Keyword(s):  
Heat Exchanger ◽  
Transfer Function ◽  
Differential Equations ◽  
Transfer Functions ◽  
Counter Flow ◽  
Transfer Function Matrix ◽  
Rational Transfer ◽  
Flow Heat ◽  
Double Pipe ◽  
Function Matrix

The transfer functions G(s) for different types of heat exchangers obtained from their partial differential equations usually contain some irrational components which reflect quite well their spatio-temporal dynamic properties. However, such a relatively complex mathematical representation is often not suitable for various practical applications, and some kind of approximation of the original model would be more preferable. In this paper we discuss approximate rational transfer functions G^(s) for a typical thick-walled double-pipe heat exchanger operating in the counter-flow mode. Using the semi-analytical method of lines, we transform the original partial differential equations into a set of ordinary differential equations representing N spatial sections of the exchanger, where each nth section can be described by a simple rational transfer function matrix Gn(s), n=1,2,…,N. Their proper interconnection results in the overall approximation model expressed by a rational transfer function matrix G^(s) of high order. As compared to the previously analyzed approximation model for the double-pipe parallel-flow heat exchanger which took the form of a simple, cascade interconnection of the sections, here we obtain a different connection structure which requires the use of the so-called linear fractional transformation with the Redheffer star product. Based on the resulting rational transfer function matrix G^(s), the frequency and the steady-state responses of the approximate model are compared here with those obtained from the original irrational transfer function model G(s). The presented results show: (a) the advantage of the counter-flow regime over the parallel-flow one; (b) better approximation quality for the transfer function channels with dominating heat conduction effects, as compared to the channels characterized by the transport delay associated with the heat convection.

Effectiveness-NTU Relations for Heat Exchangers With Streams Having Significant Kinetic Energy Variation

2003 ◽  
Vol 125 (2) ◽  
pp. 377-387 ◽  
Author(s):  
Gregory F. Nellis
Keyword(s):  
Heat Exchanger ◽  
Kinetic Energy ◽  
Differential Equations ◽  
Heat Exchangers ◽  
Parallel Flow ◽  
Temperature Profiles ◽  
Cryogenic Temperatures ◽  
Cold Side ◽  
Counter Flow ◽  
Flow Heat

Effectiveness-NTU equations are derived for counter and parallel-flow heat exchangers with fluids having high velocities. In this case, the change in the kinetic energy occurring within the heat exchanger will significantly affect the temperature profiles. The effectiveness is found to depend on the usual non-dimensional variables that compare the heat exchanger conductance to the hot- and cold-side capacity rates and on four additional nondimensional quantities that reflect the magnitude and distribution of the kinetic energy on the hot and cold-sides of the heat exchanger. The governing differential equations are derived, nondimensionalized, and solved analytically for the case of an exponentially distributed kinetic energy. Graphical solutions are presented and interpreted for several cases. The solutions are applied to a particular case involving high velocities within a counter-flow heat exchanger used to produce cryogenic temperatures.

PERFORMANCE ANALYSIS OF MICROCHANNEL COUNTER FLOW HEAT EXCHANGER USING DIFFERENT NANOFLUIDS

2018 ◽  
Author(s):  
Bharath P ◽  
Doddamani Hithaish ◽  
Saravanan Venkatesh ◽  
C K Umesh
Keyword(s):  
Heat Exchanger ◽  
Performance Analysis ◽  
Counter Flow ◽  
Flow Heat

scholarly journals PENGARUH SUDUT LOUVERED STRIPS TERHADAP LAJU PERPINDAHAN PANAS PADA COUNTER FLOW HEAT EXCHANGER

2011 ◽  
Vol 8 (2) ◽  
Author(s):  
Nyoman Arya Wigraha
Keyword(s):  
Heat Exchanger ◽  
Performance Ratio ◽  
Counter Flow ◽  
Tube Heat Exchanger ◽  
Plain Tube ◽  
Flow Heat

Pengaruh turbulator Louvered strips terhadap laju perpindahan kalor dan faktor gesekan aliran turbulen pada double tube heat exchanger dapat memecah (partitioning) dan mengganggu (blockage) pola streamline dari fluida yang mengalir ke saluran pipa dalam (inner tube) sehingga mengakumulasi aliran turbulensi dan meningkatkan laju perpindahan kalor dalam pipa. Louvered strips memiliki variasi sudut serang (q = 15°, 25°, 30°) yang terpasang ditengah-tengah pipa bagian dalam dan searah aliran fluida masuk. Laju aliran fluida (air) panas di bagian pipa dalam diteliti dengan interval 400 lt/jam sampai 900 lt/jam dan laju aliran air dingin di bagian pipa luar konstan 900 lt/jam. Data hasil pengujian dari masing – masing sudut serang turbulator ini dibandingkan data tanpa turbulator (plain tube),  secara keseluruhan terjadi peningkatan laju perpindahan kalor sebesar 26 % sampai 58 % dari pada tanpa turbulator serta menghasilkan faktor gesekan dari 25 % sampai 40 %. Dengan performance ratio rata –rata tertinggi pada turbulator dengan sudut 30O sebesar 0,948.   Kata kunci:  Louvered strips, Heat Exchanger, Counter flow, turbulensi, faktor gesekan, turbulator, efektifitas

scholarly journals PENGARUH SUDUT LOUVERED STRIPS TERHADAP LAJU PERPINDAHAN PANAS PADA COUNTER FLOW HEAT EXCHANGER

2011 ◽  
Vol 8 (2) ◽  
Author(s):  
Nyoman Arya Wigraha
Keyword(s):  
Heat Exchanger ◽  
Performance Ratio ◽  
Counter Flow ◽  
Tube Heat Exchanger ◽  
Plain Tube ◽  
Flow Heat

Pengaruh turbulator Louvered strips terhadap laju perpindahan kalor dan faktor gesekan aliran turbulen pada double tube heat exchanger dapat memecah (partitioning) dan mengganggu (blockage) pola streamline dari fluida yang mengalir ke saluran pipa dalam (inner tube) sehingga mengakumulasi aliran turbulensi dan meningkatkan laju perpindahan kalor dalam pipa. Louvered strips memiliki variasi sudut serang (q = 15°, 25°, 30°) yang terpasang ditengah-tengah pipa bagian dalam dan searah aliran fluida masuk. Laju aliran fluida (air) panas di bagian pipa dalam diteliti dengan interval 400 lt/jam sampai 900 lt/jam dan laju aliran air dingin di bagian pipa luar konstan 900 lt/jam. Data hasil pengujian dari masing – masing sudut serang turbulator ini dibandingkan data tanpa turbulator (plain tube),  secara keseluruhan terjadi peningkatan laju perpindahan kalor sebesar 26 % sampai 58 % dari pada tanpa turbulator serta menghasilkan faktor gesekan dari 25 % sampai 40 %. Dengan performance ratio rata –rata tertinggi pada turbulator dengan sudut 30O sebesar 0,948.   Kata kunci:  Louvered strips, Heat Exchanger, Counter flow, turbulensi, faktor gesekan, turbulator, efektifitas

Modelling and Dynamics Analysis of Heat Exchanger as a Distributed Parameter Process

2004 ◽  
Author(s):  
B. Savic ◽  
D. Lj. Debeljkovic
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Heat Exchanger ◽  
Fuel Oil ◽  
Distributed Parameter ◽  
Dynamics Analysis ◽  
Real Process ◽  
Cooling Chamber ◽  
Constant Coefficients ◽  
Process Behavior

On the basis accepted and critically clarified assumptions, a non–linear and afterwards linearized mathematical model of fuel oil cooling chamber has been developed in engineering sense sufficiently correct. The model is in the form of set of partial differential equations with constant coefficients. Using the appropriate numerical simulation of the results derived, the dynamic of this process has been shown in the form of appropriate transient processes responses which quite well correspond to the real process behavior.

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