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## Complex Heat Exchangers for Improved Performance

- Author(s): Bran, Gabriela Alejandra
- Advisor(s): Lavine, Adrienne S
- Kavehpour, Pirouz H
- et al.

## Abstract

A counter-flow heat exchanger transient one-dimensional numerical model was developed and verified against other authors results. Heat exchangers have been extensively studied due to their vast number of industrial applications where steady state operation is usually assumed. However, heat exchangers are also used in systems that operate under transient conditions such as energy generation, energy conversion, or energy storage.

After a detailed literature review, it was determined that there was a need for a more comprehensive study on the transient behavior of heat exchangers. Computational power was not readily available when most of the work on transient heat exchangers was done (1956 – 1986), so most of these solutions have restrictions, or very specific assumptions. More recently, authors have obtained numerical solutions for more general problems (2003 - 2013), but they have investigated very specific conditions, and cases. For a more complex heat exchanger (i.e. with heat generation), the transient solutions from literature are no longer valid. There was a need to develop a numerical model that relaxes the restrictions of current solutions to explore conditions that have not been explored.

A one dimensional transient heat exchanger model was developed. There are no restrictions on the fluids and wall conditions. The model is able to obtain a numerical solution for a wide range of fluid properties and mass flow rates. Another innovative characteristic of the numerical model is that the boundary and initial conditions are not limited to constant values. The boundary conditions can be a function of time (i.e. sinusoidal signal), and the initial conditions can be a function of position. Four different cases were explored in this work. In the first case, the start-up of a system was investigated where the whole system is assumed to be at the same temperature. In the second case, the new steady state in case one gets disrupted by a smaller inlet temperature step change. In the third case, the new steady state in case one gets disrupted by a step change in one of the mass flow rates. The response of these three cases show that there are different transient behaviors, and they depend on the conditions imposed on the system. The fourth case is a system that has a sinusoidal time varying inlet temperature for one of the flows. The results show that the sinusoidal behavior at the inlet propagates along the channel. However, the sinusoidal behavior on one of the fluids does not fully translate to the other gets damped by the wall and the heat transfer coefficients that can be barely seen on the other flow.

A scaling analysis and a parametric study were performed to determine the influence the different parameters on the system have on the time a heat exchanger takes to reach steady state. The results show the dependency of tst* (time a system takes to reach steady state) on the dimensionless parameters M, C, NTUh, NTUc, and Cw. tst* depends linearly on C and Cw, and it is a power function of M. It was also shown that tst* has a logarithmic dependency on NTUh and NTUc. A correlation was generated to approximate the time a system takes to reach steady state for systems where Cw << 1.

A more complex heat exchanger with the specific application of solar energy storage was also investigated. This application involves a counter-flow heat exchanger with a reacting flow in one of the channels, and it includes varying properties, heat generation, varying heat transfer coefficient, and axial conduction. The application for this reactor heat exchanger is on solar energy storage, and the goals is to heat up steam to 650 °C by using the ammonia synthesis heat of reaction. One of the concerns for this system is the start-up time and also how disturbances in reacting flow can affect the steam outlet temperature. The transient behavior during the system start-up was presented. In order to achieve the desired outlet steam temperature at a reasonable time, the system must operate at high gas mass flow rates. If the inlet temperature of the gas suffers a step change, it affects the reaction rate as well as the outlet steam temperature. A small perturbation on the gas mass flow rate has an effect on the profile shape. However, the maximum temperature reached by the gas due to reaction is not affected, and consequently, it has little effect on the steam temperature.

Axial conduction in the reactor heat exchanger was also investigated, specifically in the gas section. Axial conduction cannot be assumed to be negligible in the reactor heat exchanger because of the iron-based catalytic bed. Results in this section show that axial conduction is detrimental for the system. It was found that for Peclet number greater than 100, axial conduction can be neglected. An alternative solution to address axial conduction was proposed, namely to include a well-insulated non-reacting section (without a catalytic bed) upstream of the reactor. The modified reactor heat exchanger was a novel solution to avoid the negative effect of axial conduction. Results show that by having a non-reacting section, axial conduction becomes unimportant.