Design of an Algorithm for Modeling Multiple Thermal Zones Using a Lumped-Parameter Model

Abstract

The generation of mathematical models for the analysis of buildings with multiple thermal zones is a large and complex task. Furthermore, the order and complexity of the dynamical model are increased by the number of included thermal zones. To overcome this problem, this paper presents an algorithm to define the mathematical model automatically, using the geometric and physics parameters as inputs. Additionally, the spatial position of each thermal zone must be recorded in an arrangement called a contact matrix. The algorithm for modeling systems with multiple thermal zones is the main contribution of this work. This algorithm is presented in pseudocode format and as an annex, an implementation in MATLAB software. One of the advantages of this methodology is that it allows us to work with parallelepipeds and not necessarily cubic thermal zones. The algorithm allows us to generate mathematical models with symbolic variables, starting from the knowledge of how many thermal zones compose the system and its geometric organization. This information must be organized in a matrix arrangement called a contact matrix. Different arrays of thermal zones were constructed with wooden boxes to verify the functionality of the models generated with the algorithm. Each case provided information that allowed us to adjust the mathematical models and their simulations, obtaining a range of errors between experimental and simulated temperatures from 2.08 to 5.6, depending on the number of thermal zones studied.

Modelling a Loop Heat Pipe as Heat Switch for Transient Application in Space Systems

“…This functionality is achieved by enabling the control of the temperature differential between the evaporator and the compensation chamber, as described in [20,21]. To implement it, a 1D thermo-hydraulic lumped parameter model mathematical model, as in [22][23][24][25][26][27][28][29][30], capable of predicting design and thermal performance, is necessary. This model should account for transient responses, complex interactions involving two-phase fluid flow, heat transfer, flow through porous structures, dry-out and priming phenomena, as well as condensation and evaporation within the loop heat pipe.…”

“…This paper, which aims to develop a 1D thermo-hydraulic lumped parameter model [22][23][24][25][26][27][28][29][30] for a loop heat pipe working as a heat switch, is organized as follows: Section 2 presents the mathematical model of the loop heat pipe working as a heat switch, Section 3 focuses on the dimensioning parameters, such as geometry and fluid properties, which are used in the simulations, and the corresponding results are presented in Section 4. Section 5 involves a discussion on the challenges and achievements from the proposed model.…”