A new HVAC ductwork steady-state flow analysis method: The Minimum Energy Dissipation Principle applied to flow networks including the effects of branched junctions

Francés, Víctor Manuel Soto; Ojer, José Manuel Pinazo; Sarabia-Escrivá, Emilio-José; Navarro-Esbrí, Joaquin

doi:10.1016/j.enbuild.2021.111504

Cited by 2 publications

(10 citation statements)

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“…Therefore, in fact, the only independent parameters of the internal model are three: {ϕ r , ϕ b , d}. Similarly to the conventional ϕ † (see [9]), the following equations can be written:…”

Section: Branched Junction: External and Internal Modelsmentioning

confidence: 99%

“…In the next sections, it will be shown how the MinEDP provides the missing equation which allows the transformation of one model into the other. The §3 presents only the key conclusions from [7] [8] [9], needed here. Before going into the mathematical details, §4 is employed to describe qualitatively the physical implications of the following sections.…”

Section: Branched Junction: External and Internal Modelsmentioning

confidence: 99%

“…The aim of this section is just to provide some new key ideas developed in our previous works [7] [8] [9]. For any flow network, by fixing beforehand one or several flows, its global energy dissipation under such imposed flow rate/s, can be expressed as:…”

Section: Brief Review Of Minedpmentioning

confidence: 99%

“…( 14), although it tries to get as close as possible to that minimum. Stated in other words, finding the steady-state of the network becomes solving a constrained minimization problem, due to the internal work exchange (see [9] for the details).…”

Section: Brief Review Of Minedpmentioning

confidence: 99%

“…In [7] the MinEPD was applied to tree-shaped networks without work interaction at the junctions and the same year these results were extended to any type of network in [8]. Finally, in [9] the previous results were extended to any flow network with work interaction at its branched junctions. In doing so, the Herwig's split of the head change coefficients into two head loss coefficients and a work coefficient was used to develop and prove that the new method, based on MinEDP, was equivalent to the energy balance.…”

mentioning

confidence: 99%

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Characteristic differential equation of a T-junction: diffusive shear work exchange from its head loss coefficients

Francés¹,

Ojer²,

Sarabia-Escrivá³

et al. 2021

Preprint

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Negative head loss coefficients in branched junctions, has been controversial for long. Herwig et al. showed, that the cause is a diffusive shear work exchange.Based on their work, a new junction internal model is described, while the conventional head loss is named external. The latter is obtained experimentally, while the first cannot. This fact seems to push back reaching a practical solution. Conventionally two head 'loss' coefficients are required. However the internal model needs three: two 'pure' head loss coefficients and a work coefficient. Based on previous works, the paper shows that the missing equation comes from the Minimum Energy Dissipation Principle (MinEDP). The characteristic differential equation of a T-junction is discovered, which relates the two 'pure' head loss coefficients. A particular case is presented to illustrate how to obtain the internal model from the external one by using it. The results are applied to empirical and numerical data from the same branched junction; Zhu's measurements (external) and Herwig's CFD computations (internal), respectively. Finally, an example illustrates how powerful this new method is to analyse a new, recently published, exhaust return duct.

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Section: Branched Junction: External and Internal Modelsmentioning

confidence: 99%

Section: Branched Junction: External and Internal Modelsmentioning

confidence: 99%