A modified nodal pressure method for calculating flow distribution in hydraulic circuits for the case of unconventional closing relations

Mikhailovsky, Egor; Novitsky, Nikolay

doi:10.1016/j.spjpm.2015.07.007

Cited by 10 publications

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“…Consistently with what was discussed in the literature, see e.g. [23], this set up has a unique solution. Indeed, to verify this we need to start from generators and solve the set of Eqs.…”

Section: Formulating and Solving Stationary Advection-diffusion-lossesupporting

confidence: 85%

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Thermal Transients in District Heating Systems

Chertkov

Novitsky

2019

Energy

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Heat fluxes in a district heating pipeline systems need to be controlled on the scale from minutes to an hour to adjust to evolving demand.There are two principal ways to control the heat flux -keep temperature fixed but adjust velocity of the carrier (typically water) or keep the velocity flow steady but then adjust temperature at the heat producing source (heat plant). We study the latter scenario, commonly used for operations in Russia and Nordic countries, and analyze dynamics of the heat front as it propagates through the system. Steady velocity flows in the district heating pipelines are typically turbulent and incompressible. Changes in the heat, on either consumption or production sides, lead to slow transients which last from tens of minutes to hours. We classify relevant physical phenomena in a single pipe, e.g. turbulent spread of the turbulent front. We then explain how to describe dynamics of temperature and heat flux evolution over a network efficiently and illustrate the network solution on a simple example involving one producer and one consumer of heat connected by "hot" and "cold" pipes. We conclude the manuscript motivating $ Thermal Transients in District Heating Systems: Physics Modeling for better Control Highlights• Advection-Diffusion-Loss of heat in district heating networks is analyzed.• Parameters of the basic model follow from turbulence phenomenology.• Superposition of running and spreading fronts forms a typical transient.• We suggest an efficient computational scheme to describe the transients.

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“…Consistently with what was discussed in the literature, see e.g. [23], this set up has a unique solution. Indeed, to verify this we need to start from generators and solve the set of Eqs.…”

Section: Formulating and Solving Stationary Advection-diffusion-lossesupporting

confidence: 85%

“…(22), supplemented by Eqs. (23) and defined over a single-connected district heating network, set up an example of the steady "network heat flow" problem:…”

Section: Formulating and Solving Stationary Advection-diffusion-lossementioning

confidence: 99%

Thermal Transients in District Heating Systems

Chertkov

Novitsky

2019

Energy

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“…So set ̃2 consists of continuous function, which for any ∈̃ as functions of and for any ∈ −̃ as function of . Examples of such functions are given in [12][13][14]. Like in case of ̃, conditions 1)-3) are physically naturalwhile conditions 4)-6) are mathematical extrapolation.…”

Section: Problem Definition and Closure Relationsmentioning

confidence: 99%

“…In this case there are no evident way to effectively reduce the problem to optimization task [6]. But (as a rule) it is possible to use modified variants of classical algorithms for finding solutions for such networks можно эффективно (such modified algorithms proposed by Mikhailovsky and Novitsky [12,13,14]). But lack of mathematically accurate proof of uniqueness and existence of solution remained some filling of dissatisfactionespecially because it is known for long time, that in similar problems of non-isothermal flow, especially gas-liquid flow, solution can be not unique!…”

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confidence: 99%

Existence, uniqueness and monotonic behavior of the solution of classical flow distribution problem for hydraulic networks with pressure-dependent closure relations

Korelstein¹

2019

E3S Web Conf.

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Existence, uniqueness and monotonic behavior of the solution of classical flow distribution problem for hydraulic networks with pressure-dependent closure relations was proved. The closure relation can have very general form, restricted only by continuity and monotonicity conditions necessary for providing existence, uniqueness and continuity of flow distribution problem for each branch. It is shown that network as a whole “inherits” monotonicity and continuity of its branches behavior, and this provides existence and uniqueness of solution.

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“…Matrix ̃= ( + ), which relates and (also called modified Maxwell matrix [3,4]), is Jacobian of Ψ . This matrix has several wonderful properties which will be discussed further.…”

Section: Notementioning

confidence: 99%

Hydraulic networks with pressure-dependent closure relations, under restrictions on the value of nodal pressures. Maxwell matrix properties and monotonicity of flow distribution problem solution

Korelstein¹

2019

E3S Web Conf.

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In the article, which continues the research of article [1], the results of previous article are generalized to “abstract” hydraulic networks. Additional existence theorems are proved for classical flow distribution problem (CFDP) for hydraulic networks with pressure-dependent closure relations, under restriction on nodal pressures. Hydraulic network Maxwell matrix properties are establish, related to monotonicity of CFDP solution.

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A modified nodal pressure method for calculating flow distribution in hydraulic circuits for the case of unconventional closing relations

Cited by 10 publications

References 0 publications

Thermal Transients in District Heating Systems

Thermal Transients in District Heating Systems

Existence, uniqueness and monotonic behavior of the solution of classical flow distribution problem for hydraulic networks with pressure-dependent closure relations

Hydraulic networks with pressure-dependent closure relations, under restrictions on the value of nodal pressures. Maxwell matrix properties and monotonicity of flow distribution problem solution

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