[Paper Review] The Flowing System Gasdynamics Part 2: Euler momentum conservation equation solution

S. L. Arsenjev, I. B. Lozovitski+1 more|ArXiv.org|Feb 7, 2003

Gas Dynamics and Kinetic Theory3 citations

TL;DR

This paper presents an analytical solution to the Euler momentum conservation equation for gas and liquid flows in flowing systems such as pipes, nozzles, and diffusers, using a modern contact interaction framework. The solution yields a distribution law of static head along the flow path, enabling accurate modeling of non-stationary flows under time-varying conditions like surface roughness, variable cross-sections, heat exchange, and additional mass flow rates.

ABSTRACT

The solution of a momentum conservation equation for the gas and liquid stream in the flowing element is obtained on the basis of the modern approach to a problem on contact interaction of bodies and mediums. A flowing element, system are: pipe, tube, orifice, mouthpiece, diffuser, etc. and its combination. The integration of the differential equation has reduced to distribution law of static head along the length of flowing element and has proved the elementary algebraic solution that introduced in the previous paper by these authors. The received solution allows to describe the motion of fluid medium in non-stationary conditions, under action of any time-varying physical factors: a roughness of streamlined surface, the area of the section of the flowing element, the heat exchange with the streamlined surface, the technical work, the additional weight flow of fluid medium.

Motivation & Objective

• To develop a rigorous solution for the Euler momentum conservation equation in flowing fluid systems using a modern contact interaction approach.
• To model fluid flow in non-stationary conditions with time-varying physical factors such as surface roughness and heat exchange.
• To derive a distribution law for static head along the length of flowing elements like pipes and nozzles.
• To extend the algebraic solution introduced in the prior paper to a broader class of dynamic and complex flow configurations.
• To enable the description of fluid motion under technical work, variable cross-sectional areas, and additional mass flow inputs.

Proposed method

• Formulates the momentum conservation equation for compressible and incompressible flows in flowing elements using a modern contact interaction theory.
• Integrates the differential momentum equation to derive a closed-form solution for static head distribution along the flow path.
• Applies the solution to various flow components including orifices, nozzles, diffusers, and tubes with variable cross-sections.
• Incorporates time-varying factors such as surface roughness, heat transfer, and external work into the momentum balance.
• Uses an elementary algebraic formulation derived from the integration process, validated in the prior work.
• Considers the influence of additional mass flow rates and variable area changes on momentum and static head evolution.

Experimental results

Research questions

• RQ1 How can the Euler momentum equation be solved analytically for fluid flows in complex flowing systems under non-stationary conditions?
• RQ2 What is the resulting distribution law of static head along the length of a flowing element such as a pipe or nozzle?
• RQ3 How do time-varying factors like surface roughness, heat exchange, and variable cross-sections affect the momentum balance in flowing systems?
• RQ4 Can the solution be generalized to include technical work and additional mass flow inputs in the momentum equation?
• RQ5 What is the role of the contact interaction theory in enabling a consistent and physically grounded solution for fluid momentum in flowing systems?

Key findings

• The integration of the Euler momentum equation results in a distribution law for static head along the length of the flowing element.
• The solution is algebraic and explicitly accounts for time-varying physical factors such as surface roughness and heat exchange.
• The method allows modeling of fluid motion in non-stationary conditions, including variable cross-sections and additional mass flow rates.
• The derived solution is consistent with the elementary algebraic form introduced in the authors' prior work, now extended to dynamic and complex systems.
• The approach enables accurate prediction of static head variation in components like diffusers, orifices, and tubes under real-world operational conditions.
• The solution is applicable to both gas and liquid flows in systems with technical work and heat transfer effects.