Determining local heat transfer coefficient by a model of temperature boundary layer in gas turbine cavity of rotation

Aeronautical and Space-Rocket Engineering

Thermal engines, electric propulsion and power plants for flying vehicles


Аuthors

Zuev A. A.1*, Nazarov V. P.1**, Arngol’d A. A.2***

1. Siberian State University of Science and Technology named after academician M.F. Reshetnev, 31, Krasnoyarsky Rabochy av., Krasnoyarsk, 660014, Russia
2. Krasnoyarsk Machine-Building Plant, 29, Krasnoyarsky Rabochy newspaper av., Krasnoyarsk, 660123, Russia

*e-mail: dla2011@inbox.ru
**e-mail: nazarov@.sibsau.ru
***e-mail: arngoldanna@mail.ru

Abstract

Accounting for heat transfer specifics in flow­through parts of turbo-pump assemblies of liquid rocket engines (LRE) is a topical task. Currently, accounting for the specifics of the flow with heat transfer while realizing both potential and vortex rotary flow in the flow-through parts is implemented generally by the following methods: employing empirical equations, numerical and analytical methods for solving partial differential equations [1].

High temperatures of the working fluid lead to thermal deformations of components, including the turbine disks [18]. When designing the flow-through parts of the LRE turbo-pump units and assemblies, it is necessary to account for the temperature change of the working fluid flow along the working channel, since the viscosity parameter is a function of temperature and determines the flow regime and, as a result, losses, particularly disk friction and hydrodynamic losses in the flow-through part. The LRE turbo-pump energy parameters modelling is a topical scientific and technical task. The issues of the workflow parameters optimization, and the propulsion system mathematical model were reviewed in the V.A. Grigoriev’s treatise [19], where analysis of the models was performed, and merits and demerits for various design stages were disclosed.

A model for dynamic and thermal spatial boundary layers distribution with convective component for the combustion products turbulent flow in the LRE gas turbines rotation cavities is proposed. For combustion products, the Prandtl number is less then unity (Pr < 1), and dynamic boundary layer thickness is less than the thermal boundary layer one. It was assumed, that the temperature change and thickness of energy loss within the dynamic boundary layer border occurs due to the dynamic velocity transfer, and beyond the border – due to thermal conductivity only. This assumption complies well with the inferences of many authors [20, 21, 24]. Thermal resistance manifests itself over the entire thermal boundary layer thickness. Thermal resistance exists within the dynamic boundary layer borders due to the turbulent heat transfer, and beyond the border – due to thermal conductivity [24]. The distribution model of the dynamic and thermal spatial boundary layers with convective component is necessary for analytical determination of the local heat transfer coefficient in the LRE turbines rotation cavities.

The main objects of research, where the potential and vortex rotational flow is realized, are the flow­through components of LRE gas turbines such as inlet and outlet devices, as well as cavities between the stator and the working wheel [20].

An integral relation for the thermal spatial boundary layer energy equation, allowing integration over the surface of any shape, which is necessary for determining the thickness of energy loss, was obtained. The expressions for determining the energy loss thickness for thermal spatial boundary layer are necessary to determine the local heat transfer coefficients for the typical flow cases with account for the heat exchange.

Expressions for determining the local heat transfer coefficient in the Stanton number form for the straight linear uniform flow, rotational flow according to the rigid body law, and rotational flow of the free vortex of a power profile distribution for dynamic and thermal boundary layers parameters in case of Pr < 1 were obtained analytically.

Local heat transfer coefficient in the Stanton number form for straight linear uniform turbulent flow is


where m — is the turbulization degree of spatial boundary layer dynamic velocity profile,

– is the dynamic and thermal boundary layers ratio of the thickness, λ — is the coefficient of thermal conductivity,


 – the laminar sublayer coefficient of turbulent velocity distribution profile (obtained considering the two-layer turbulence model with a viscous laminar sublayer), Re — the Reynolds number.

Local heat transfer coefficient in the Stanton number form for rotational flow according to the rigid body law is

where ε — is the angle tangent of the bottom streamlines bevel, J — is the relative characteristic thickness.

Local heat transfer coefficient in the Stanton number form for rotational flow of a free vortex is



Analytical expressions for heat transfer coefficients agree well with the experimental data and dependencies of other authors [7–10].

The obtained analytical expressions well agree with the data of other authors and are necessary for engineering calculations while designing the LRE flow-through parts of turbo-pumps.

Keywords:

temperature boundary layer, heat transfer coefficient, integral relation of energy equation, flow-through part of turbo-pump assembly

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