Bayesian Mass Averaging in Rigs and Engines

TL;DR

This paper proposes a Bayesian approach to calculating mass averages in engines and rigs, accounting for flow complexity and sensor limitations, with analytical and sampling methods demonstrated through temperature examples and a real engine case study.

Contribution

It introduces the Bayesian mass average concept, providing analytical and sampling methods for its computation under complex flow conditions.

Findings

Analytical calculation of Bayesian mass average for specific flow profiles

Sampling procedure for Gaussian random field flow rates

Application to real engine temperature data

Abstract

This paper introduces the Bayesian mass average and details its computation. Owing to the complexity of flow in an engine and the limited instrumentation and the precision of the sensor apparatus used, it is difficult to rigorously calculate mass averages. Building upon related work, this paper views any thermodynamic quantity's spatial variation at an axial plane in an engine (or a rig) as a Gaussian random field. In cases where the mass flow rate is constant in the circumferential direction but can be expressed via a polynomial or spline radially, this paper presents an analytical calculation of the Bayesian mass average. In cases where the mass flow rate itself can be expressed as a Gaussian random field, a sampling procedure is presented to calculate the Bayesian mass average. Examples of the calculation of the Bayesian mass average for temperature are presented, including with a real engine case study where velocity profiles are inferred from stagnation pressure measurements.