A new non-ideal second order thermal model with additional loss effects for simulating beta Stirling engines

Abstract

In this paper, comprehensive governing differential equations of Stirling engines have been developed by coupling the effect of gas leakage through the displacer gap, gas leakage into the crank case and the shuttle loss rate into the traditional model. Instantaneous pressures and temperatures of the working fluid in the engine were evaluated at same time step.The present model was deployed for the thermal simulation of the GPU-3 Stirling engine and the obtained results were robustly compared to experimental data as well as results from previous numerical models. Then, parametric studies were conducted to assess the impact of geometrical and operating parameters on the performance of Stirling engines working with helium or hydrogen. Results suggest that the modifications made in this model led to better accuracy and consistency in predicting the experimental data of the prototype engine at all speeds, compared with most previous models. It was found that there exists a minimum dimensionless gap number, for every engine pressure below which mass leakage into the compression volume may not impact the brake power and energetic efficiency of the engine.In addition, an optimum mean effective pressure was found for maximum energetic efficiency of the engine. This optimum value is higher for helium gas than for hydrogen gas. Further results indicated that the brake power and energetic efficiency of the prototype Stirling engine can be significantly improved by 30% and 18%, respectively, provided that the heater temperature is raised to 850 ℃ while the cooler temperature is reduced to 0 ℃.

A techno-enviro-economic assessment of a biomass fuelled micro-CCHP driven by a hybrid Stirling and ORC engine

“…In a previous study, Udeh et al [27] developed a non-ideal thermal model of the Stirling engine to predict the performance of the experimental engine. This model is obtained by coupling the losses in the engine to the ideal adiabatic model.…”

“…The flow energy equation applied to any CV if we account for the losses in energy due to the pressure drop in the heat exchangers, leakage of energy into the crankcase, shuttle heat loss, leakage of energy via the displacer clearance, and several other work losses is given as [27]:…”

“…Heat leakage loss to the buffer space [27] 𝑄𝑄 r,non−ideal = 𝑄𝑄 r,ideal (1 − 𝜀𝜀 r ) Non-ideal heat loss in the regenerator [27] 𝜀𝜀 r = 𝑁𝑁𝑇𝑇𝑈𝑈 𝑁𝑁𝑇𝑇𝑈𝑈 + 1…”

“…Hydraulic diameter [27] 𝑁𝑁𝑁𝑁 = (1 + 0.99(𝑅𝑅𝑒𝑒𝑃𝑃𝑟𝑟) 0.66 )𝜙𝜙 1.79 Nusselt number [35] Third category (work) losses…”

Exchanging data between computational fluid dynamic and thermodynamic models for improving numerical analysis of Stirling engines

“…Cheng and coworkers 10,11 modified the adiabatic condition by distinguishing temperatures of thermal sources and working gas and reckoning pressure loss through the regenerator. Udeh et al 12 investigated a β-type Stirling engine by using a non-ideal second-level model dealing with the shuttle heat losses and mass leakage between the expansion chamber and the compression chamber and between the workspace and the crankcase.…”