Partial derivatives of thermodynamic state properties for dynamic simulation

Thorade, Matthis; Saadat, Ali

doi:10.1007/s12665-013-2394-z

Cited by 52 publications

(26 citation statements)

References 18 publications

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“…To derive the relative Mach number, the following rules (see Thorade & Saadat 2013) Note that according to the first law of thermodynamics, p = −(∂e/∂ϑ| s ). The relative Mach number in (4.7) can thus be derived from (4.6).…”

Section: Boundarymentioning

confidence: 99%

Boundary-layer stability of supercritical fluids in the vicinity of the Widom line

2019

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We investigate the hydrodynamic stability of compressible boundary layers over adiabatic walls with fluids at supercritical pressure in the proximity of the Widom line (also known as the pseudo-critical line). Depending on the free-stream temperature and the Eckert number that determines the viscous heating, the boundary-layer temperature profile can be either sub-, trans-or supercritical with respect to the pseudo-critical temperature, T pc . When transitioning from sub-to supercritical temperatures, a seemingly continuous phase change from a compressible liquid to a dense vapour occurs, accompanied by highly non-ideal changes in thermophysical properties. Using linear stability theory (LST) and direct numerical simulations (DNS), several key features are observed. In the sub-and supercritical temperature regimes, the boundary layer is substantially stabilized the closer the free-stream temperature is to T pc and the higher the Eckert number. In the transcritical case, when the temperature profile crosses T pc , the flow is significantly destabilized and a co-existence of dual unstable modes (Mode II in addition to Mode I) is found. For high Eckert numbers, the growth rate of Mode II is one order of magnitude larger than Mode I. An inviscid analysis shows that the newly observed Mode II cannot be attributed to Mack's second mode (trapped acoustic waves), which is characteristic in high-speed boundary-layer flows with ideal gases. Furthermore, the generalized Rayleigh criterion (also applicable for non-ideal gases) unveils that, in contrast to the trans-and supercritical regimes, the subcritical regime does not contain an inviscid instability mechanism.

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Section: Boundarymentioning

confidence: 99%

Boundary-layer stability of supercritical fluids in the vicinity of the Widom line

2019

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“…Saturation temperature, bubble and dew enthalpy are quantities that can be calculated directly from the pressure. The 2D-functions take two independent state properties (Thorade & Saadat, 2013) and calculate thermodynamic properties and a few partial derivatives.…”

Section: Methodsmentioning

confidence: 99%

Optimization-friendly thermodynamic properties of water and steam

Åberg

Wíndahl

Runvik

et al. 2017

Linköping Electronic Conference Proceedings

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This paper describes the development of an optimization-friendly thermodynamic property model of water and steam that covers liquid, vapor, 2-phase as well as the super-critical region. All equations are at least twice continuously differentiable with respect to all model variables and can be used in dynamic optimization problems solved by efficient derivativebased algorithms. The accuracy has been verified against the industry standard IAPWS IF97 and performance and robustness have been tested by solving a trajectory optimization problem where the start-up time of a gas power plant has been minimized while satisfying constraints on temperature gradients, pressure and flows. Simulations of various plant models have also been performed to verify and benchmark the implementation. The results show that the new media can be used in both solving dynamic optimization and simulation problems yielding reliable results. The new media has been integrated into Modelon's Thermal Power library 1.13. This article is built upon the work in (Åberg, 2016).

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“…Each of these properties can be calculated from the state variables through a fundamental equation of state [15]. The partial derivatives of the density with respect to pressure and specific enthalpy in the two-phase region can be calculated similarly [16]. For ease of computation, it is often useful to compute the derivatives of pressure and specific enthalpy not with respect to density, but rather with respect to specific volume; these two sets of derivatives can be interrelated through the identity…”

Section: Cycle Mass Variationmentioning

confidence: 99%

On the influence of state selection on mass conservation in dynamic vapour compression cycle models

Laughman

Qiao

2017

Mathematical and Computer Modelling of Dynamical Systems

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Many dynamic models of vapour compression systems experience nonphysical variations in the total refrigerant mass contained in the system when common modelling approaches are used. Rather than using the traditional state variables of pressure and specific enthalpy, the use of density as a state variable can eliminate these variations. The reasons for these variations are explained, and a set of test models is developed to study the effect of the state variable selection on the overall system charge. Results from both a simplified cycle model and a realistic airsource heat pump model indicate that this alternative approach has significant benefits for maintaining a fixed mass of refrigerant in the cycle. ARTICLE HISTORY

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Partial derivatives of thermodynamic state properties for dynamic simulation

Cited by 52 publications

References 18 publications

Boundary-layer stability of supercritical fluids in the vicinity of the Widom line

Boundary-layer stability of supercritical fluids in the vicinity of the Widom line

Optimization-friendly thermodynamic properties of water and steam

On the influence of state selection on mass conservation in dynamic vapour compression cycle models

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