Shape Optimization for Dense Gas Flows in Turbine Cascades

Computational Fluid Dynamics 2004, 2006

This paper provides a comprehensive introduction to compressible flow, exploring key concepts such as Mach number and the conditions that define compressible flow. It delves into the historical evolution of compressible flow research, including one-dimensional compressible flow theory, choked flow, and the behavior of normal and oblique shockwaves. The Mach-area relationship is examined in detail, highlighting its importance in the design and analysis of high-speed flows. Finally, real-world applications are discussed, showcasing how these principles are essential in modern engineering, from aerospace design to propulsion systems.

This chapter deals with the thermodynamic aspects of simple compressible flows through nozzles and passages. Several of the cycles covered in Chapter 11 have flow inside components where it goes through nozzles or diffusers. For instance, a set of nozzles inside a steam turbine converts a high-pressure steam flow into a lower pressure high-velocity flow that enters the passage between the rotating blades. After several sections, the flow goes through a diffuser-like chamber and another set of nozzles. The flow in a fan-jet has several locations where a high-speed compressible gas flows; it passes first through a diffuser followed by a fan and compressor, then through passages between turbine blades, and finally exits through a nozzle. A final example of a flow that must be treated as compressible is the flow through a turbocharger in a diesel engine; the flow continues further through the intake system and valve openings to end up in a cylinder. The proper analysis of these processes is important for an accurate evaluation of the mass flow rate, the work, heat transfer, or kinetic energy involved, and feeds into the design and operating behavior of the overall system.

Physics of Fluids, 2004

Insights into symmetric and asymmetric vortex mergers using the core growth model Phys. Fluids 24, 073101 (2012) Nonlinear finite amplitude torsional vibrations of cantilevers in viscous fluids J. Appl. Phys. 111, 124915 (2012) A subgrid-scale model for large-eddy simulation based on the physics of interscale energy transfer in turbulence Phys. Fluids 24, 065104 (2012) An efficient approach for eigenmode analysis of transient distributive mixing by the mapping method Phys. Fluids 24, 053602 (2012) Dynamics of freely swimming flexible foils Phys. Fluids 24, 051901 (2012)

Meccanica

Journal of Fluid Mechanics, 2004

The influence of fluid thermal sensitivity on the centrifugal flow instabilities in pressure-driven (Dean) and drag-driven (Taylor-Couette) Newtonian shear flows is investigated. Thermal effects are caused by viscous heating or an externally imposed temperature difference between the outer and inner cylinders, T * , or a combination of both. In all cases considered, the maximum temperature difference within the gap is small enough such that the base-state velocity profile and consequently the distribution of angular momentum are practically unchanged from those in the isothermal flow. The base-state temperature gradient can be approximated as a linear superposition of T * /d, where d is the gap width, and that caused by viscous heating. Numerical linear stability analysis shows that when T * = 0, viscous heating causes the critical Reynolds number, Re c , to be greatly reduced when the Nahme number, defined as the product of the Brinkman number, Br, and the dimensionless activation energy associated with the fluid viscosity, ε, is O(α 2 /Pr) where α and Pr denote the dimensionless critical axial wavenumber and Prandtl number respectively. Since α 2 is O(10) and typical Pr values for thermal sensitive liquids could be O(10 4 ), appreciable flow destabilization occurs even when Na is O(10 −3 ). In the absence of viscous heating, an externally imposed temperature gradient can lead to significant reduction in Re c when S ≡ (ε T * )/T * 1 < 0 and |S| is O(α 2 /Pr), where T * 1 denotes the temperature of the inner cylinder. The numerical linear stability analysis results are explained based on a simplified model derived from the linearized governing equations by invoking the narrow-gap approximation. This model shows that the thermo-mechanical coupling, arising from the convection of the base-state temperature gradient by radial velocity perturbation, amplifies the temperature fluctuations within the flow by a factor proportional to Pe/α 2 where Pe denotes the Péclet number. This results in the reduction of local viscosity. Hence, the rate of dissipation of the velocity perturbations decreases causing the centrifugal instability to occur at lower values of the Reynolds number compared to the isothermal flow. Thermo-mechanical destabilization caused by viscous heating for T * = 0 can be quantified by a scaling law of the form Λ = [1 + Pr c 1 Na/α 2 ] −1/2 where Λ is the ratio of the critical Reynolds number of the non-isothermal flow to that of the isothermal one and c 1 is a flow-dependent constant. Similarly, in the absence of viscous heating and for T * < 0, Λ = [1 + Prc 2 S/α 2 ] −1/2 , where c 2 is a flow-dependent constant. When T * > 0 and viscous heating are present, a numerical linear stability analysis shows that Λ ∝ Na k where k < 0 and it is dependent on T * and the flow type. Finally, we perform a nonlinear stability analysis

Journal of Fluid Mechanics, 2019

Flows in the close proximity of the vapour-liquid saturation curve and critical point are examined for supersonic turbine cascades, where an expansion occurs through a converging-diverging blade channel. The present study illustrates potential advantages and drawbacks if turbine blades are designed for operating conditions featuring a nonmonotonic variation of the Mach number through the expansion process, and non-ideal oblique shocks and Prandtl-Meyer waves downstream of the trailing edge. In contrast to ideal-gas flows, for a given pressure ratio across the cascade, the flow field and the turbine performance are found to be highly dependent on the thermodynamic state at the turbine inlet, in both design and off-design conditions. A potentially advantageous design, featuring stationary points of the Mach number at the blade trailing edge, is proposed, which induces a nearly uniform outlet Mach number distribution in the stator-rotor gap with a low sensitivity to slight variations in the outlet pressure. These findings are relevant for turbomachines involved in high-temperature organic Rankine cycle power systems, in particular for supercritical applications.

Physics of Fluids, 2009

This paper presents an investigation about the effect of the complexity of a fluid molecule on the fluid dynamic quantities sound speed, velocity, and Mach number in isentropic expansions. Ideal-gas and dense-gas expansions are analyzed, using the polytropic ideal gas and Van der Waals thermodynamic models to compute the properties of the fluid. In these equations, the number of active degrees of freedom of the molecule is made explicit and it is taken as a measure of molecular complexity. The obtained results are subsequently verified using highly accurate multiparameter equations of state. For isentropic expansions, the Mach number does not depend on the molecular weight of the fluid but only on its molecular complexity and pressure ratio. Remarkably enough, the Mach number can either increase or decrease with molecular complexity, depending on the considered pressure ratio. The exit speed of sound and flow velocity, however, are dependent on both molecular complexity and weight, as well as on the inlet total temperature. The exit flow velocity is found to be a monotonically increasing function of molecular complexity for all expansion ratios, whereas the speed of sound monotonically increases with molecular complexity only at high pressure ratios. The speed of sound is not monotone for pressure ratios around 3, which leads to the Mach number being nonmonotone at pressure ratios around 10. It should be noted that the sound speed and flow velocity depend much more strongly on molecular weight than on molecular complexity, which in realistic expansions often obscures the influence of the latter. Quantitative differences are observed between ideal and dense-gas expansions, which are dependent on the reduced inlet conditions. The present study concludes with the numerical simulation of two-dimensional expansions in a turbine nozzle to document the occurrence of real-gas effects and their dependence on molecular complexity in realistic applications. the region where volumetric properties can be calculated from the ideal-gas equation of state Pv = RT, where P denotes pressure, v specific volume, R the specific gas constant, and T temperature, to those occurring close to the liquidvapor saturation line and to the critical point, namely, within the so-called dense-gas thermodynamic region. The latter is, for example, the case for supercritical CO 2 nozzle flows, which are increasingly adopted in the pharmaceutical industry for the nucleation of chemicals. 7,8 Exemplary ideal-and dense-gas expansion processes are represented by the isentropes depicted in the reduced pressure-specific-volume dia-a͒ Electronic mail: [email protected].