Open Access
Liu, Tao
Graduate Program:
Mechanical Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
October 02, 2007
Committee Members:
  • Vigor Yang, Committee Chair
  • Andre Louis Boehman, Committee Member
  • Daniel Connell Haworth, Committee Member
  • Richard A Yetter, Committee Member
  • Robert John Santoro, Committee Member
  • LES
  • supercritical
  • jet
  • turbulence
The present research focuses on the modeling and simulation of shear-coaxial cryogenic fluid injection and mixing processes under supercritical conditions. The objectives are as follows: 1) to establish a unified theoretical framework that accommodates full conservation laws, turbulence closure, real-fluid thermodynamics, and transport phenomena; 2) to implement a high-fidelity modeling technique to systematically investigate underlying physiochemical mechanisms and essential physics at supercritical conditions, and 3) to construct a parametric study identifying dominant design parameters and flow variables that affect the injector dynamics. Several computational and modeling challenges must be overcome in order to perform numerical simulations on high-pressure cryogenic fluid dynamics. A comprehensive theoretical framework capable of treating turbulence, high-pressure property variations, and a general fluid model is developed. A modified Soave-Redlich-Kwong (SRK) equation of state is selected in the present study because of its reasonable accuracy over the high-pressure and low-temperature regime and its ease of implementation. Thermodynamic properties including enthalpy, internal energy and heat capacity are directly calculated by means of fundamental thermodynamic theories. Transport properties including viscosity and thermal conductivity are estimated by means of the corresponding state principles along with the use of the 32-term Benedict-Webb-Rubin (BWR) equation of state, which are implemented using high-precision curve fits. Large-eddy-simulation (LES) technique is employed for the present analysis, in which large-scale turbulent motions are explicitly computed and small scales are modeled by using appropriate turbulence models. A static Smagorinsky model and dynamic subgrid scale (SGS) model are used to treat small-scale motions. The theoretical formulation outlined above was solved by means of a density-based, finite volume methodology. Temporal discretization was obtained using a four-step fourth-order Runge-Kutta scheme which has been commonly and successfully used in turbulence simulation. Further numerical efficiency is achieved by utilizing a parallel computation scheme that involves the message-passing interface (MPI) library and multi-block treatment. Validation and verification have been performed against data from experiments and direct numerical simulations on decaying isotropic turbulence, theoretical relations regarding oblique shock wave and experimental shadowgraphs of rapid expansion of supercritical solutions. Reasonably good agreement was obtained, and the effects of SGS models and artificial dissipations were well investigated. Efforts were also applied to examine the flow dynamics of a shear-coaxial injector. As a specific case, the injection of liquid nitrogen through the inner tube at a lower velocity and gaseous nitrogen through the outer annulus at a higher velocity was explored. The near-field flow evolution is characterized by the three mixing layers originating from the rims of the two concentric tubes. Emphasis was placed on the effects of chamber pressure, velocity ratio, momentum flux ratio, and external imposed acoustic excitation on the near-field flow evolution. The characteristic frequency of the recirculating wake flow downstream of the inner tube is smaller than the dominant vortex shedding frequency in the shear layers. A larger velocity ratio of the outer-to-inner jets enhances entrainment of the outer stream into the inner region and, consequently, results in a shorter inner potential core and a larger spreading angle of the outer shear layer. A higher chamber pressure results in a shorter inner potential core and a smaller spreading angle. The phenomena can be attributed to the momentum flux ratio and density ratio effects. The effect of acoustic excitation on the jet flow evolution is apparent even at small amplitude of acoustic pressure oscillation at 0.3% of the mean chamber pressure. The jet exhibits sinuous-like structures in the slices perpendicular to the acoustic velocity direction. Finally, efforts were first applied to investigate the spatial and temporal instabilities of real-fluid mixing layers with strong density stratification, to better understand the nature of cryogenic fluid injection and mixing. A local inviscid instability model based on a modified Soave-Redlich-Kwong equation of state was derived and discussed in detail. The density and velocity distribution effects on mixing layer instabilities have been investigated extensively. Results indicate that velocity variation coupled with density stratification will influence the flow stability dramatically. Detailed density distributions, especially large density dilation when mixing layers pass through inflection point, have obvious effects on flow instability.