The purpose of this study is to establish an Inside Temperature (IT) method for estimating temperatures in steady wave fronts in a thermoviscous material. A fundamental assumption that the material in the wave front, was approximately in an equilibrium state was used in this method. A further assumption that heat transport was neglected was used in the IT dQ=0 method, while in the IT IM method, the work done by the thermal stress was offset by heat transport. Two irreversible thermodynamic equations for the temperature in the wave front derived were connected with the Hugoniot function and the Mie-Grüneisen equation, respectively. To verify the efficacy of the IT method, three temperature distributions were estimated qualitatively using an equation for entropy including no assumption on heat transport, that including the assumption used in the IT dQ=0 method, and that in the IT IM method. These three distributions suggested that the temperatures were overestimated by the IT dQ=0 method, while the IT IM method was effective for shock compressions where the effect of viscosity was distinguished.

In the previous study, two Inside Temperature (IT dQ=0 and IT IM ) methods for estimating the temperature distributions in steady wave fronts in a thermoviscous material were established and the IT IM method was shown qualitatively to be effective for shock compressions where the effect of viscosity was distinguished. In this paper, these two methods are applied to the shock compressions of Yittria-doped Tetragonal Zirconia (YTZ) that is a thermoviscous material with a multiple shock Hugoniot. The YTZ Hugoniot consists of three partial curves including two kinks, that are the Hugoniot Elastic Limit (HEL) and the phase transition point. The shock temperatures evaluated by the IT IM method were close to the accurate temperatures obtained by the Walsh-Christian method in the whole stress range to 140 GPa examined here. Furthermore, the inside temperature distributions were approximately accurate because the effect of viscosity was distinguished in the shock compression. By these facts, it was considered that the fundamental assumption and the assumption on heat transport used in the IT IM method were valid and as a result, this method was effective. In addition, the influence of heat transport on the temperatures and thermoelastic stresses was examined.

The temperature distributions in overdriven steady wave fronts in 2024 Al shocked up to 80 GPa were predicted using the thermoelastic theory (Wallace theory), where the viscous stress is neglected, and the thermoviscous theory (Sano-Abe theory). The Wallace theory was improved by applying a more exact equation to the bulk modulus. As shock loading was increased, the difference between the temperature distributions predicted using each theory was greater. This tendency of the difference was similar for shocks up to 250 GPa in Pt. Thus, temperature distributions in overdriven steady wave fronts cannot be effectively evaluated using thermoelastic theory.

The mechanistic model of Taitel and Dukler [1] has previously been reported to exhibit a region in which three solutions exist for the height of the gas-liquid interface in the stratified/wave flow regime. Most laboratory studies have not dealt with flow rates in the ranges where the multiple solutions occur. An experimental study has been carried out at the University of Calgary to obtain such data. The object of this work is to review the relevant theory, investigate situations where theory suggests that multiple solutions should exist, and attempt to show whether or not such solutions do physically exist.

In order to accurately predict particle velocity profiles of steady shock wave fronts propagating in solid materials, a new numerical calculation method was proposed. The present method was based on one-dimensional Lagrangian finite difference wave code, and shock viscous stresses evaluated theoretically were introduced into the present numerical code. The shock viscous stress that is one of the important parameters to shape the rising profile of the shock wave front was calculated by the inside temperature estimate method for the steady shock wave fronts. The present calculation method was applied to the uniaxial strain problem of 6061-T6 aluminum at some stress levels below 8.86 GPa, where the elastic and plastic steady shock waves will appear. The results of the present calculation could reproduce more accurately the experimental data measured by the velocity interferometer system (VISAR). In addition, the present calculation was applied to a shock stress level of 20 GPa to investigate the shock viscous effects in the overdriven shock wave rising profile.

The mechanisms of phase re-distribution of gas/condensate flow in a deepwater steel lazy-wave riser after system shutdown have been studied numerically. The investigated system consists of a 15-mile long subsea pipeline tieback to a floating vessel, via a 9,800-ft long lazy-wave production riser. The subsea well is located at 6,350 ft of water. The system is insulated, and transports a gas-condensate mixture with liquid loading of 10 stb/mmscfd. This study reveals that besides pressure, the internal heat transfer during system cool-down is a key factor for the phase re-distribution between gas and liquid, and along the system. The liquid holdup variations are caused by the interfacial mass transfer between gas-liquid interface and phase re-distribution due to the combined effects of gravitational and buoyancy forces. Fluid cool down temperature “overshoot” in the lazy wave riser valley during system cool down has been observed. The pressure effect on the cool down temperature overshoot has been studied. The phenomenon is discussed based on fundamental heat transfer, phase equilibrium, and multiphase flow principles. The lazy wave riser configuration is a promising option for deepwater development, and gas/condensate flow is a multiphase flow phenomenon commonly encountered in raw gas transportation. The results of this study improve the understanding of multiphase flow transient behavior in deepwater pipeline/riser systems, and benefits gas/condensate production system design.