Research paperNumerical investigation on cryogenic liquid jet under transcritical and supercritical conditions
Introduction
At present, with the development of a series of new concepts for engine combustion, including the HCCI (Homogeneous Charge Compression Ignition), RCCI (Reactivity Controlled Compression Ignition) and LTC (Low Temperature Combustion), the average pressure in the combustion chamber usually exceeds the critical pressure of fuel, and the chamber temperature is also far beyond the critical temperature [1], [2], [3]. This makes fuels with low initial temperatures (below or slightly above the critical temperature) undergo a transition from low-temperature subcritical or supercritical to high-temperature supercritical states during the injection, resulting in transcritical or supercritical jets. While the definition of “supercritical” has been given by Oschwald (i.e. both the pressure and temperature of the injected fluid are above their critical values) [4], [5], the one of “transcritical” is ambiguous in the literature. In this article, we defined transcritical injection as follows: a fluid with an initial temperature below the critical temperature is injected into an environment where both temperature and pressure exceed the critical values of the injected fluid. It is well known that for a supercritical fluid there is a pseudo-boiling phenomenon [6], [7], [8]. The pseudo-boiling point temperature is referred to the temperature at which the constant-pressure specific heat attains its maximum. As we all know, the thermophysical properties of fluid are changed dramatically when across the critical point or pseudo-boiling point, thereby affecting the mixing of fuel and oxidant, and then the combustion efficiency and emissions. It is worth mentioning that several new concept engines with a supercritical fluid as fuel has been developed by Anitescu [9], [10], Oschwald [5] and Oefelein [11]. Therefore, the study on transcritical and supercritical jets is important to improving fuel combustion efficiency and reducing emissions for the next generation engine.
The supercritical fluid has completely different characteristics from the subcritical ones. In the supercritical state, the surface tension and vaporization enthalpy disappear, and the significant difference between gas and liquid is no longer present. The fluid exhibits a continuous state, whose density is close to the liquid, but the transport properties are similar to the gas. However, in contrast to the classical viewpoint of the supercritical state space as a homogeneous domain, Nishikawaand Tanaka [12] firstly discovered by experiment that under lowly supercritical conditions or transcritical conditions the fluid is not homogeneously distributed, but can be divided into liquid-like and gas-like supercritical states. Recently, Simeoni [7] and Banuti [6], [13] carried out intensive investigations on this issue. They found that the jet can be divided into three different regions: in the core of the jet there exists a liquid-like region while the edge of the jet would be supercritical gas-like region, and between them there is a transitional region. In this transition region, the gas and liquid are inter-miscible and inter-soluble, and the thermodynamic properties change dramatically, especially the pseudo-boiling behavior occurs under the transcritical conditions. Besides, Banuti [13] discussed differences between transcritical and supercritical jets from seven aspects in detail.
Experimental studies on trans/supercritical jets have been extensively conducted and mainly based on single or multi-component cryogenic fluids, which were injected into a high temperature and pressure chamber [14], [15], such as, injection of liquid nitrogen and coaxial injection of liquid nitrogen and gaseous helium into a supercritical nitrogen chamber [16], [17], [18], [19], [20], [21], [22]. Previous investigations indicated that the supercritical jet exhibits characteristics similar to a gas jet, and the thermodynamic and transport properties of the fluid are between the gas and the liquid. And strips, filaments and droplets that commonly appear in the subcritical spray and atomization are no longer produced at the jet surface, a clear interface between gas and liquid is undetected, but is replaced by a continuous phase, i.e. a mixing layer, with highly pleated folds. Falgout [23] and Wensing [24] respectively used nitrogen and diesel oil to visualize the mixing layer of supercritical jet under diesel engine conditions. By using the ballistic imaging technology, they found that the supercritical interface is a continuous turbulent mixing layer, and there is a transcritical and supercritical phase change without evaporation. Areas of high density with pronounced fluctuations were visible. In the aspect of numerical simulation, Oefelein and Yang [2] used a large eddy simulation (LES) method to simulate the mixing and combustion processes in liquid rocket engines in an supercritical environment. It is proved that the density gradient plays a decisive role in the development of the mixing layer, and at the critical point, the mass diffusion rate is close to zero. Zong [25] also simulated the mixing process of liquid nitrogen injected into a supercritical chamber by means of LES. The results show that there is a large density gradient at the surface of the jet, which plays a role similar to a “solid wall”, enhancing the axial oscillation of the jet and weakening the radial oscillation. Selle and Taskinoglu [26], [27] performed a LES and direct simulation of a transcritical and supercritical mixing layer, and demonstrated that the density gradient is of significance in the global stability and turbulence characteristics of the mixing layer. Dukhin et al. [28] have shown that the jet is not instantaneous gasified even at critical or slightly supercritical conditions, but there is an interface in the form of a mixing layer between the liquid jet and the high density gas. Dahms and Oefeleinet [29] theoretically and numerically analyzed the non-equilibrium dynamics of gas-liquid interface. They demonstrated that the transition to mixing layers occurs due to the substantial statistical fluctuations about the average interface molecule number and the presence of significant interfacial free energy forces. With the broadening of the interface, the interfacial free energy forces and present interfacial statistical fluctuations are gradually diminished once the interface enters the continuum regime. Mülleret [30] used two CFD codes, the density-based version INCA and a pressure-based version of OpenFOAM, to perform a LES study on transcritical and supercritical nitrogen jets. The numerical results of both codes are nearly identical, indicating that thermophysical modeling is the key to supercritical jet simulation.
In recent years, Mayer’s [18], [19] experiments have been widely used in the simulation of supercritical jets. Kim [31] used an extended k–ε turbulence model to simulate the effects of different equations of state on trans- and supercritical jets; Park [32] compared the effects of different turbulence models and equations of state on supercritical jet under RANS and LES. From the results, the suitable adoption of real-fluid EOS is more significant than the selection of turbulence model for the numerical performance; Schmitt [33] used the LES code AVBP to simulate trans- and supercritical flows, and a good agreement of the results with measurements was shown.
In the present work, a new solver for real-fluid is developed to study the cryogenic fluid injection and mixing under transcritical and supercritical conditions. In the new solver, a real-fluid equation of state is used to solve the thermodynamic properties, the classic PISO algorithm (Pressure Implicit with Splitting of Operators) is applied to coupling the pressure and velocity, and the real-fluid pressure equation is also corrected by introducing the isothermal compressibility. Since the main interest of this study is to examine the mean geometrical and physical properties of the mixing layer rather than its transient and detailed characteristics, and considering the computational cost, we use a RANS model for the turbulence. To verify and validate the new solver, two Mayer experimental cases of transcritical and supercritical jets are selected for the simulation. Besides, we add a typical transcritical injection case (Case3) into the study with emphasis on the differences in the mechanism and characteristics between transcritical and supercritical injections. We identify two different cases in the supercritical injection, i.e. “lowly supercritical” (Case 1), in which the initial jet temperature just exceeds the critical temperature but is below the pseudo-boiling temperature, and “highly supercritical” (case 2), in which the initial jet temperature already exceeds the pseudo-boiling temperature. Furthermore, the mixing layer of transcritical and supercritical jets is analyzed in detail, and a mixing layer thickness is introduced and its evolution rules are revealed and discussed.
Section snippets
Theoretical formulation
There are significant differences between transcritical and supercritical liquid injections. Under the transcritical condition, the surface tension and evaporation latent heat of the fluid do not disappear immediately when the jet temperature reaches the critical point. Even at a relatively lowly supercritical pressure, because the jet temperature will cross the corresponding pseudo-boiling point, the mixing layer will exhibit the pseudo-boiling behavior that is similar to the liquid boiling [6]
Thermodynamics verification
Before performing three-dimensional transient flow simulations, it is necessary to verify the reliability and accuracy of the thermodynamic model of the real fluid under transcritical and supercritical conditions. Fig. 3 presents a comparison of the thermodynamic models with the NIST data in the temperature range from 80 K to 300 K for nitrogen at a pressure of 40 bar. In the full temperature range, except that the calculated viscosity at low temperatures and the constant-pressure specific heat
Geometric and boundary conditions
To validate the new solver for transcritical and supercritical cryogenic liquid jet flow, we carried out test calculations for a cryogenic nitrogen jet injected into a gaseous nitrogen environment with a constant temperature and pressure exceeding its critical values. The test cases and the initial and boundary conditions are listed in Table 1, where the subscript inj and ∞ represent the initial injection conditions and chamber conditions, respectively. Re and Ma represent the jet Reynolds
Results and discussion
As shown in Table 1, the injection temperature of case 1 is 126.9 K that just exceeds the critical temperature (T = 126.2 K) but below the pseudo-boiling temperature (T = 129.8 K), we consider this case as “lowly supercritical”. However, as the case 1 still has a relatively strong pseudo-boiling behavior, so it also can be considered transcritical. While the injection temperature in Case 2 is 137 K which exceeds significantly the pseudo-boiling temperature, thus this is a strictly supercritical
Summary
By using a new solver, which has been incorporated into the CFD software OpenFOAM, cryogenic fluid injection and mixing under transcritical and supercritical conditions is numerically investigated with emphasis on the difference of the mechanism and characteristics between the two injections. Based on the previous studies, the characteristics of transcritical and supercritical jets are farther explored, and the major findings from our numerical results can be summarized as follows.
In the
Acknowledgement
This work is supported by National Natural Science Foundation of China (grant numbers: 51376029, 51576029).
Conflict of interest
We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled, “Numerical investigation
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