The simulation of high-pressure turbulent flows, where the pressure, p, is larger than the critical value, p(sub c), for the species under consideration, is relevant to a wide array of propulsion systems, e.g. gas turbine, diesel, and liquid rocket engines. Most turbulence models, however, have been developed for atmospheric-p turbulent flows. The difference between atmospheric-p and supercritical-p turbulence is that, in the former situation, the coupling between dynamics and thermodynamics is moderate to negligible, but for the latter it is very significant, and can dominate the flow characteristics. The reason for this stems from the mathematical form of the equation of state (EOS), which is the perfect-gas EOS in the former case, and the real-gas EOS in the latter case. For flows at supercritical pressure, p, the large eddy simulation (LES) equations consist of the differential conservation equations coupled with a real-gas EOS. The equations use transport properties that depend on the thermodynamic variables. Compared to previous LES models, the differential equations contain not only the subgrid scale (SGS) fluxes, but also new SGS terms, each denoted as a correction. These additional terms, typically assumed null for atmospheric pressure flows, stem from filtering the differential governing equations, and represent differences between a filtered term and the same term computed as a function of the filtered flow field. In particular, the energy equation contains a heat-flux correction (q-correction) that is the difference between the filtered divergence of the heat flux and the divergence of the heat flux computed as a function of the filtered flow field. In a previous study, there was only partial success in modeling the q-correction term, but in this innovation, success has been achieved by using a different modeling approach. This analysis, based on a temporal mixing layer Direct Numerical Simulation database, shows that the focus in modeling the q-correction should be on reconstructing the primitive variable gradients rather than their coefficients, and proposes the approximate deconvolution model (ADM) as an effective means of flow field reconstruction for LES heat flux calculation. Further, results for a study conducted for temporal mixing layers initially containing oxygen in the lower stream, and hydrogen or helium in the upper stream, show that, for any LES, including SGS-flux models (constant-coefficient Gradient or Scale-Similarity models, dynamic-coefficient Smagorinsky/Yoshizawa or mixed Smagorinsky/Yoshizawa/Gradient models), the inclusion of the q-correction in the LES leads to the theoretical maximum reduction of the SGS heat-flux difference. The remaining error in modeling this new subgrid term is thus irreducible.

A new modeling approach is based on the concept of large eddy simulation (LES) within which the large scales are computed and the small scales are modeled. The new approach is expected to retain the fidelity of the physics while also being computationally efficient. Typically, only models for the small-scale fluxes of momentum, species, and enthalpy are used to reintroduce in the simulation the physics lost because the computation only resolves the large scales. These models are called subgrid (SGS) models because they operate at a scale smaller than the LES grid. In a previous study of thermodynamically supercritical fluid disintegration and mixing, additional small-scale terms, one in the momentum and one in the energy conservation equations, were identified as requiring modeling. These additional terms were due to the tight coupling between dynamics and real-gas thermodynamics. It was inferred that if these terms would not be modeled, the high density-gradient magnitude regions, experimentally identified as a characteristic feature of these flows, would not be accurately predicted without the additional term in the momentum equation; these high density-gradient magnitude regions were experimentally shown to redistribute turbulence in the flow. And it was also inferred that without the additional term in the energy equation, the heat flux magnitude could not be accurately predicted; the heat flux to the wall of combustion devices is a crucial quantity that determined necessary wall material properties. The present work involves situations where only the term in the momentum equation is important. Without this additional term in the momentum equation, neither the SGS-flux constant-coefficient Smagorinsky model nor the SGS-flux constant-coefficient Gradient model could reproduce in LES the pressure field or the high density-gradient magnitude regions; the SGS-flux constant- coefficient Scale-Similarity model was the most successful in this endeavor although not totally satisfactory. With a model for the additional term in the momentum equation, the predictions of the constant-coefficient Smagorinsky and constant-coefficient Scale-Similarity models were improved to a certain extent; however, most of the improvement was obtained for the Gradient model. The previously derived model and a newly developed model for the additional term in the momentum equation were both tested, with the new model proving even more successful than the previous model at reproducing the high density-gradient magnitude regions. Several dynamic SGS-flux models, in which the SGS-flux model coefficient is computed as part of the simulation, were tested in conjunction with the new model for this additional term in the momentum equation. The most successful dynamic model was a mixed model combining the Smagorinsky and Gradient models. This work is directly applicable to simulations of gas turbine engines (aeronautics) and rocket engines (astronautics).

For flows at supercritical pressure, p, the large-eddy simulation (LES) equations consist of the differential conservation equations coupled with a real-gas equation of state, and the equations utilize transport properties depending on the thermodynamic variables. Compared to previous LES models, the differential equations contain not only the subgrid-scale (SGS) fluxes but also new SGS terms, each denoted as a 'correction'. These additional terms, typically assumed null for atmospheric pressure flows, stem from filtering the differential governing equations and represent differences, other than contributed by the convection terms, between a filtered term and the same term computed as a function of the filtered flow field. In particular, the energy equation contains a heat-flux correction (q-correction) which is the difference between the filtered divergence of the molecular heat flux and the divergence of the molecular heat flux computed as a function of the filtered flow field. We revisit here a previous a priori study where we only had partial success in modelling the q-correction term and show that success can be achieved using a different modelling approach. This a priori analysis, based on a temporal mixing-layer direct numerical simulation database, shows that the focus in modelling the q-correction should be on reconstructing the primitive variable gradients rather than their coefficients, and proposes the approximate deconvolution model (ADM) as an effective means of flow field reconstruction for LES molecular heat-flux calculation. Furthermore, an a posteriori study is conducted for temporal mixing layers initially containing oxygen (O) in the lower stream and hydrogen (H) or helium (He) in the upper stream to examine the benefit of the new model. Results show that for any LES including SGS-flux models (constant-coefficient gradient or scale-similarity models; dynamic-coefficient Smagorinsky/Yoshizawa or mixed Smagorinsky/Yoshizawa/gradient models), the inclusion of the q-correction in LES leads to the theoretical maximum reduction of the SGS molecular heat-flux difference; the remaining error in modelling this new subgrid term is thus irreducible. The impact of the q-correction model first on the molecular heat flux and then on the mean, fluctuations, second-order correlations and spatial distribution of dependent variables is also demonstrated. Discussions on the utilization of the models in general LES are presented.

A large eddy simulation (LES) a posteriori study is conducted for a temporal mixing layer which initially contains different species in the lower and upper streams and in which the initial pressure is larger than the critical pressure of either species. A vorticity perturbation, initially imposed, promotes roll-up and a double pairing of four initial spanwise vortices to reach a transitional state. The LES equations consist of the differential conservation equations coupled with a real-gas equation of state, and the equations utilize transport properties depending on the thermodynamic variables. Unlike all LES models to date, the differential equations contain, additional to the subgrid-scale (SGS) fluxes, a new SGS term denoted a ‘pressure correction’ (p correction) in the momentum equation. This additional term results from filtering the Navier–Stokes equations and represents the gradient of the difference between the filtered p and p computed from the filtered flow field. A previous a priori analysis, using a direct numerical simulation (DNS) database for the same configuration, found this term to be of leading order in the momentum equation, a fact traced to the existence of regions of high density-gradient magnitude that populated the entire flow; in that study, the appropriateness of several SGS-flux models was assessed, and a model for the p-correction term was proposed.In the present study, the constant-coefficient SGS-flux models of the a priori investigation are tested a posteriori in LES devoid of, or including, the SGS p-correction term. A new p-correction model, different from that of the a priori study, is used, and the results of the two p-correction models are compared. The results reveal that the former is less computationally intensive and more accurate than the latter in reproducing global and structural features of the flow. The constant-coefficient SGS-flux models encompass the Smagorinsky (SMC) model, in conjunction with the Yoshizawa (YO) model for the trace, the gradient (GRC) model and the scale similarity (SSC) models, all exercised with the a priori study constant-coefficient values calibrated at the transitional state. Further, dynamic SGS-flux model LESs are performed with the p correction included in all cases. The dynamic models are the Smagorinsky (SMD) model, in conjunction with the YO model, the gradient (GRD) model and ‘mixed’ models using SMD in combination with GRC or SSC utilized with their theoretical coefficient values. The LES comparison is performed with the filtered-and-coarsened DNS (FC-DNS) which represents an ideal LES solution. The constant-coefficient models including the p correction (SMCP, GRCP and SSCP) are substantially superior to those devoid of it; the SSCP model produces the best agreement with the FC-DNS template. For duplicating the local flow structure, the predictive superiority of the dynamic mixed models is demonstrated over the SMD model; however, even better predictions in capturing vortical features are obtained with the GRD model. The GRD predictions improve when LES is initiated at a time past the initial range in which the p-correction term rivals in magnitude the leading-order term in the momentum equation. Finally, the ability of the LES to predict the FC-DNS irreversible entropy production is assessed. It is shown that the SSCP model is the best at recovering the domain-averaged irreversible entropy production. The sensitivity of the predictions to the initial conditions and grid size is also investigated.

A Direct Numerical Simulation (DNS) database of supercritical temporal mixing layer simulations of binary mixtures is studied to identify the Large Eddy Simulation (LES) subgrid scale model needs for high pressure flows. For the oxygen/hydrogen (OH) mixture studied here, an earlier a priori study showed that in addition to the usual subgrid scale flux terms, a new term in the filtered energy equation must be modeled. A model formulation was proposed for this term called heat flux correction (q-correction), but the model was only partially successful in the a priori tests. In this study, the earlier a priori analysis is revisited to investigate the reasons for the limited success of the previously proposed model for the q-correction. In addition, a new modeling strategy is proposed and examined a priori. Finally, an a posteriori study is conducted to test the viability of the newly proposed model.

One of the major challenges in hypersonic flow research is the accurate prediction of transition location. There is a wide range of scatter in transition data obtained from numerous experiments conducted since the 1960’s. It is believed that most of the experimental data obtained in conventional ground test facilities are contaminated by high levels of noise due to acoustic fluctuations from the turbulent boundary layers on the wind tunnel walls. One method to reduce noise is to delay boundary layer transition using, among other features, bleed slots before the nozzle throat. The Purdue Mach 6 quiet tunnel has been designed to reduce the noise level an order of magnitude below that in conventional facilities. However, in this tunnel quiet flow is achieved only for low Reynolds numbers. For high Reynolds numbers the level of noise measured in the test section is dominated by early transition of the boundary layer on the tunnel walls which now appears to be caused by laminar boundary layer separation at the bleed slot. This paper summarizes the numerical analysis performed for one of the bleed slot designs of the Purdue Mach 6 quiet tunnel. The objective of the numerical study is to understand the eect of bleed slot design on the wind tunnel performance where the slot is considered as an upstream perturbation source. The steady state numerical solutions for two dierent stagnation pressures are obtained and analyzed using a commercial flow solver GASPex, version 4.1.0+. To quantify the numerical error in the solutions, a grid sensitivity analysis is conducted. For comparison purposes the Langley Mach 6 quiet tunnel is also analyzed numerically. The presence of large separation on the bleed lip of the unsuccessful Purdue tunnel, and the absence of large separation on the successful Langley tunnel, suggests that the separations are the most likely cause of early transition in the Purdue facility.

We summarize a study that compares experimental laboratory data for gravity-driven coastal surface currents with corresponding theoretical results obtained from a new geostrophic model describing such currents. It is found that experiment and theory are, generally, in good agreement.