Study on the sonic point in unsteady shock reflections via numerical flowfield analysis

A current literature review revealed that unsteady shock reflection is an active research field in terms of the number of still unanswered questions in this area. One of the unresolved aspects of unsteady shock reflection is the relationship between the catch-up and sonic points. In a recent experiment, Skews and Kleine found that the catch-up point is reached at a higher wall angle than the theoretical sonic point predicted by the steady-state two-shock theory. This thesis attempts to shed some light on these matters via numerical flowfield analysis of unsteady shock reflections. Two-dimensional computations are performed using a locally adaptive unstructured unsteady Euler/Navier-Stokes code. At the first stage, a general guideline for numerical modeling of shock wave front structure using the Navier-Stokes equations on adaptive unstructured grid is presented. Obtained results can be directly used for selection of grid resolution required to study shock reflection problems in a viscous flowfields. Then, various techniques for determination of the location of the sonic/catch-up points in unsteady shock reflection based on numerical flowfield analysis are introduced. The results obtained with these techniques regarding the sonic/catch-up points locations are not in agreement with the experimental results of Skews and Kleine. The causes of this disagreement between the experiments and the present CFD study are studied by imitating the experimental technique used for catch-up point determination. It is shown that the reason for this disagreement is that the shock thickness captured in experimental images exceeds the shock physical thickness by a few orders of magnitude, which leads to detection of the catch-up point at higher wall angles. Three flow models are studied to investigate the location of the sonic/catch-up points on a circular cylinder. The first model is based on the Euler (inviscid, non-heat-conducting) equations and an ideal reflecting surface (impermeable wall boundary condition). The computational experiment for this case shows that the sonic and catch-up points are actually the same points, which approach to the theoretical sonic point with grid refinement. The other two models are intend to study the effect of viscosity on the sonic/catch-up points. At first, the ideal reflecting surface (slip boundary condition) is considered. It is shown that for this case the sonic and catch-up points are again the same points, but the viscous effects (finite shock thickness) cause the sonic/catch-up point to be delayed (to occur at lower wall angles) as compared to the two-shock theory predictions. The final model employs the non-slip reflecting surface. Since in this model the flow velocity at the wall is zero, the sonic point cannot be obtained on the reflection surface; however, the catch-up point can be defined and analyzed. The results of the simulations show that even larger delay for the catch-up point is obtained for the viscous case with the non-slip reflecting surface (in the presence of the boundary layer) as compared to the viscous case with the ideal reflecting surface.De nos jours, la réflexion instationnaire de choc est un domaine de recherche en plein essor dans lequel subsistent de nombreuses questions qui demeurent sans réponses. Un des aspects non résolus de la réflexion instationnaire de choc est la relation entre le rattrapage et les points soniques. Dans une expérience récente, Skews et Kleine ont constaté que le point de rattrapage est atteint à un angle de paroi plus élevé que le point sonique théorique prédit par la théorie de l'état stationnaire de deux-chocs. Cette thèse tente de faire la lumière sur ces questions via lanalyse numérique d´ecoulement des réflexions instationnaires de choc. Les calculs 2D sont effectués en utilisant un code localement adaptif non structuré pour la résolution numérique des équations d'Euler/Navier-Stokes instationnaire. A la première étape, un cadre général est présenté pour la modélisation numérique de la structure de l'onde de choc en utilisant les équations de Navier-Stokes sur un maillage adaptatif non structuré. Les résultats ainsi obtenus sont directement utilisés afin de choisir une grille de résolution nécessaire lorsque l'on étudie les problèmes de réflexion de choc dans un écoulement visqueux. Par la suite, diverses techniques basées sur l'analyse numérique d'écoulement sont introduites pour localiser le point sonique/rattrapage dans la réflexion instationnaire de choc. En vue de la localisation du point sonique/rattrapage les résultats obtenus avec ces techniques ne sont pas en accord avec les résultats expérimentaux de Skews et Kleine. Les raisons de ce désaccord entre les résultats expérimentaux et les études CFD actuelles sont étudiées en imitant la technique expérimentale utilisée pour la détermination du point de rattrapage. Il est démontré que la raison de ce désaccord réside dans le fait que l'épaisseur de choc sur les images expérimentales dépasse l'épaisseur physique de choc de quelques ordres de grandeur, ce qui entraîne une prédiction du point de rattrapage à des angles de paroi supérieur. Trois modèles d'écoulement sont étudiés afin de localiser le point sonique/rattrapage sur un cylindre circulaire. Le premier modèle est basé sur les équations d'Euler (non visqueux, non conducteur de chaleur) et les équations d'une surface réfléchissante idéale (conditions aux limites de paroi imperméable). L'expérience numérique sur ce cas montre que les points soniques et rattrapages sont identiques, convergeant vers le point sonique théorique après le raffinement de maillage. Les deux autres modèles sont destinés à étudier l'effet de la viscosité sur le point soniques / rattrapage. Dans un premier temps, la surface réfléchissante idéale (condition de glissement) est considérée. Il est démontré que pour ce cas, les points sonique et rattrapage sont encore les mêmes, mais les effets visqueux (l'épaisseur finie de choc) provoquent le point sonique/rattrapage d'être retardé (de se produire à des angles paroi inférieure) par rapport aux prédictions de la théorie de deux-chocs. Le modèle final utilise la surface réfléchissante réelle (condition non-glissement). Etant donné que la vitesse d'écoulement à la paroi est nulle dans ce modèle, le point sonique ne peut être obtenu sur la surface de réflexion. Cependant, le point de rattrapage peut être déterminé et analysé. Les résultats des simulations montrent quun retard encore plus grand est obtenu pour le point de rattrapage pour le cas visqueux avec la surface réfléchissante réelle (en présence de la couche limite) par rapport au cas visqueux avec la surface réfléchissante idéale

Optimized Design of the District Heating System by Considering the Techno-Economic Aspects and Future Weather Projection

High mountains and cold climate in the north-west of Iran are critical factors for the design of optimized District Heating (DH) systems and energy-efficient buildings. It is essential to consider the Life Cycle Cost (LCC) that includes all costs, such as initial investment and operating costs, for designing an optimum DH system. Moreover, considering climate change for accurately predicting the required heating load is also necessary. In this research, a general optimization is carried out for the first time with the aim of a new design concept of a DH system according to a LCC, while considering all-involved parameters. This optimized design is based on various parameters such as ceiling and wall insulation thicknesses, depth of buried water and heating supply pipes, pipe insulation thickness, and boiler outlet temperature. In order to consider the future weather projection, the mentioned parameters are compared with and without climate change effects in a thirty-year period. The location selection was based on the potential of the region for such a system together with the harsh condition of the area to transport the common fossil fuel to the residential buildings. The obtained results show that insulation of walls is more thermally efficient than a roof with the same area in the selected case. In this case, polyurethane is the best material, which can cause a reduction of 59% in the heating load and, consequently, 2332 tons of CO2 emission annually. The most and the least investment payback periods are associated with the polyurethane and the glass wool insulation materials with the amounts of seven and one years. For the general optimization of the DH system, the Particle Swarm Optimization (PSO) method with a constriction coefficient was chosen. The results showed that the optimal thickness of the polyurethane layer for the thermal insulation of the building exterior walls is about 14 cm and the optimal outlet temperature of the boiler is about 95 °C. It can be also concluded that the optimal depth for the buried pipes is between 1.5 to 3 m underground. In addition, for the pipe with elastomeric insulation layer, the thickness of 2 cm is the optimal choice

Estimation of Boundary Conditions in the Presence of Unknown Moving Boundary Caused by Ablation

Ablative materials can sustain very high temperatures in which surface thermochemical processes are significant enough to cause surface recession. Existence of moving boundary over a wide range of temperatures, temperature-dependent thermophysical properties of ablators, and no prior knowledge about the location of the moving surface augment the difficulty for predicting the exposed heat flux at the receding surface of ablators. In this paper, the conjugate gradient method is proposed to estimate the unknown surface recession and time-varying net surface heat flux for these kinds of problems. The first order Tikhonov regularization is employed to stabilize the inverse solution. Considering the complicated phenomena that are taking place, it is shown via simulated experiment that unknown quantities can be obtained with reasonable accuracy using this method despite existing noises in the measurement data