About the Aerothermoelastic Stability of Panels in Supersonic Flows

This article provides new insights into the aerothermoelastic stability of thin plates. Particularly, the issue of loss of stability of an isotropic plate-strip of constant thickness immersed in a supersonic flow field and subjected to a variable temperature field through the thickness is examined. Using the basic principles of the theory of aerothermoelasticity of isotropic bodies, the theories of flexible panels, and the linear law of temperature field through the thickness of the panel, the stability equations and associated boundary conditions are obtained. As expected, the coefficients of the aerothermoelastic governing equations depend on the thermal load, and consequently the panel-flutter critical speed depends on temperature. The model takes into account quadratic and cubic aerodynamic non-linearities as well as cubic geometric non-linearities. Due to the inhomogeneity of the temperature field distribution across the thickness plate buckling instability occurs. This instability accounts for the deformed shape of the plate and the stability boundary depends on the variables characterizing the flow speed, the temperature of the middle plane and the temperature gradient in the direction normal to the plane. It is shown that the combined effect of the temperature field and free-stream regulates the process of stability and the temperature field can significantly change the flutter critical speed and flutter behavior. The problem of stability is also considered in the non-linear framework. The existence and behavior of flutter-type vibrations is investigated at pre- and post-critical speeds. The influence of the temperature field on the dependency of the limit cycle amplitude as a function of speed is studied. Results and discussions are presented along with pertinent concluding remarks.     

Buckling of functionally graded plates under thermal,axial, and shear in-plane loading using complex finite strip formulation

A complex finite strip method was used to study the buckling of functionally graded plates (FGPs) under thermal and mechanical (longitudinal, transverse, and shear in-plane) loading. The mechanical characteristics of FGPs were assumed to vary through the thickness, according to power law distribution. The nonlinear temperature distribution in the direction of the plate thickness was assumed according to thermal conduction steady state conditions. In complex finite strip method, the polynomial Hermitian functions were assumed in the transverse direction and the complex exponential functions were used in the longitudinal direction to evaluate the standard and geometric stiffness matrices that have the ability of calculating the critical shear stress in contrast to trigonometric shape functions. The solution was obtained by the minimization of the total potential energy and solving the corresponding eigenvalue problem. In addition, numerical results for FGPs with different boundary conditions were presented and compared with those available in the literature and the interaction curves of mechanical and thermal buckling capacity of FGPs were obtained.     

Aerothermoelastic Post-Critical and Vibration Analysis of Temperature-Dependent Functionally Graded Panels

This paper deals with the aerothermoelastic post-critical and vibration characteristics of temperature-dependent functionally graded panels in a supersonic airflow. The structural formulation is based on the von Karman plate theory and material properties are assumed to be temperature-dependent and graded in the thickness direction according to power law distribution in terms of the volume fractions of the constituents. The two-dimensional panel under study is simply supported, for which the first order piston theory is used to account for the supersonic aerodynamic loading. The Galerkin method is applied to convert the partial differential governing equation into a set of ordinary differential equations. Panel vibration responses are investigated through time history responses, state-space trajectories, frequency spectra and the bifurcation diagrams of Poincaré maps. Moreover, post-critical behaviors are detected using numerical and analytical methodologies such as bifurcation diagrams of Poincaré maps, Lyapunov exponents and Lyapunov dimension. Finally, it is shown that the Lyapunov dimensions for stable and divergence conditions are zero value, while these values for limit-cycle and chaos vibration conditions are integer and non-integer quantity, respectively.     

Multiple fluid flow and heat transfer solutions in a two-sided lid-driven cavity

This study presents a continuation method to calculate flow bifurcation with/without heat transfer in a two-sided lid-driven cavity with an aspect ratio of 1.96. The top and bottom lids of the cavity move in opposite directions and are allowed to be of different temperatures, thereby establishing a temperature gradient in the cavity flow and generating thermal transport. A comprehensive bifurcation diagram of the cavity flow is derived via the continuation method and linear stability analysis is used to identify the nature of the various flow solutions. For the isothermal flow case, the Reynolds number is used as the continuation parameter and three symmetric flows and two asymmetric flows are identified. For the non-isothermal flow case, the Grashof number is used as a continuation parameter. The flow evolution is studied for different temperature gradients, and bifurcation diagrams are constructed as a function of the continuation parameter. A thumb-shaped boundary line is established which identifies a restricted region defined in terms of the Grashof and Reynolds numbers within which a stable flow state exists.     

THERMAL BUCKLING OF FUNCTIONALLY GRADED PLATES BASED ON HIGHER ORDER THEORY

Equilibrium and stability equations of a rectangular plate made of functionally graded material (FGM) under thermal loads are derived, based on the higher order shear deformation plate theory. Assuming that the material properties vary as a power form of the thickness coordinate variable z and using the variational method, the system of fundamental partial differential equations is established. The derived equilibrium and stability equations for functionally graded plates (FGPs) are identical to the equations for laminated composite plates. A buckling analysis of a functionally graded plate under four types of thermal loads is carried out and results in closed-form solutions. The critical buckling temperature relations are reduced to the respective relations for functionally graded plates with a linear composition of constituent materials and homogeneous plates. The results are compared with the critical buckling temperatures obtained for functionally graded plates based on classical plate theory given in the literature. The study concludes that higher order shear deformation theory accurately predicts the behavior of functionally graded plates, whereas the classical plate theory overestimates buckling temperatures.     

AEROTHERMOELASTIC PHENOMENA OF AEROSPACE AND COMPOSITE STRUCTURES

The thermal postbuckling and aerodynamic-thermal load analysis of cylindrical laminated panels has been performed using the finite element method. To consider large deflections due to thermomechanical loads, the von Karman nonlinear displacement-strain relationships based on layerwise theory are applied. The cylindrical arc-length method is used to take account of the snapping phenomena. The panel flutter analysis of cylindrical panels subject to thermal stresses is carried out using Hans Krumhaar's supersonic piston theory. For the enhancement of the postbuckling and panel flutter behavior subjected to thermal load, the shape memory alloy hybrid composite (SMAHC) panel is investigated.     

Analysis of Al A359/SiCp Functionally Graded Cylinder Subjected to Internal Pressure and Temperature Gradient with Elastic-Plastic Deformation

In this article, an analytical elastic-plastic solution for thick-walled cylinders made of Functionally Graded Materials (FGMs) subjected to internal pressure and thermal loading is presented. Based on the experimental results, a mathematical model to predict the yielding through the thickness of FG AlA359/SiCp cylinder is developed. It is shown that under the temperature gradient loading, there is a point in the cylinder where the circumferential stress changes from compressive to tensile. The position of this point depends on the geometry and material properties of the FG cylinder and is independent of the temperature gradient.     

Visualiztion of Unsteady Gas／Vapor Expansion Flows

INTRODUCTIONReleaseoflatentheataftercondensationofpureva-porsorinvaPor/carriergasmixturesleadstocomplexdynamicalinteractionsoftheflowwiththephasetran-sitionprocess.Infastexpansionflowstheformationoftheliquidphaseisdominatedbyhomogeneouscon-densation.If,asinmanyinternalflowsofwatervapor,thecoolingrateoftheexpansion-dT/dtisoftheor-der1"/ps,heterogeneouscondensationeffectscanbeneglected.TyPicalwatervaporcontentsinthesupplyleadtotransoniccondensationonsetMachnumbers,wheretheflowisnearthemaxi…     

Pressure testing of large-scale torispherical heads subject to knuckle buckling

Two fabricated steel torispherical heads were tested under internal pressure to determine their buckling and rupture strengths. Both models had cylindrical diameters of 192 in, knuckle radii of 32·64 in, sphere radii of 172·8 in and measured thicknesses of 0·196 in (Model 1) and 0·270 in (Model 2).For Model 1, initial buckling was noted at 58 psi. Pressurization was continued to rupture at 229 psi. During the test, 14 buckles formed and a maximum strain of 3·5% was recorded in the spherical portion of the model.For Model 2, initial buckling was noted at 106 psi. Pressurization was continued to rupture at 332 psi. During the test 14 buckles formed and maximum strains of 4·3–4·7% were recorded in the spherical portion of the model.     

Numerical Study on Flow and Cooling Characteristics for Supersonic Film Cooling

With the booming performances of the gas turbine engine, the turbine vane of the gas turbine engine experiences more extreme thermal environment with supersonic flows. The film cooling applied in the supersonic flow condition has essential difference from that used in the subsonic flow condition in the flow characteristics and cooling effectiveness. This article focused on the film cooling of two parallel flows (primary flow and coolant flow) with supersonic or subsonic velocity, respectively. The results show that: on the condition of supersonic primary flow and subsonic coolant flow, the coolant flow with lower momentum is sheared and dragged by the higher momentum primary flow because of the viscous property of fluid． At the meantime, the thermal and momentum of the primary flow transfers into the coolant flow rapidly． It causes the great damage of the film coverage, and the decrease of the cooling effectiveness dramatically． In contrast, on the condition of supersonic primary flow and supersonic coolant flow, the film coverage of the supersonic coolant flow can last further far than that of the subsonic coolant flow on the same blowing ratio． The turbulence kinetic energy seems to be depressed by the shorten of velocity difference of two supersonic flow. Therefore, the cooling effectiveness is enhanced by 45% for the supersonic primary and coolant flow.     

INELASTIC THERMAL BUCKLING OF METAL MATRIX LAMINATED PLATES

A method is proposed for determining the critical temperature changes that cause inelastic thermal bifurcation buckling of metal matrix composite plates. The inelastic behavior of the metallic matrix is described by an elastic-viscoplastic temperature-dependent constitutive law; the fibers are allowed to be either elastic or elastic-viscoplastic material. The approach is based on the applied thermal load and the history-dependent instantaneous effective thermomechanical properties of metal matrix composites, which are established by a micromechanical analysis. The method is illustrated by the prediction of the inelastic thermal buckling of SiC/Ti metal matrix angle-ply laminated plates by employing the classical and first-order shear deformable laminated plate theories.     

Deformation process of a straight fillet welded joint

Single-curvature polyhedron hydrobulging technology for manufacturing spherical vessels can be adopted to build spherical pressure vessels without using heavy presses and large-size dies. It has been proved that the cost and production time is greatly reduced. When using the technology, one of the difficulties to be overcome is buekling of a straight fillet weided joint that can increase the pressure under which the polyhedron is bulged into a spherical vessel and makes the straight fillet welded joint split along the tangential direction of the fillet welded joint. This paper studies the buckling mechanism of a latitudinal straight fillet welded joint of an orange polyhedron. The result shows that the buckling process of a straight fillet welded joint can be divided into three stages: (a) single-buckle stage: (b) multiple-buckle stage: (c) circularizing stage. A direct reason for buckling of a straight fillet welded joint is the action of unevenly distributed tensile stress perpendicular to the fillet welded joint. Avoiding serious geometry discontinuity on a polyhedron wall, adopting a polyhedron structure with greater dihedral angles or increasing loading capability of the polyhedron can decrease the height of buckles although using these measures can not prevent buckles from emerging.     

Numerical investigations of mixed supersonic and subsonic combustion modes in a model combustor

Flame dynamics and statistics of mixed supersonic and subsonic combustion modes under different air inflow and global equivalence ratio conditions in a hydrogen-fueled model combustor are numerically studied. Three methods including spanwise-averaged Mach number, spanwise-averaged Mach number conditioning on the local heat release, and fraction of heat release are proposed to identify supersonic and subsonic combustion modes. The probability distributions of supersonic and subsonic combustion modes are also analyzed based on the statistics on multiple instantaneous snapshots of the numerical results. The critical global equivalence ratio for thermal choking in a range of supersonic inflow conditions is derived theoretically based on a one-dimensional duct flow with heat addition. Furthermore, it is found that the flame lift-off distance in both supersonic and subsonic flows decreases with increased air inflow velocity, but increases with global equivalence ratio. The fraction of supersonic heat release and its oscillation increase with increased air inflow velocity.     

Numerical simulation of natural gas flows in diffusers for supersonic separators

Diffusers play a vital role in the supersonic separator to convert kinetic energy into pressure energy. The natural gas flows in diffusers were numerically calculated using the navier-stokes equations with the RSM (reynolds stress model). The behavior of gas dynamic parameters was analyzed under conditions of shock waves and boundary layers. The results show that the conical diffuser with high pressure recovery performance is a good choice for the supersonic separator. The shock waves appear as bifurcation structures as a result of the interaction between the shocks and the boundary layer in the conical diffuser. When the swirling flow goes into the diffuser, the strength of the swirl changes the shock positions and the static pressure. The strong swirl results in the shift forward of the shock and the non-uniform distributions of the static pressure.     

Buckling of Functionally Graded Cylindrical Shells Under Combined Thermal and Compressive Loads

This article focuses on analytical solutions for bifurcation buckling of FGM cylindrical shells under thermal and compressive loads. A new solution methodology is established based on Hamilton's principle. The fundamental problem is subsequently transformed into the solutions of symplectic eigenvalues and eigenvectors, respectively. Then, by applying a unidirectional Galerkin method, imperfection sensitivity of an imperfect FGM cylindrical shell is discussed in detail. The solutions reveal that boundary conditions, volume fraction exponent, FGM properties, and temperature rise distribution significantly influence the buckling behavior. Critical stresses are reduced greatly due to the existence of initial geometric imperfections.     

Thermal-structural dynamic analysis of a satellite antenna with the cable-network and hoop-truss supports

Abstract

Thermally induced structural disturbances of the flexible appendages on a satellite usually occur during eclipse transitions. As a large-scale space structure consists of rod members, cyclic thermal shock induced vibrations such as the divergent thermal flutter may be crucial for its functional serving. In this article, the motivation is to estimate the dynamical behaviors of the AstroMesh antenna under solar flux shock. For this purpose, we developed a numerical approach for the thermal-structural coupling analysis of tensegrity structures considering the pre-stressed state after the form-finding process. The Euler-Bernoulli beam theory, the pre-stressed bar model, and the Fourier thermal element are employed in conjunction with the special consideration on the effect of structural deformations on absorbing solar flux. It is found that, unlike the single boom structure, thermal deformations of the AstroMesh antenna are mainly caused by the temperature variation along rod axis-direction, rather than the temperature gradient on rod cross-section. Besides, the phenomenon of thermally induced vibrations can hardly happen in the AstroMesh antenna.     

层流脉动流中平行圆柱体的温度边界层

采用数值模拟方法研究了一个平行圆柱体在层流脉动流中的温度边界层特性。数值模拟结果与实验数据一致。研究发现脉动流中平行圆柱体形成了形状不规则但相对稳定的温度边界层,并在流动方向上周期性脉动。脉动流中平行圆柱体的温度边界层平均厚度小于稳定流动下的温度边界层平均厚度,并以脉动流的频率进行脉动。此外, 脉动流中平行圆柱体的壁面温度小于稳定流动下的壁面温度,表明脉动流下圆柱体的对流传热得到了强化。在一个脉动周期内,圆柱体在后半周期的温度边界层厚度和热阻均小于前半周期的温度边界层厚度和热阻。     

Flow Patterns and Thermal Drag in Supersonic Duct Flow with Heating

ＦｌｏｗＰａｔｔｅｒｎｓａｎｄＴｈｅｒｍａｌＤｒａｇｉｎＳｕｐｅｒｓｏｎｉｃＤｕｃｔＦｌｏｗｗｉｔｈＨｅａｔｉｎｇ￥Ｚｅｎｇ－ＹｕａｎＧｕｏ；Ｚｈｉ－ＨｏｎｇＬｉｕ（ＤｅｐａｒｔｍｅｎｔｏｆＥｎｇｉｎｅｅｒｉｎｇＭｅｃｈａｎｉｃｓ，ＴｓｉｎｇｈｕａＵ...     

Heat transfer in a supersonic flow

At present it is commonly assumed that some peculiar surface exists which bounds a viscous region around a body in a supersonic flow. This region is identified with a laminar or turbulent Prandtl layer, the process of transition of visible motion into heat being described by the procedures developed by Prandtl and von Kármán for subsonic flows.

In the present work another approach is used based on the ideas of Osborne Reynolds and the so-called resolution equation where transition of thermal motion into pulsating one is fixed which, in its turn establishes relationship between the Nusselt and Reynolds numbers. This is a power-law relationship in which the coefficients and power exponent may be pre-calculated based on simple considerations. This has been done in the present work.     

Numerical Analysis of Constructal Water-Cooled Microchannel Heat Sinks with Multiple Bifurcations in the Entrance Region

The Constructal Theory is applied to obtain better thermal performance from a type of microchannel heat sink. Based on a smooth, straight, rectangular microchannel heat sink (Case 1), three different configurations of constructal multiple bifurcation are designed for the entrance region of each microchannel. These types are one bifurcation (Case 2), two bifurcations with the second placed in the front part (Case 3), and two bifurcations with the second bifurcation placed in the front part (Case 4). The corresponding laminar flow and heat transfer fields are investigated numerically by means of computational fluid dynamics. The effects of the bifurcation number and length ratio on pressure drop and overall thermal resistance are observed. The overall thermal resistance for the four microchannel heat sinks is compared when subjected to pumping power. It is found that designing one or two bifurcations (Cases 2, 3, 4) in the entrance region can improve thermal performance effectively. It is also recommended to place the second bifurcation in the back part (Case 4) of the microchannel heat sinks to obtain good overall thermal performance by proper design of the bifurcation position and number of channels.