Solving many important industrial problems requires knowing the values of the heat transfer coefficient of passing of one or more FLUID streams in different equipment, systems or pipes. In the present study, a numerical model has been developed to simulate COMPRESSIBLE FLUID FLOW at the inlet of a hot pipe with different angles to the horizon. In this zone, the hydrodynamic and thermal boundary layers of the FLUID FLOW are developing. Due to the turbulence of the FLUID FLOW due to the interaction of heat and FLUID FLOW inside this tube, a three-dimensional turbulent model was used for this simulation. For this purpose, continuity and COMPRESSIBLE Navier-Stokes equations, Reynolds stress model, and turbulent and COMPRESSIBLE energy equation have been solved simultaneously. Then, using a set of numerical runs by the concepts of experimental design and optimization methods, a predictive formula for the Nusselt number for these FLOWs has been obtained. Finally, the ability of this formula has been investigated using a set of laboratory data.

The study of COMPRESSIBLE FLOW plays a fundamental role in the design of heat exchangers at high temperature and pressure. COMPRESSIBLE FLOW is used to design the aerodynamic structure, engines, and high-speed vehicles. In view of these utilities, this paper is deliberated to acquire the analysis of the unsteady COMPRESSIBLE FLOW of a viscous FLUID through an inclined asymmetric channel with thermal effects. Special attention is paid to convective heat transfer with impact of viscous dissipation, source/sink, and joule heating effects. In addition, thermal FLOW is analyzed through slip boundary conditions. The current problem is modeled through the laws of energy, momentum, and mass with the help of a FLUID’s response towards compression. As a result, the coupled nonlinear partial differential equations are obtained, which are investigated through a well-known numerical approach, the explicit finite difference method. The study examines impact of several parameters on the FLOW rate, velocity, and temperature with the help of graphical representations. The behavior of FLOW rate is intended to change with time.

Several studies of COMPRESSIBLE FLOWs show that the pressure-strain is the main indicator of the structural compressibility effects. Undoubtedly, this term controls the change in the Reynolds stress anisotropy. Regarding the model of Adumitroiae et al., the slow part of the pressure strain correlation like the Rotta model uses the standard coefficient C1. The model predictions do not show large differences when compressibility increases. Correction of this coefficient using the turbulent Mach number is proposed. The two forms models of Adumitroiae et al. (with and without correction of C1) are considered to study COMPRESSIBLE mixing layers. The obtained results show that the predictions of the proposed compressibility correction model agree with the experiment results of Goebel and Dutton.

In this paper, an explicit finite element based numerical procedure is presented for simulating three-dimensional inviscid COMPRESSIBLE FLOW problems. The implementation of the first-order upwind method and a higher-order artificial dissipation technique on unstructured grids, using tetrahedral elements, is described. Both schemes use a multi-stage Runge-Kutta time-stepping method for time integration. The use of an edge-based data structure in the finite element formulation and its computational merits are also elaborated. Furthermore, the performance of the two schemes in solving a benchmark problem involving transonic FLOW about an ONERA M6 wing is compared and detailed solutions are presented.

In this paper, three new schemes based on normalized variable diagram (NVD) to calculate convection term of conservative equations are developed. The solution technique is of the finite volume type utilizing a co-located arrangement for storage of variables and a uniform mesh. The working variables are velocity and pressure which makes the schemes applicable to both COMPRESSIBLE and in COMPRESSIBLE FLOWs. The interpolation of these schemes has been done with smooth functions and this point improves the convergence and accuracy of the solution. These methods are applied to the computation of steady transonic over bump in channel geometry as well as to the transient shock-tube problem. The results are compared with other computations published in the literature.

Existing solutions of the problem of axisymmetric stagnation-point FLOW and heat transfer on either a cylinder or flat plate are for inCOMPRESSIBLE FLUID. Here, FLUID with temperature dependent density is considered in the problem of axisymmetric stagnation-point FLOW and heat transfer on a cylinder with constant heat flux. The impinging free stream is steady and with a constant strain rate, `k. An exact solution of the Navier-Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by use of appropriate transformations introduced for the first time. The general self-similar solution is obtained when the wall heat flux of the cylinder is constant. All the solutions above are presented for Reynolds numbers, Re=`ka2/2u, ranging from 0.01 to 1000, selected values of compressibility factors, and different values of Prandtl number, where a is cylinder radius and u is the kinematic viscosity of the FLUID. For all Reynolds numbers and surface heat flux, as the compressibility factor increases, both components of the velocity field, the heat transfer coefficient and the shear-stresses increase, and the pressure function decreases.

In this paper, oscillations of a thin high flexible strip attached to a three-dimensional body in viscous subsonic FLOW were simulated. The aim is to analyze the interactions of FLUID and structure using a proper coupling algorithm that can couple the FLUID and structure solvers and provide the proper data exchange between them. A computational FLUID dynamics solver is used for FLUID FLOW simulation and Euler-Bernoulli cantilevered beam model is used for structural analysis. For analyzing the FLUID-structure interaction, iterative partitioned coupling algorithm is used for interrelation and data exchange between structure and FLUID. Then, the results of vibration characteristics including the amplitude and frequency and forces and moments variations are presented with respect to different bending stiffness and strip masses. The simulation is done in 2D and 3D conditions which 3D case is for a cylinder and flexible strip attached to the bottom of the body. Results show that the developed framework captures the physics of FLUID-structure interaction successfully. Also, parametric study shows that for the flexible thin strip attached to the end of the body in the specified regime of FLOW, three deformation types consist of static deformation, stable oscillations, and chaotic unstable oscillations will occur based on the strip characteristics.

In this paper, the preconditioned nonlinear multigrid algorithm is used with aim of improving convergence rates and reducing CPU time for solving COMPRESSIBLE FLOW equations. MultiGrid (MG) methods are a group of algorithms that are used for accelerating convergence of differential equations using a series of discretizations. This method is based upon the principle that explains when the global (low-frequency) error of a fine mesh is represented on a coarse mesh, it retains the same characteristics as of the local (high-frequency) error, thus the same method for removing high frequency errors is also applicable in such situation. When the nonlinear multigrid algorithm drives the external iterations, the choice of smoother on each grid level plays an important role in the performance. In this research, a preconditioning method has been used to reduce instabilities of the linear system that arise in each iteration. Some important results of this research are: choosing the best preconditioning scheme to be coupled with MG method, assessment of MG method performance in equations of turbulence, laminar and inviscid FLOWs and analysis of different cycling schemes.

Ejector is important equipment in the chemical industry. It is mainly used for vacuuming and mixing of FLOWs. In the present work a computer modeling of the FLOW inside an ejector is used to give a better understanding of the principle of the operation of an ejector. Since the FLUID inside an ejector passes through sub sonic, sonic and super sonic regimens, the pressure field is used as the controlling variable and the density is found through the constitutive equations. The control volume method with a co-location grid, attached to the boundary is used to discretize the domain. The overall solution is obtained by the SIMPLE method and to dissociate the pressure and the velocity grid Rhie-Chow interpolation method is employed A central difference approximation method is used to approximate the density on the element borders and the upwind approximation is used to correct the density correction factors. Both upwind, quick and minimum gradient methods were used to approximate the momentum variables on the control volumes. The resultant matrices are solved with the tri-diagonal method the accuracy of the model is checked by simulating a FLOW regimen in a converging-diverging nozzle, and comparing the results with the available experimental data. The results show that for an inviscid FLUID the first order approximation produce as accurate results as the higher order approximations while it has a better stability. However, for the viscous FLUID the second order approximation produces a better understanding of the physics of the problem. The solution also shows that the FLOW field inside an ejector is a complex one and the shock wave has a great influence on the pressure field especially close to the walls. The upper convective quick method did not converg well in the shock calculations while the slowest descent method had a very stable behavior in the analysis of the shock behavior.

This paper is devoted to the second-order closure for COMPRESSIBLE turbulent FLOWs with special attention paid to modeling the pressure-strain correlation appearing in the Reynolds stress equation. This term appears as the main one responsible for the changes of the turbulence structures that arise from structural compressibility effects. The structure of the gradient Mach number is similar to that of turbulence, therefore this parameter may be appropriate to study the changes in turbulence structures that arise from structural compressibility effects. Thus, the inCOMPRESSIBLE model (LRR) of the pressure-strain correlation and its corrected form by using the turbulent Mach number, fail to correctly evaluate the compressibility effects at high shear FLOW. An extension of the widely used inCOMPRESSIBLE model (LRR) on COMPRESSIBLE homogeneous shear FLOW is the major aim of the present work. From this extension the standard coefficients Ci became a function of the compressibility parameters (the turbulent Mach number and the gradient Mach number). Application of the model on COMPRESSIBLE homogeneous shear FLOW by considering various initial conditions shows reasonable agreement with the DNS results of Sarkar. The ability of the models to predict the equilibrium states for the FLOW in cases A1 and A4 from DNS results of Sarkar is examined, the results appear to be very encouraging.Thus, both parameters Mt and Mg should be used to model significant structural compressibility effects at high-speed shear FLOW.