Low Speed Compressible Flow Research Articles

The impact of random 3D roughness on natural convection along a vertical plate

This study simulates natural convection on vertical surfaces with random roughness under Reynolds number conditions of 106. The roughness of these surfaces is arranged randomly, making the simulation closer to real-world conditions. To handle natural convection in low-speed compressible flows, our solver treats the fluid as compressible to solve the complete Navier-Stokes equations. Observations show that adjacent peaks generate vortices, limiting the heat circulation between valleys and the surrounding cooler air. Influenced by buoyancy, the slower upstream flow over rough surfaces stabilize heat transfer in the valleys and slightly accelerates the flow near the peaks, resulting in higher local Nusselt numbers on the peaks. As the flow velocity increases, the disturbances caused by rough elements become more pronounced, leading to a more chaotic flow pattern downstream, thereby affecting the overall heat transfer. This phenomenon becomes more pronounced with increasing surface roughness. The overall distribution of Nusselt numbers shows higher and more concentrated values upstream compared to downstream. Despite local Nusselt numbers on rough surfaces generally being higher than those on smooth surfaces, the average Nusselt numbers are lower on the rough surfaces due to the longer time required for heat transfer on rough surfaces.

Investigation of the influence of the dimensionless centrifugal work number on spanwise rotating channel low-speed compressible flow

Investigation of the influence of the dimensionless centrifugal work number on spanwise rotating channel low-speed compressible flow

The numerical investigation of aerodynamics and aeroacoustics effects in a full-scale true wireless headphone

Abstract This study investigates the flow characteristics and aeroacoustic effects in a true wireless (TWS) headphone using computational fluid dynamics simulations. A low-speed compressible flow solver is employed to analyze the flow fields and pressure variations associated with fluid-induced noise. The accuracy of the simulations is validated through comparisons with experimental and numerical data, demonstrating good consistency. The analysis reveals the presence of asymmetric vortex shedding patterns, attributed to the angle of airflow and the irregular surface of the headphones. The examination of the microphone chamber highlights the significance of design parameters in shaping flow patterns and acoustics. Optimized designs have the potential to achieve noise reductions of up to 10.62% or amplifications of up to 24.95%. These findings contribute to the development of improved active noise cancellation systems and the enhancement of TWS headphone technology, aiming to reduce external noise and enhance sound quality.

Investigation of boundary layer thickness and turbulence intensity on film cooling with a fan-shaped hole by direct numerical simulation

Effects of the mainstream boundary layer thickness and the turbulence intensity on film cooling under low Reynolds number conditions are studied in this work by the direct numerical simulation (DNS). In other to solve low-speed compressible flow problems, several methods of Roe scheme, preconditioning, dual time stepping, and LUSGS are adopted to solve governing equations. Results reveal that a horseshoe vortex appears with a thicker mainstream boundary layer, and thus the lateral coverage of the coolant fluid has increased significantly. In addition, the existence of turbulence intensity eliminates the blow-off phenomenon, which happens in a thin mainstream boundary layer condition and enhances the film cooling effectiveness.

Direct numerical simulation of film cooling with a fan-shaped hole under low Reynolds number conditions

Shaped film cooling holes have several features that can greatly improve film cooling effectiveness, and it has been studied and utilized in gas turbine engines for decades. Few studies, however, have reported the effects of low mainstream Reynolds number on shaped film cooling holes. In this study, the effects of mainstream Reynolds number on film cooling with a fan shaped hole are studied by utilizing direct numerical simulation (DNS). In addition, the compressibility and the viscosity of the working fluid are simultaneously considered, and the non-reflecting and absorbing boundary conditions are adopted at the exit of the main channel. The methods of the Roe scheme, preconditioning, and dual time stepping are employed together to solve the governing equations of a low-speed compressible flow problem. This study considers the mainstream Reynolds numbers of ReD = 480 and 3200 with 0% and 5% turbulence intensity in the mainstream. Results reveal that the coolant jet penetrates into the mainstream with a mainstream Reynolds number of 480. However, at the higher Reynolds number, the coolant jet develops along the wall and results in better film cooling effectiveness. In addition, special attention is paid to the structures of the vortices developed from the crossflow. Hairpin vortices become smaller at higher mainstream Reynolds numbers. On the contrary, horseshoe vortices appear when the mainstream Reynolds number is increased. A detailed comparison of the vortices is presented in this study.

Flow downward penetration of vertical parallel plates natural convection with an asymmetrically heated wall

Phenomena of the flow downward penetration in vertical parallel plates natural convection with an asymmetrically heated wall are investigated numerically. For clarifying the occurrence of flow downward penetration, the width of parallel plates is further broadened and broader than that investigated in the previous study in which the flow reversal was studied in detail. In order to simulate realistically, the compressibility and the viscosity of the working fluid are simultaneously considered, and the non-reflecting boundary is adopted at apertures of plates. The methods of the Roe scheme, preconditioning, and dual time stepping matching LUSGS are coordinated to solve governing equations of a low-speed compressible flow problem. The flow downward penetration, in which fluids are sucked from surroundings outside the outlet to flow into the parallel plates and through the inlet flow out of parallel plates, is composed of a few fluids and firstly observed. Also, two flow reversal caused by the buoyancy force appear in the upper left region, and one flow reversal induced by the flow downward penetration appears in the low right region. The usage of the existing results and present study, an equivalent ratio of the width to the length of parallel plates, of which the heat transfer rate is the same as the single vertical heated plate, can be expediently obtained. In this study, the ratio is about 0.6.

An investigation of natural convection in a three dimensional square wavy channel

Natural convection in a three dimensional wavy channel, which is composed of numerous two dimensional cross sections, is investigated numerically. The method of elliptic partial differential equations grid generation is adopted to construct a distribution of grids on each cross section. The distributions of the whole cross sections are piled up in sequence from the inlet to outlet to form a three dimensional channel. In order to solve a low speed compressible flow problem, the compressibility and viscosity of the working fluid are taken into consideration, and the non-reflecting boundaries at the inlet and outlet of the channel are held. The Bossinesq assumption is then no longer necessary. As well, the methods of the Roe scheme, preconditioning and dual time stepping matching the implicit LUSGS algorithm (Implicit Lower Upper symmetric Gauss–Seidel algorithm) are simultaneously used to solve governing equations. Effects of the Rayleigh number and the ratio of the amplitude to wave length on heat transfer rates of the channel are examined. Results of both this study and existing studies have good agreements.

An investigation of unsteady flow reversal of natural convection in vertical parallel plates by the modified local one-dimensional inviscid relations method

An unsteady flow reversal of natural convection in vertical parallel plates with an asymmetrically heated wall is investigated numerically. For clarifying the occurrence of flow reversal, the width of the plates is regarded as a variable, and the non-reflecting boundary condition is adopted at apertures. The methods of the Roe scheme, preconditioning and dual time stepping matching LUSGS are simultaneously used to solve governing equations which are available for a low speed compressible flow problem. The flow reversal is observed under broad width situations and absent under narrow width situations. Distributions of the pressure differences at the apertures are revealed to indicate the occurrence of flow reversal. The present Nusselt numbers, which mean time and area-averaged ones, display relatively good agreement with those of the existing works.

An investigation of natural convection in parallel square plates with a heated top surface by a hybrid boundary condition

Natural convection in parallel squares plats with a heated top surface is investigated numerically. For solving a problem induced by different directions between the thermal diffusion and main flow streams, a hybrid boundary condition composed of the absorbing boundary condition and local one-dimensional inviscid relations (LODI) method is then adopted in artificial buffer zones. Methods of the Roe scheme, preconditioning and dual time stepping matching the Monotone Upstream-centered Schemes for Conservation Laws (MUSCL) are used to solve low speed compressible flows caused by natural convection. The results show that the hybrid boundary condition successfully prevents the rebound of heat energy from the artificial buffer zone back to the domain. The area-averaged Nusselt numbers of this study are slightly larger than those of existing experimental results, and the averaged deviation is about 10%.

Estimation of turbulent natural convection in horizontal parallel plates by the Q criterion

An investigation of estimation of turbulent structures of natural convection in horizontal parallel plates by the Q criterion is studied numerically. It is difficult to adopt a definite criterion like the critical Reynolds number adopted in forced convection to distinguish laminar and turbulent flows of natural convection in horizontal parallel plates because the angle between directions of the buoyancy force and main stream flow is changed in the whole process of the flowing. The Q criterion is then used to make up for a deficiency of the definite criterion and examines mechanisms of the occurrence of rotation behaviors which are often regarded as turbulent structures in detail. Methods of the Roe scheme, preconditioning and dual time stepping matching the method of LUSGS are simultaneously used to solve a low speed compressible flow. As well, non-reflecting boundary conditions are held at apertures to prevent the reflection caused by pressure waves. Under a low height situation, the shear force is dominant, and then a few rotation behaviors are observed near the central region where flow directions are changed. Oppositely, the space is almost filled with active rotation behaviors because natural convection fully develops in a high height situation.

An investigation of natural convection in parallel square plates with a heated bottom surface by an absorbing boundary condition

A study of natural convection in three dimensional square plates is investigated numerically. Several open boundaries co-exist in the physical domain, and a non-reflecting boundary condition applied at the aperture is no longer suitable for solving the problem of this study. An absorbing boundary condition is then adopted and modified in the solution processes. Methods of the Roe scheme, preconditioning and dual time stepping matching LSUGS scheme are used to solve a situation of a low speed compressible flow. The geometry of the physical model is the parallel square plates, and the parameter of Rayleigh number is not high, and then phenomena observed are almost symmetrical. The results of the work have good agreements with the experimental results of a previous paper.

An investigation of natural convection of three dimensional horizontal parallel plates from a steady to an unsteady situation by a CUDA computation platform

The heat transfer of natural convection in three dimensional horizontal parallel plates with a heated bottom surface is investigated numerically. For enlarging the application domain, the compressibility of the fluid is taken into consideration instead of the Boussinesq assumption. Numerical methods of the Roe scheme, preconditioning and dual time stepping are adopted for solving governing equations of a low speed compressible flow. A non-reflection condition is used at both apertures in order to decrease computational grids and a CUDA computational platform is developed to economize massive computing time. Variations of thermal and flow fields are examined in detail. The results show that accompanied with elongating the length of the heated bottom surface, both thermal and flow fields are changed from a steady to an unsteady situation.

An investigation of natural convection in a three dimensional tapered chimney without Boussinesq assumption

Natural convection in a three dimensional tapered chimney is investigated numerically. In order to investigate the natural convection under a high temperature difference situation, Boussinesq assumption is not adopted instead of consideration of the compressibility of fluid. Methods of Roe scheme, preconditioning and dual time stepping are used to solve governing equations for a low speed compressible flow. Coordinates transformation of algebraic grid generation and non-reflecting boundary condition are used to facilitate computation processes. The results reveal that in the expanding duct local Nusselt numbers distributed around the corner region are larger than those distributed around the central region. An available correlation equation is proposed and is well consistent with the numerical results.

Incompressible Criterion and Pressure Drop for Gaseous Slip Flow in Circular and Noncircular Microchannels

Slip flow in various noncircular microchannels has been further examined, and a simple model for a normalized Poiseuille number is proposed. As for slip flow, no solutions or graphical and tabulated data exist for most geometries; the developed simple model fills this void and can be used to predict the Poiseuille number, mass flow rate, tangential momentum accommodation coefficient, pressure distribution, and pressure drop of slip flow in noncircular microchannels by the research community for the practical engineering design of microchannels. The incompressible flow criterion for gas flow in microchannels is given. A Mach number less than 0.3 is not sufficient to ensure that the flow is incompressible. Compressibility depends on the product of two dimensionless parameters: L/L(DRe)(DRe) and Ma (Arkilic et al., 1997, “Gaseous Slip Flow in Long Microchannels,” J. Microelectromech. Syst., 6(2), pp. 167–178). Some flows where Ma < 0.3 are low speed compressible flows. A fresh general pressure drop model for isothermal low Mach number compressible flow in microchannels is proposed. If the pressure drop is less than 10% of the outlet pressure, the flow can be considered as incompressible for practical engineering applications. This paper improves and extends previous studies on slip flow in noncircular microchannels.

Implicit methods for viscous incompressible flows

Numerical methods and simulation tools for incompressible flows have been advanced largely as a subset of the computational fluid dynamics (CFD) discipline. Especially within the aerospace community, simulation of compressible flows has driven most of the development of computational algorithms and tools. This is due to the high level of accuracy desired for predicting aerodynamic performance of flight vehicles. Conversely, low-speed incompressible flow encountered in a wide range of fluid engineering problems has not typically required the same level of numerical accuracy. This practice of tolerating relatively low-fidelity solutions in engineering applications for incompressible flow has changed. As the design of flow devices becomes more sophisticated, a narrower margin of error is required. Accurate and robust CFD tools have become increasingly important in fluid engineering for incompressible and low-speed flow. Accuracy depends not only on numerical methods but also on flow physics and geometry modeling. For high-accuracy solutions, geometry modeling has to be very inclusive to capture the elliptic nature of incompressible flow resulting in large grid sizes. Therefore, in this article, implicit schemes or efficient time integration schemes for incompressible flow are reviewed from a CFD tool development point of view. Extension of the efficient solution procedures to arbitrary Mach number flows through a unified time-derivative preconditioning approach is also discussed. The unified implicit solution procedure is capable of solving low-speed compressible flows, transonic, as well as supersonic flows accurately and efficiently. Test cases demonstrating Mach-independent convergence are presented.

An investigation of a dual-reflection phenomenon of a natural convection in a three dimensional horizontal channel without Boussinesq assumption

An investigation of a dual-reflection phenomenon of a natural convection induced by a high temperature difference in a three dimensional horizontal channel is studied numerically. Because of a situation of high temperature difference, the Boussinesq assumption usually made in the natural convection problem is no longer available, the effects of the compressibility of fluid on all related factors must be considered. Solution methods of Roe, preconditioning and dual time stepping are appropriate for low speed compressible flow field and combined to solve the governing equations. For saving computation time, the computational process is parallel and 8 processors are used. At the aperture of the horizontal channel, the directions of fluid flows in the upper and lower regions are opposite which results in the reflection problems in the upper and lower regions induced by the large difference between the velocities of acoustic waves and fluids being completely different. The two different reflections phenomena occurring at the same aperture is conveniently named as a dual-reflection phenomenon which has never been investigated.

Preconditioned methods for simulations of low speed compressible flows

A time-derivative preconditioned system of equations suitable for the numerical simulation of inviscid compressible flow at low speeds is formulated. The preconditioned system of equations are hyperbolic in time and remain well-conditioned in the incompressible limit. The preconditioning formulation is easily generalized to multicomponent/multiphase mixtures. When applying conservative methods to multicomponent flows with sharp fluid interfaces, nonphysical solution behavior is observed. This stimulated the authors to develop an alternative solution method based on the nonconservative form of the equations which does not generate the aforementioned nonphysical behavior. Before the results of the application of the nonconservative method to multicomponent flow problems is reported, the accuracy of the method on single component flows will be demonstrated. In this report a series of steady and unsteady inviscid flow problems are simulated using the nonconservative method and a well-known conservative scheme. It is demonstrated that the nonconservative method is both accurate and robust for smooth low speed flows, in comparison to its conservative counterpart.

A finite element method for low-speed compressible flows

The derivation and justification for various low-speed approximations to the fully compressible, Navier–Stokes equations are presented. A numerical formulation based on the finite element method is developed and implemented as an extension to the standard Boussinesq equations. Example steady and transient flow problems are simulated to examine the performance of the numerical algorithm and the solution differences with the more commonly studied Boussinesq approximation.

Spectral/ hp least-squares finite element formulation for the Navier–Stokes equations

We consider the application of least-squares finite element models combined with spectral/ hp methods for the numerical solution of viscous flow problems. The paper presents the formulation, validation, and application of a spectral/ hp algorithm to the numerical solution of the Navier–Stokes equations governing two- and three-dimensional stationary incompressible and low-speed compressible flows. The Navier–Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity or velocity gradients as additional independent variables and the least-squares method is used to develop the finite element model. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton’s method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method. Spectral convergence of the L 2 least-squares functional and L 2 error norms is verified using smooth solutions to the two-dimensional stationary Poisson and incompressible Navier–Stokes equations. Numerical results for flow over a backward-facing step, steady flow past a circular cylinder, three-dimensional lid-driven cavity flow, and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation.

Least-squares finite element models of two-dimensional compressible flows

We present numerical simulation results for the compressible Euler equations and compressible Navier–Stokes equations using least-squares finite element models. Alternative least-squares formulations are first exemplified by a Poisson problem and ideas extended to the Euler and Navier–Stokes equations. For the compressible Navier–Stokes equations we introduce velocity gradients and heat fluxes as additional primary variables to arrive at an equivalent first-order system. The least-squares models developed herein are found to be effective for the high- and low-speed compressible flow regimes.