Steady-state Incompressible Flow Research Articles

3D topology optimization design of air natural convection heat transfer fins

This study focuses on the fin-tube heat exchanger and utilizes topology optimization methods to design a completely new fin structure. In this optimization process, complete Navier-Stokes (N-S) equations were used to describe the steady-state incompressible flow, and the Boussinesq model was employed to simulate natural convection. The flow equations were coupled with the heat convection–diffusion equation to achieve topology optimization for natural convection heat transfer. Topology optimization was conducted using density-based optimization methods, and interpolation was performed on the permeability and conductivity of the distributed materials. Given the initial fin structure, an interpolation progressive approach was adopted to obtain a new “ airfoil-shaped” optimized structure through density-based topology optimization method for natural convection. The new structure enhances the convective heat transfer by perforating the fins. The perforations are mainly concentrated in the central region of the heat exchanger and the upper half of the fins. The new structure, compared to the prototype structure, not only has a reduced volume but also exhibits a decrease in convective thermal resistance within a larger range of heat flux densities, as revealed by CFD simulations. Moreover, as the heat flux density increases, the rate of reduction in convective thermal resistance shows an upward trend for the new structure compared to the prototype structure.

On the extremum dissipation for steady state incompressible flow past a sphere at low Reynolds number

Abstract A methodology based on sound non-equilibrium thermodynamics principles is developed to estimate the extremum dissipation point for steady-state incompressible flow past a sphere at low Reynolds numbers. It is shown, that the extremum dissipation point appears at the point when both the shear stress and the pressure at the surface of the sphere are equal to zero. The Reynolds number and the position of the extremum dissipation flow past a sphere were further estimated with the aid of a mathematical model for pressure distribution on the sphere surface, accounting for both creeping and ideal flow. The parameters of the model were determined by comparison of the calculated pressure distribution at the surface with the available literature data. The conditions at which the separation angle and the extremum dissipation angle coincide were also investigated. It is believed that this work could be used to further elucidate the flow past a sphere.

Computational Fluid Dynamics Modeling of Steam Condensation in the Presence of Noncondensable Gas in Inclined Tubes

In this paper, film condensation of steam in inclined tubes in the presence of noncondensable gases is modeled using numerical method. A single-phase fluid model incorporating a wall-function boundary condition is proposed to simulate the heat and mass transfer interaction between the liquid condensate and the gas-vapor mixture region. A user defined function is implemented to impose the proposed boundary to the governing equations for steady state incompressible flow. The performance of applying this boundary condition and subsequent treatment of the heat transfer at the liquid-mixture interface is validated against published experimental results. The calculated profiles of local and average Nusselt number for various inlet conditions compares favorably to the previous published experimental results and correlations. For all simulated cases, increases in inlet and bulk concentrations of noncondensable gases resulted in a decrease in the thermal performance of the condensing tube. Additionally, it is found that the inclination angle of the condensing tube can impact the local distribution of the heat transfer coefficient and Nusselt number, while there is only small effect on the average along the length of the entire tube.

Effect of aspect ratio of a corrugated cavity filled with porous media on the coefficient of heat transfer.

Solar power, thermal storage facilities, reactor cooling and microelectronic devices are all examples of renewable energy use natural convection heat transfer from a heated supplier to a chilly environment or enclosure. The purpose of this research is to investigate the influence of porous media on the convective heat transfer coefficient and the modified Rayleigh number as a function of the cavity's aspect ratio. This study investigated the free convective 3D flow then heat transmission in a cavity that has a width of 20 cm in width, a depth of 2.7 cm in depth, and varying heights of 20, 25 and 30 cm. The cavity has an anisotropic fluid-filled porous wavy enclosure with steady-state incompressible flow. The bottom surface radiates heat with a steady heat flux. (300, 500, 700, 900, 1100 W/m²), while the top is exposed to the environment at 25 C˚ (h=25 W/m²) and other walls are adiabatic. Rayleigh’s number range (3.13* to 2.61* ) (1.9* ), aspect ratio (As=1,1.25,1.5), porosity (ɛ=0.36), permeability (k=7.593* m²), amplitude (a=1.5 cm). The findings indicate that increasing the heat flow alters the temperature profile. progressively increases the pressure and velocity. The highest value for the heat transfer coefficient and modified Rayleigh No. was obtained when the aspect ratio was 1.

Physics-informed PointNet: A deep learning solver for steady-state incompressible flows and thermal fields on multiple sets of irregular geometries

We present a novel physics-informed deep learning framework for solving steady-state incompressible flow on multiple sets of irregular geometries by incorporating two main elements: using a point-cloud based neural network to capture geometric features of computational domains, and using the mean squared residuals of the governing partial differential equations, boundary conditions, and sparse observations as the loss function of the network to capture the physics. While the solution of the continuity and Navier-Stokes equations is a function of the geometry of the computational domain, current versions of physics-informed neural networks have no mechanism to express this functionally in their outputs, and thus are restricted to obtain the solutions only for one computational domain with each training procedure. Using the proposed framework, three new facilities become available. First, the governing equations are solvable on a set of computational domains containing irregular geometries with high variations with respect to each other but requiring training only once. Second, after training the introduced framework on the set, it is now able to predict the solutions on domains with unseen geometries from seen and unseen categories as well. The former and the latter both lead to savings in computational costs. Finally, all the advantages of the point-cloud based neural network for irregular geometries, already used for supervised learning, are transferred to the proposed physics-informed framework. The effectiveness of our framework is shown through the method of manufactured solutions and thermally-driven flow for forward and inverse problems.

A novel efficient segregated pressure-based algorithm for steady-state incompressible flow

In order to enhance the calculation efficiency of steady-state incompressible fluid flow, based on the existing IDEAL (i.e. the inner doubly iterative efficient algorithm for linked equations) algorithm, a novel segregated pressure-based algorithm (named as IDEALC) has been developed in this paper. The novel algorithm inherits the superiorities of the original IDEAL algorithm and at the same time improves its potential shortcomings. The specific promotions of the IDEALC algorithm consist of three aspects, including the first approximation of the SIMPLE algorithm, the approach to solving the momentum equation and the second approximation of the SIMPLE algorithm. Detailed comparisons between the IDEAL and the IDEALC algorithms are carried out by three numerical experiments on structured collocated grids. The numerical results demonstrate that the IDEALC algorithm can accurately predict the information of the flow field and has substantial advantages over the IDEAL algorithm in terms of the efficiency because of the consistent property of the former. The superiority of the IDEALC algorithm over the IDEAL algorithm is especially remarkable when the time step multiplier gets a moderate value.

Quantitative impact of a micro-cylinder as a passive flow control on a horizontal axis wind turbine performance

Adding micro-cylinder as a passive flow control is a new trend to enhance the power output of wind turbines. The impact of adding micro-cylinder, with different configurations, around horizontal axis wind turbine blade (HAWT) is examined using 3-dimensional simulations. The conventional turbine National Renewable Energy Laboratory (NREL Phase II) straight-bladed wind turbine is selected to validate the present numerical arrangements, where it hasn't been tested before with adding micro-cylinder. The Reynolds Average Navier-Stokes (RANS) equations for steady-state incompressible flow combined with Shear Stress Transport (k-ω SST) turbulence model are employed for the current numerical analysis. In this study, a parametric study is conducted for different diameters and locations of micro-cylinder. In total, seven cases are examined. The influence of micro-cylinder size is examined by changing the cylinder diameter (three different diameters, diameter/chord = 0.0131, 0.0175, 0.022). It has been found that the output power increases with decreasing the micro-cylinder diameter. The effect of micro-cylinder locations is investigated by introducing four different cases (four different locations around the leading edge). The power output increases for all cases. Additionally, it has been found that locating the micro-cylinder on the pressure side has less effect on the power output comparing to locating it on front of the blade leading edge.

Multi-physics adjoint modeling of Earth structure: combining gravimetric, seismic, and geodynamic inversions

We discuss the resolving power of three geophysical imaging and inversion techniques, and their combination, for the reconstruction of material parameters in the Earth’s subsurface. The governing equations are those of Newton and Poisson for gravitational problems, the acoustic wave equation under Hookean elasticity for seismology, and the geodynamics equations of Stokes for incompressible steady-state flow in the mantle. The observables are the gravitational potential, the seismic displacement, and the surface velocity, all measured at the surface. The inversion parameters of interest are the mass density, the acoustic wave speed, and the viscosity. These systems of partial differential equations and their adjoints were implemented in a single Python code using the finite-element library FeNICS. To investigate the shape of the cost functions, we present a grid search in the parameter space for three end-member geological settings: a falling block, a subduction zone, and a mantle plume. The performance of a gradient-based inversion for each single observable separately, and in combination, is presented. We furthermore investigate the performance of a shape-optimizing inverse method, when the material is known, and an inversion that inverts for the material parameters of an anomaly with known shape.

Effect of Rotor Spacing and Duct Diffusion Angle on the Aerodynamic Performances of a Counter-Rotating Ducted Fan in Hover Mode

The aerodynamic performance of a counter-rotating ducted fan in hover mode is numerically analyzed for different rotor spacings and duct diffusion angles. The design of the counter-rotating fan is inspired by a custom-designed single rotor ducted fan used in a previous study. The numerical model to predict the aerodynamic performance of the counter-rotating ducted fan is developed by adopting the frozen rotor approach for steady-state incompressible flow conditions. The relative angle between the front and the rear rotor is examined due to the usage of the frozen rotor model. The results show that the variation of thrust for the different relative angles is extremely low. The aerodynamic performances are evaluated by comparing the thrust, thrust coefficient, power coefficient, and figure of merit (FOM). The thrust, thrust coefficient, and FOM slightly increase with increasing rotor spacing up to 200 mm, regardless of the duct diffusion angle, and reduce on further increase in the rotor spacing. The duct diffusion angle of 0° generates about 9% higher thrust and increases the FOM by 6.7%, compared with the 6° duct diffusion angle. The duct diffusion angle is highly effective in improving the thrust and FOM of the counter-rotating ducted fan, rather than the rotor spacing.

A numerical study on mechanisms of energy dissipation in a pump as turbine (PAT) using entropy generation theory

Abstract The utilization of pumps in reverse function is one of the economically beneficial methods for off-grid power generation in micro-hydropower capacities. The traditional method of hydraulic loss calculation in turbomachinery based on pressure drop calculations is unable to determine the exact location of losses. In this paper, the irreversible energy losses within the PAT has been studied for the first time using entropy generation theory and the second law of thermodynamics point of view. In order to conduct numerical simulation, the 3-dimensional incompressible steady-state flow within the PAT is simulated by solving the Reynolds averaged Navier-Stokes (RANS) equations. The shear stress transport (SST) turbulence model is considered for turbulence modeling. The quantity of direct (viscous) and turbulent entropy generation rate is calculated in different PAT components in 9 different flow rates in the range of 0.7QBEP to 1.3QBEP. The numerical results show that the turbulent term is the main factor of entropy production within the PAT (86.89%–90.98%), and thus, turbulent entropy generation is the dominant mechanism for hydraulic losses. More than 50% of the energy dissipation occurs within the PAT runner. Most of the losses within the runner take place at the blade leading edge, blade trailing edge and flow separation regions of the blade suction and pressure sides. The volumetric entropy generation rate analysis demonstrates that the draft tube has the most potential to generate irreversible losses among all the components (47.37%). Flow field analysis reveals that the blade inlet shock, flow deviation at the blade outlet, flow separation, backflow and vortices in flow passages are categorized as the main reasons for entropy production and irreversible hydraulic losses within the PAT components. The advantages of the entropy generation method including the determination of the exact location and quantity of energy dissipation within the PAT are indicated in this investigation.

Computation of Design Sensitivities in Steady-State Incompressible Laminar Flows Based on New Semi-Analytical Method

In this paper, a new semi-analytic method (SAM) is proposed as a robust and efficient approach based on complex variables to compute the sensitivity of steady-state incompressible laminar flows. This method combines the complex variable method (CVM) via the discrete sensitivity analysis in order to obtain the sensitivity of response accurately and efficiently. The governing Navier–Stokes equations are solved using the finite element method and then new SAM is employed. The proposed procedure retains the computational efficiency of SAM with higher accuracy. In addition, the scheme is not sensitive to the step size, a characteristic that eases its application in practical problems. It is proved that the discrete sensitivity analysis is equivalent to CVM and solves the same equation. Finally, the accuracy of the method is investigated through various numerical cases compared to other methods and reveals that this scheme is reliable and independent to the step size. The proposed approach is applicable to a wide range of engineering problems.

Heat transfer and hydrodynamics of slip confusor flow under second-order boundary conditions

The paper focused on an analytical analysis of the main features of heat transfer in incompressible steady-state flow in a microconfusor with account for the second-order slip boundary conditions. The second-order boundary conditions serve as a closure of a system of the continuity, transport, and energy differential equations. As a result, novel solutions were obtained for the velocity and temperature profiles, as well as for the friction coefficient and the Nusselt number. These solutions demonstrated that an increase in the Knudsen number leads to a decrease in the Nusselt number. It was shown that the account for the second-order terms in the boundary conditions noticeably affects the fluid flow characteristics and does not influence on the heat transfer characteristics. It was also revealed that flow slippage effects on heat transfer weaken with an increase in the Prandtl number.

Pore Network Modeling of the Effects of Viscosity Ratio and Pressure Gradient on Steady-State Incompressible Two-Phase Flow in Porous Media

We perform steady-state simulations with a dynamic pore network model, corresponding to a large span in viscosity ratios and capillary numbers. From these simulations, dimensionless steady-state time-averaged quantities such as relative permeabilities, residual saturations, mobility ratios and fractional flows are computed. These quantities are found to depend on three dimensionless variables, the wetting fluid saturation, the viscosity ratio and a dimensionless pressure gradient. Relative permeabilities and residual saturations show many of the same qualitative features observed in other experimental and modeling studies. The relative permeabilities do not approach straight lines at high capillary numbers for viscosity ratios different from 1. Our conclusion is that this is because the fluids are not in the highly miscible near-critical region. Instead they have a viscosity disparity and intermix rather than forming decoupled, similar flow channels. Ratios of average mobility to their high capillary number limit values are also considered. Roughly, these vary between 0 and 1, although values larger than 1 are also observed. For a given saturation, the mobilities are not always monotonically increasing with the pressure gradient. While increasing the pressure gradient mobilizes more fluid and activates more flow paths, when the mobilized fluid is more viscous, a reduction in average mobility may occur.

An Efficient Strategy to Deliver Understanding of Both Numerical and Practical Aspects When Using Navier-Stokes Equations to Solve Fluid Mechanics Problems

An efficient and thorough strategy to introduce undergraduate students to a numerical approach of calculating flow is outlined. First, the basic steps, especially discretization, involved when solving Navier-Stokes equations using a finite-volume method for incompressible steady-state flow are developed with the main aim being for the students to follow through from the mathematical description of a given problem to the final solution of the governing equations in a transparent way. The well-known ‘driven-cavity’ problem is used as the problem for testing coding written by the students, and the Navier-Stokes equations are initially cast in the vorticity-streamfunction form. This is followed by moving on to a solution method using the primitive variables and discussion of details such as, closure of the Navier-Stokes equations using turbulence modelling, appropriate meshing within the computation domain, various boundary conditions, properties of fluids, and the important methods for determining that a convergence solution has been reached. Such a course is found to be an efficient and transparent approach for introducing students to computational fluid dynamics.

Rapid design approach for U-bend of a turbine serpentine cooling passage

The goal of this study is to propose a rapid design approach for designing a minimum pressure loss U-bend in a turbine internal cooling passage using topology optimization. The total pressure loss in the bend region is critical, as the presence of U-bend dominates the pressure loss so that it demands increased coolant feed pressure. However, it is challenging to come up with general design rule for U-bend with minimum pressure loss. The proposed rapid design approach can be applied as a 3D U-bend geometry optimization tool. The minimization of the total pressure loss is achieved by implementing topology optimization that uses a continuous adjoint approach with steepest-descent method. An incompressible steady-state flow (low-fidelity simulation) solver is applied for the design space, which is modeled as a porous medium with variable porosity. A series of design optimization in 2D and 3D is conducted at a Reynolds number of 100,000 based on the bulk inlet velocity. 3D U-bend configurations are produced by the proposed rapid design approach in a few hours.High-fidelity computational simulations are also carried out on the optimized 2D and 3D U-bend configurations to evaluate the proposed rapid design approach. The computational studies are performed by solving the compressible, turbulent steady-state Reynolds-averaged Navier-Stokes (RANS) equations applying two turbulence models: Spalart-Allmaras and Shear Stress Transport (SST) model. The high-fidelity simulations predict a relative improvement of maximum 26.8% in total pressure drop with respect to the 3D baseline configuration. The results indicate that the proposed approach can be reliable fast design tool for optimizing U-bend geometry in incompressible flow regime.

SLAC – a semi-Lagrangian artificial compressibility solver for steady-state incompressible flows

PurposeThe purpose of this paper is the development of a new density-based (DB) semi-Lagrangian method to speed up the conventional pressure-based (PB) semi-Lagrangian methods.Design/methodology/approachThe semi-Lagrangian-based solvers are typically PB, i.e. semi-Lagrangian pressure-based (SLPB) solvers, where a Poisson equation is solved for obtaining the pressure field and ensuring a divergence-free flow field. As an elliptic-type equation, the Poisson equation often relies on an iterative solution, so it can create a challenge of parallel computing and a bottleneck of computing speed. This study proposes a new DB semi-Lagrangian method, i.e. the semi-Lagrangian artificial compressibility (SLAC), which replaces the Poisson equation by a hyperbolic continuity equation with an added artificial compressibility (AC) term, so a time-marching solution is possible. Without the Poisson equation, the proposed SLAC solver is faster, particularly for the cases with more computational cells, and better suited for parallel computing.FindingsThe study compares the accuracy and the computing speeds of both SLPB and SLAC solvers for the lid-driven cavity flow and the step-flow problems. It shows that the proposed SLAC solver is able to achieve the same results as the SLPB, whereas with a 3.03 times speed up before using the OpenMP parallelization and a 3.35 times speed up for the large grid number case (512 × 512) after the parallelization. The speed up can be improved further for larger cases because of increasing the condition number of the coefficient matrixes of the Poisson equation.Originality/valueThis paper proposes a method of avoiding solving the Poisson equation, a typical computing bottleneck for semi-Lagrangian-based fluid solvers by converting the conventional PB solver (SLPB) to the DB solver (SLAC) through the addition of the AC term. The method simplifies and facilitates the parallelization process of semi-Lagrangian-based fluid solvers for modern HPC infrastructures, such as OpenMP and GPU computing.

On the influence of turbulent kinetic energy level on accuracy of k − ε and LRR turbulence models

This paper presents research regarding the influence of turbulent kinetic energy (TKE) level on accuracy of Reynolds averaged Navier?Stokes (RANS) based turbulence models. A theoretical analysis of influence TKE level on accuracy of the RANS turbulence models has been performed according to the Boussinesq hypothesis definition. After that, this theoretical analysis has been investigated by comparison of numerically and experimentally obtained results on the test case of a steady-state incompressible swirl-free flow in a straight conical diffuser named Azad diffuser. Numerical calculations have been performed using the OpenFOAM CFD software and first and secondorder closure turbulence models. TKE level, velocity profiles and Reynolds stresses have been calculated downstream in four different cross sections of the diffuser. Certain conclusions about modeling turbulent flows by ?? ??? and LRR turbulence models have been made by comparing the velocity profiles, TKE distribution and Reynolds stresses on the selected cross sections.

Numerical Analysis of Thermal and Aerodynamic Fields in a Channel with Cascaded Baffles

A computational fluid dynamic analysis of thermal and aerodynamic fields for an incompressible steady-state flow of a Newtonian fluid through a two-dimensional horizontal rectangular section channel with upper and lower wall-attached, vertical, staggered, transverse, cascaded rectangular-triangular (CRT), solid-type baffles is carried out in the present paper using the Commercial, Computational Fluid Dynamics, software FLUENT. The flow model is governed by the Reynolds averaged Navier-Stokes (RANS) equations with the SST k-ω turbulence model and the energy equation. The finite volume method (FVM) with the SIMPLE-discretization algorithm is applied for the solution of the problem. The computations are carried out in the turbulent regime for different Reynolds numbers. In this study, thermo-aeraulic fields, dimensionless axial profiles of velocity, skin friction coefficients, local and average heat transfer coefficients, and thermal enhancement factor were investigated, at constant surface temperature condition along the heated upper wall of the channel, for all the geometry under investigation and chosen for various stations. The impact of the cascaded rectangular-triangular geometry of the baffle on the thermal and dynamic behavior of air is shown and this in comparing the data of this obstacle type with those of the simple flat rectangular-shaped baffle. This CFD analysis can be a real application in the field of heat exchangers, solar air collectors, and electronic equipments.

A Numerical Investigation of the Effect of Increasing Blade Numbers on Cavitation and Performance of Centrifugal Pumps at Constant Parameters

In the present paper, a numerical study has been investigated by using computational fluid dynamics (CFD) to analyze pressure, head, head coefficient, pressure coefficient, input power, and volume fraction of cavitation at three cases of simulation in which each one has constant parameters; however, with modifying number of blades which is changed from five to sixteen. The constant parameters are rotating speed, volume flow rate, mass flow rate, outlet diameter, suction specific speed Nss, Reynolds number and NPSHr. These parameters have been fixed to have the same conditions for each case. The shear stress transport (SST) turbulence model has been used to inspect a steady state incompressible flow through centrifugal pump numerically. The simulation has done by using ANSYS®, Vista CPDTM Release 15.0. The results are plotted and discussed to describe and find a relation among cavitation, pump behavior, and variation of blade numbers at constant conditions. The results show a strong relation among increasing blade numbers, centrifugal pump performance and reducing pump cavitation.

Design of a Kaplan turbine for a wide range of operating head -Curved draft tube design and model test verification-

As for turbomachine off-design performance improvement is challenging but critical for maximising the performing area. In this paper, a curved draft tube for a medium head Kaplan type hydro turbine is introduced and discussed for its significant effect on expanding operating head range. Without adding any extra structure and working fluid for swirl destruction and damping, a carefully designed outline shape of draft tube with the selected placement of center-piers successfully supresses the growth of turbulence eddy and the transport of the swirl to the outlet. Also, more kinetic energy is recovered and the head lost is improved. Finally, the model test results are also presented. The obvious performance improvement was found in the lower net head area, where the maximum efficiency improvement was measured up to 20% without compromising the best efficiency point. Additionally, this design results in a new draft tube more compact in size and so leads to better construction and manufacturing cost performance for prototype.The draft tube geometry parameter designing process was concerning the best efficiency point together with the off-design points covering various water net heads and discharges. The hydraulic performance and flow behavior was numerically previewed and visualized by solving Reynolds-Averaged Navier-Stokes equations with Shear Stress Transport turbulence model. The simulation was under the assumption of steady-state incompressible turbulence flow inside the flow passage, and the inlet boundary condition was the carefully simulated flow pattern from the runner outlet. For confirmation, the corresponding turbine efficiency performance of the entire operating area was verified by model test.