Unsteady Heat Research Articles

Lattice Boltzmann method for heat transfer in transitional flows with unified single-node curved boundary conditions

Laminar separation bubbles in transitional flows of low-Reynolds-number airfoils significantly affect aerodynamic efficiency and heat transfer characteristics, which can be dealt with using the numerical method with boundary treatment of complex geometry. This work proposes the unified single-node curved boundary conditions based on the thermal lattice Boltzmann method, and several benchmarks verify the higher accuracy and parallel scalability over conventional schemes. Multi-GPU simulations for airfoil Eppler 61 and SD8020 are carried out, and the lift coefficients CL are accurately simulated by the parametric combined momentum-exchange method. Furthermore, time-averaged pressure coefficients Cp and local Nussel number Nu of airfoil surfaces are obtained, and the unsteady flow and heat transfer characteristics of laminar separation bubbles are captured. Simulated average Nussel numbers Nu¯ for an Eppler 61 airfoil with different Reynold numbers are equivalent to and modify the Hilpert correlation. The numerical method can quickly and accurately predict transitional flows of low-Reynolds-number airfoils and guide the design and application of heat transfer with blade configuration.

Treatment of the Unsteady Heat Equation Subject to Heat Flux Boundary Conditions: The Method of Discretization in Time Complemented With Regression Analysis

Treatment of the Unsteady Heat Equation Subject to Heat Flux Boundary Conditions: The Method of Discretization in Time Complemented With Regression Analysis

Impact of porosity on two-dimensional unsteady MHD boundary layer heat and mass transfer stagnation point flow with radiation and viscous dissipation

The purpose of the present research is to examine the effect of porosity in the presence of radiation and viscous dissipation on two-dimensional unsteady MHD mixed convection heat and mass transport at the stagnation point. The governing time-dependent nonlinear PDEs are converted into nonlinear ODEs by utilizing similarity transformations. The mathematical formulation is produced as ordinary differential equations. The achieved coupled system has been analyzed using the Keller–Box technique. Newton’s system dictates that the coefficients must be accurate and refined. To assess the influence of flow-controlling factors on relevant profiles, quantitative, and qualitative analysis are conducted. With the use of graphs and tables, beneficial talks were conducted. Under the restricting conditions, prior findings were compared and determined to be satisfactory. The conclusions of this study are widely accepted by the scientific community.

A one‐point second‐order Dirichlet boundary condition for the thermal lattice Boltzmann method

AbstractA one‐point second‐order Dirichlet boundary condition for convection‐diffusion equation based on the lattice Boltzmann method has been proposed. The unknown temperature distribution is interpolated from the distributions at the wall node and fluid node nearest to the wall in the direction of the lattice velocity. At the wall node, the unknown temperature distribution is expressed as a summation of equilibrium and nonequilibrium distributions. The equilibrium distribution is obtained using the wall temperature, while the nonequilibrium distribution is approximated from the nearest fluid node in the direction of the lattice velocity. Both asymptotic analysis and numerical simulations of heat conduction indicate that the Dirichlet boundary condition is second‐order accurate. Further comparisons demonstrate that the newly proposed boundary method is sufficiently accurate to simulate natural convection, convective and unsteady heat transfer involving straight and curved boundaries.

Unsteady Hybrid (Ag–CuO/Water) Nanofluid Flow and Heat Transfer due to a Stretching Sheet with Variable Temperature

In this paper, the focal aims are (i) to explore the transient boundary-layer flow and heat transfer of an electrically conducting hybrid (Ag–CuO water) nanofluid along a vertical stretching surface (sheet) having non-zero slot velocity at variable temperature, and (ii) to discuss the influences of momentous parameters involved on the heat transfer and skin friction coefficient graphically. The “Tiwari-Das nanofluid model” is used. The central equations (PDEs) are converted into finite difference equations by the powerful Crank Nicolson technique and numerically solved using the Thomas algorithm. The achieved outcomes for a specific case of the challenge are compared with an analytical solution computed using the Laplace transform technique and discovered to be in excellent accord.

Numerical investigation of unsteady flow and heat transfer of a free convective second-grade fluid passing through exponentially accelerated vertical porous plate

Numerical investigation of unsteady flow and heat transfer of a free convective second-grade fluid passing through exponentially accelerated vertical porous plate

A data-based reduced-order model for dynamic simulation and control of district-heating networks

This study concerns the development of a data-based compact model for the prediction of the fluid temperature evolution in district heating (DH) pipeline networks. This so-called “reduced-order model” (ROM) is obtained from reduction of the conservation law for energy for each pipe segment to a semi-analytical input–output relation between the pipe outlet temperature and the pipe inlet and ground temperatures that can be identified from training data. The ROM basically is valid for generic pipe configurations involving 3D unsteady heat transfer and 3D steady flow as long as heat-transfer mechanisms are linearly dependent on the temperature field. Moreover, the training data can be generated by physics-based computational “full-order” models (FOMs) yet also by (calibration) experiments or field measurements. Performance tests using computational training data for a single-pipe configuration demonstrate that the ROM (i) can be successfully identified and (ii) can accurately describe the response of the outlet temperature to arbitrary input profiles for inlet and ground temperatures. Application of the ROM to two case studies, i.e. fast simulation of a small DH network and design of a controller for user-defined temperature regulation of a DH system, demonstrate its predictive ability and efficiency also for realistic systems. Dedicated cost analyses further reveal that the ROM may significantly reduce the computational costs compared to FOMs by (up to) orders of magnitude for higher-dimensional pipe configurations. These findings advance the proposed ROM as a robust and efficient simulation tool for practical DH systems with a far greater predictive ability than existing compact models.

Effects of Reynolds number on thermal wake in conjugate heat transfer between a sphere and its surrounding fluid

Unsteady conjugate heat transfer between an aluminum sphere and its surrounding water was investigated. The mass, momentum and energy equations were solved, and for Reynolds number greater than 400, the large eddy simulation with the Smagorinsky–Lilly model was used. 3D transient simulations were carried out for the sphere Reynolds numbers ranging from 1 to 10,000 (6.99 ≤Pe ≤ 69,900). This study particularly focuses on the effect of Reynolds numbers on the thermal wake phenomenon. The simulation results showed that under the condition of the conductivity ratio of 337.33 and the heat capacity ratio of 0.567, thermal wake exists when 1≤ Re <8000 (6.99 ≤ Pe < 55,920). The Reynolds number of 8000 (Pe = 55,920) was determined as the turning point that thermal wake disappears. Two modes of reverse heat transfer, laminar and vortical were identified. For laminar thermal wake, the thermal inversion point starts from the rear stagnation, while for vortical thermal wake, it occurs near the separation point.

Analytic similarity solutions for fully resolved unsteady laminar boundary layer flow and heat transfer in the presence of radiation

In this paper, we have compared a new type of similarity transformation derived systematically by using Lie point symmetries with the existing similarity transformations for unsteady fluid flow and heat transfer in the boundary layer in the presence of radiation. It is observed that the existing transformations map the steady and marginally accelerating flows only, while the Lie similarity transformations provide solutions for all types of accelerating flows and are independent of unsteadiness in the fluid. The previous transformations are valid for a specific time interval which depends on a range of unsteadiness parameter, however the Lie similarity transformations provide valid solutions at any given time. This implies that the Lie similarity transformations yield solutions for previously unexplored ranges of unsteadiness in the fluid. Boundary layer flow physics for both types of transformations is discussed by employing the Homotopy analysis method. We show that for accelerating fluids, in the developing region, the boundary layer thickness first increases and than starts to decrease with increase in unsteadiness for fully developed flow. Detailed comparison of velocity and temperature profiles in the boundary layer is made using the tables and graphs which show that with Lie similarity transformations the region of study of the considered flow extends significantly for the unsteadiness parameter. The effect of the Prandtl number and radiation parameter on temperature distribution is also compared for both types of similarity transformations. The Lie symmetry similarity transformations are shown to explain the unsteady laminar boundary layer flow and heat transfer to an extent where the existing similarity transformations do not work.

Stability Analysis of Unsteady Mixed Convection Flow Near the Stagnation Point with Buoyancy Effect

This numerical study investigates the behaviour of the unsteady mixed convection flow and heat transfer near the stagnation region past a vertical plate in Al2O3-Cu/H2O hybrid nanofluids. By choosing an appropriate similarity transformation, an ordinary differential equations system is obtained, hence scrutinized via the bvp4c package embedded in the MATLAB program. The results show that as the nanoparticle volume fraction and unsteadiness parameter increase, the fluid's skin friction coefficient also increases. Also, an increase in the nanoparticle volume fraction and unsteadiness parameter has broadened the range of solutions hence, delayed the progress of boundary layer separation. In addition, the presence of the unsteadiness parameter provides a significant result in the thermal system. The first solution is declared stable by the stability analysis.

Experimental Investigation on Ice Accretion Upon Ice Particle Impacting onto Heated Surface

An experimental study was conducted to examine the dynamic ice accretion process upon the impingement of microsized, airborne ice particles/crystals onto a heated test surface pertinent to aeroengine icing phenomena. The experimental study was conducted in a specially designed ice crystal icing test facility to generate and inject microsized ice particles into a frozen-cold airflow. The microsized ice particles were forced to impinge onto a heated test plate with controllable surface temperatures. Upon impingement of the ice particles onto the heated test surface, the dynamic ice accretion process was found to take place over the heated surface in three distinct stages: 1) an ice-melting stage at the beginning, followed by 2) an ice/water mixture formation stage, and then 3) a water refreezing stage, causing the formation of a solid ice layer accreted on the heated test surface eventually. After impinging onto the test plate, while small ice particles with spheric shapes were found to be more ready to bounce off from the test surface, large, nonspheric-shaped ice particles experienced a catastrophic fragmentation process and break up into smaller pieces with noticeable impingement residues remaining on the test surface. The formation of a liquid water film layer on the test surface due to the melting of the impinged ice particles was found to be very beneficial to make more impinged ice particles stay sticking on the test surface, resulting in a rapid growth of the water/ice layer accreted on the heated test surface. A comprehensive theoretical analysis was also performed to examine the unsteady heat transfer characteristics during the dynamic ice accretion process. The theoretic predictions of the collection efficiency of the impinged ice particles on the heated test surface and the temperature variations of the water layer at the initial ice-melting stage were found to agree well with the experimental measurement results.

On the proofs of orthogonality of eigenfunctions for heat conduction, wave propagation, and advection-diffusion problems

The orthogonality of eigenfunctions in problems of unsteady heat conduction in an infinite slab with symmetric and nonsymmetric convective boundary conditions are demonstrated by performing actual integration of the products of the derived forms of eigenfunctions and by implementing the corresponding eigenvalue conditions. The analysis also applies to longitudinal vibrations of an elastic rod attached at its ends to linear elastic springs, and to advection-diffusion problems under appropriate boundary conditions. The same form of eigenfunctions and the same type of eigenvalue condition apply in all three considered cases. The proofs are compared with the well-known general proof of orthogonality of eigenfunctions, which circumvents the actual integration. The presented analysis is pedagogically appealing for use in engineering and applied physics education.

Numerical investigation of unsteady film cooling on turbine blade squealer tip with pressure side coolant

Unsteady film cooling characteristic from pressure side coolant in squealer tip in turbine stage was investigated by numerical simulation. Due to unsteady flow in turbine stage, flow characteristics and blowing ratio of coolant from various holes fluctuate and change cooling effectiveness on squealer rim, cavity floor and side wall. In unsteady simulation, deterioration of coolant coverage causes unsatisfied cooling performance on squealer tip, which results in the maximum reduction of 18.3% and 20% of cooling effectiveness on squealer rim and cavity floor at specific instants compared to steady simulation. In different moments, pressure side coolant increases average heat transfer coefficient on pressure side squealer rim by 15% ∼ 47% and forms discrete distribution of high heat transfer coefficient there. Unsteady heat transfer on squealer rim is much intense compared to steady condition. Raising blowing ratio and decreasing cavity depth promote cooling effectiveness in tip cavity. Too small blowing ratio might lead to the risk of high temperature mainstream invasion into some pressure side film holes. Cooling effectiveness in tip cavity increases with cavity depth decreasing. Due to relative motion between blade tip and shroud, scraping vortex pushed rolling vortex more closely to pressure side and thus facilitates coolant to touch cavity floor.

Numerical investigation of mixed convection from rectangular cylinders subjected to upper cross flow

Unsteady combined natural and forced convection heat transfer from a rectangular cylinder subjected to upward cross flow is investigated numerically. The working fluids are air (Pr = 0.7) and water (Pr = 7), and the flow is laminar. The governing flow and energy equations are solved using a fractional step finite-difference scheme. The effects of the cylinder aspect ratio (a = L/D), Reynolds and Richardson numbers on the flow and heat transfer characteristics are investigated. Numerical simulations were carried out for the cylinders with aspect ratios of a = 0.5, 1, and 2, while the Richardson and Reynolds numbers varied between 0 to 10, and 100 to 200, respectively. The mean drag, mean rms lift coefficients, as well as the Strouhal number and the mean Nusselt number were computed for each simulation to determine the quantitative effects on flow and heat transfer. Steady flow is observed for Pr = 0.7, Ri = 0.5, and a = 0.5 or for Re ≥ 150 and Ri ≥ 1. For Ri = 10 and Re = 200, the flow becomes unsteady in the downstream region and trigger vortex street formation for a = 0.5, 1, and 2. Decreasing the aspect ratio, as well as increasing Reynolds number, increases the heat transfer from the cylinder. The rms lift coefficient decreases sharply at Ri < 1 for Pr = 0.7, Ri < 2 for Pr = 7 due to vortex breakdown. Further increase in the Richardson leads to a slight increase in rms lift coefficient except for Re = 200 where the sharp increase is observed due to triggered vortex formation again. For air, the increase in the mean Nusselt number in Ri = 10 case with respect to the forced convection case (Ri = 0) was 54–65% and 80–98%, respectively, for a = 0.5 and 2, while these values for water were realized as 50–68% and 53–63%, respectively. Using the computed data and nonlinear regression, the mean Nusselt number and the drag coefficients were developed.

Entropy generation in unsteady stagnation flow through porous media in the presence of a high magnetic Reynolds number with a uniform heat source: renewable energy applications

The present model’s major focus is on entropy production and Newtonian, incompressible two-dimensional temperature-dependent stagnation point with uniform heat source factors in a porous channel. Furthermore, the induced magnetic field (IMF) is employed in this flow analysis, which is created by the movement of electrically conducting fluid. Entropy generation (EG) is an important aspect of any heat transfer development since it helps to reduce the irreversibility factor in a system. EG analysis has several applications in traditional industrial fields requiring fluid flows and heat transfer. As a result, the current study is concerned with the effects of EG. The relevant similar transformations are used to convert partial governing equations arising in the present model into ordinary differential equations (ODE). The bvp4c built-in code in MATLAB programming is then utilized to crack highly nonlinear equations. We arrive at numerical solutions by employing thebvp4c built-in code in MATLAB software. The results are plotted and discussed for various embedded parameters. It is discovered that because of low friction, the porosity parameter decreases the velocity and induces the magnetic boundary layer. Unsteady parameter and heat source parameters accelerate Bejan number, whereas the heat source and porosity constraints accelerate entropy analysis.

Synchronization-based model for turbulent thermoacoustic systems

We present a phenomenological reduced-order model to capture the transition to thermoacoustic instability in turbulent combustors. Based on the synchronization framework, the model considers the acoustic field and the unsteady heat release rate from turbulent reactive flow as two nonlinearly coupled sub-systems. To model combustion noise, we use a pair of nonlinearly coupled second-order ODEs to represent the unsteady heat release rate. This simple configuration, while nonlinearly coupled to another oscillator that represents the independent sub-system of acoustics (pressure oscillations) in the combustor, is able to produce chaos. Previous experimental studies have reported a route from low amplitude chaotic oscillation (i.e., combustion noise) to periodic oscillation through intermittency in turbulent combustors. By varying the coupling strength, the model can replicate the route of transition observed and reflect the coupled dynamics arising from the interplay of unsteady heat release rate and pressure oscillations.

Numerical Analysis of Unsteady Heat Transfer in the Chamber in the Piston Hybrid Compressor with Regenerative Heat Exchange

The adjoint thermodynamic and heat exchange processes in the new class piston compressor with regenerative heat exchange are considered in the paper. The implicit tridiagonal matrix algorithm is implemented to study the unsteady thermal conductivity in the cylinder–piston group. After the formulation of proper initial and boundary conditions, the optimal relationship between temporal and spatial discretization steps is determined. Two different time steps are used in the numerical solution of the two-way coupled fast thermodynamic and slow heat exchange models. The relationship between those time steps is determined as well. The conducted numerical experiments allow the analysis of the dynamics of heat exchange in the cylinder–piston group, temperature variation in different parts of the cylinder–piston group, the impact of the heat transfer processes on isothermal and adiabatic efficiency, the impact of heat exchange dynamics on the thermodynamic cycle, as well as other thermodynamic and energetic effects.

Analysis of Unsteady Heat Transfer in the Pre-Cooling Process of 300 m3 Liquid Hydrogen Tank

A mathematical model for the pre-cooling process was established to solve the problems of the long pre-cooling time and uncertain parameters of cryogenic propellant tanks. The pre-cooling parameters of a 300 m3 liquid hydrogen tank at several cooling rates were calculated and analyzed. The results show that the liquid hydrogen flow required to pre-cool the gas in the tank, tank wall, accessories, and interlayer thermal insulation materials increases first and then decreases and that the liquid hydrogen flow needed to offset the heat leakage gradually increases with the temperature reduction. When the average cooling rate rose from 0.1 K/min to 1 K/min, the pre-cooling time was shortened from 2730 min to 273 min, and the consumption of liquid hydrogen decreased from 2115 kg to 2091 kg. Among the various heat loads, the inner tank wall and accessories consumed the most significant proportion of liquid hydrogen, accounting for 87.84% to 88.61%. The cooling capacity was derived from the liquid hydrogen’s evaporation and the cryogenic hydrogen gas’s heating process, of which the liquid hydrogen accounted for 23.00%. Considering the principle of safe operation, it is recommended that stepped pre-cooling in two or three stages based on the maximum cooling rate is conducted.

Study on refined mathematical model of solar chimney power plant integrated with seawater desalination and the influence of dewing

In order to more accurately evaluate the operation and output characteristics of the solar chimney power plant integrated seawater desalination, a refined mathematical model for unsteady heat and mass transfer was built under consideration of the convection heat transfer mechanism of the collector, dewing phenomenon, and the disturbance to the hot airflow caused by the oblique-toothed flow channel boundary. The influence of nighttime dewing and humid environments on system performance was discussed. The results show that it is feasible and more appropriate to use the forced convection heat transfer coefficient of bellows to consider the influence of the oblique-toothed flow channel boundary; the refined mathematical model is also more accurate and reliable. Due to the effect of seawater heat storage, dewing has little effect on system performance, and the integrated system has a better anti-dewing negative impact characteristic. However, when the ambient humidity reached a higher level, dewing had a greater negative impact on freshwater production. The critical value of relative humidity for dewing to occur is 51 %. When the relative humidity increases from 45 % to 60 %, the daily utilization efficiency of solar energy decreases from 27.4 % to 22.5 %.

Experimental Investigation of a High-Speed Turbine With Rainbow Rotor and Rim Seal Purge Flow

AbstractThe present paper addresses the experimental and numerical study of the unsteady flow established in a high-pressure turbine stage with rim seal purge. The HPT test section, operated at engine-relevant flow conditions in the high-speed turbine rig of the von Karman Institute, is heavily instrumented for high-resolution, high-bandwidth aerothermal measurements. A rainbow rotor setup allows the simultaneous testing of six different sectors, each hosting a specific tip and platform geometry optimized for enhanced aerodynamic performance. This paper focuses on the flow over the baseline sector, equipped with an axisymmetric hub platform and a squealer tip, with a purge flowrate matching 1.74% and 1% of the stage mass flow. The numerical study relies on Reynolds-averaged Navier–Stokes (RANS) computations with test-calibrated boundary conditions. Unsteady pressure and heat transfer measurements are performed at the rotor shroud. The maximum heat transfer is achieved along the front pressure side rim, whereas the squealer cavity generates a region of uniformly low static pressure and heat flux. The experimental adiabatic wall temperature is derived to quantify the thermal contribution to the global heat flux, demonstrating an increase in over-tip gas temperature up to 1.2 T01 above the pressure side rim. A Euler-based model is proposed to evaluate the temperature-driving work-exchange mechanism in the tip gap. The peak in casing heat transfer coefficient (750 W/m2K) is found at the tip leading edge. Time-resolved measurements of outlet total pressure, Mach number, and flow angle confirm the predicted phase and intensity of the tip leakage and upper passage vortex in the near-casing region. At 20% hr, the total pressure minimum is highly underpredicted by the RANS, indicating an inaccurate modeling of the interaction between rim seal purge and main flow. The measured impact of the purge flow variation is more significant than predicted by the RANS computations, with a negative offset of about 0.5% P01 in the lower 50% hr at lower purge flowrate.