Temperature Wall Function Research Articles

Using solar energy and phase change materials to supply energy to a building to reduce environmental pollution

In this paper, a small building with a Trombe wall with a blade made of phase change material is simulated. This numerical study was performed by changing the stoutness of the blades in the range of 5–25 cm. This building has also been compared to a similar building without a Trombe wall in terms of fuel consumption and CO2 production. This evaluation is conducted in a frigid climate during several months of the year. The Energy Plus program is utilized to calculate the needed heat and fuel load, while the COMSOL software is used to solve the PCM melting front. The findings of this investigation demonstrated that using bigger blades leads in a higher nighttime wall temperature and longer wall function. The use of a 25 cm blade leaves more molten PCM at different times so that the use of this blade stoutness has caused the molten PCM to still be on the wall for more than 8 h. The effect of Trombe wall on reducing fuel consumption has been greater in the hot months of the year. The highest CO2 production occurred in the cold months of the year. The use of a Trombe wall has reduced CO2 production. This decrease was greater in the warmer months of the year.

ADAPTATION OF TEMPERATURE WALL FUNCTION FOR CALCULATION THE HEAT TRANSFER AT SUPERCRITICAL COOLANT PARAMETERS

To date, the engineering community pays special attention to the study, research and development of methods for predicting the behavior of the coolants at supercritical parameters. This paper discusses the problem of adaptation of the existing universal or specialized tools of thermohydraulic analysis for nonlinear heat transfer problems at supercritical coolant parameters with deterioration of heat transfer. Complexities of prediction the nonlinear heat transfer at supercritical parameters of the coolant by engineering methods of computational fluid dynamics are considered. A simple way to adapt the dual-zone Kader's temperature wall function on the basis of existing probe measurements for carbon dioxide is proposed. The problem of implementation into universal packages of computational fluid dynamics (CFD), which is based on the method of choosing the reference coordinate of the near-wall zone to determine the dynamic speed and dimensionless temperature, is discussed. The example on the ANSYS CFX using shows one of the ways to create a special user procedure, which has an improved tendency to predict the axial temperature profile with deteriorated heat transfer. Calibration and validation of the obtained results on the basis of experimental investigations for vertical pipes and rod assemblies of fuel simulators is carried out in the work. The paper also discusses the features of the proposed implementation, and formed recommendations for the application and further improvement of engineering approaches to predict the heat transfer deterioration at supercritical parameters of the coolant.

Numerical Aspects Affecting Heat Transfer in ICE Applications and Definition of a Temperature Wall Function Accounting for the Boundary Layer Compressibility

Numerical Aspects Affecting Heat Transfer in ICE Applications and Definition of a Temperature Wall Function Accounting for the Boundary Layer Compressibility

CFD simulation of the near-neutral atmospheric boundary layer: New temperature inlet profile consistent with wall functions

Accurate Computational Fluid Dynamics (CFD) simulations of Atmospheric Boundary Layer (ABL) flow are essential for a wide range of applications, including atmospheric heat and pollutant dispersion. An important requirement is that the imposed inlet boundary conditions should yield vertical profiles that maintain horizontal homogeneity (i.e. no streamwise gradients) in the upstream part of the computational domain for all relevant parameters, including temperature. Many previous studies imposed a uniform temperature profile at the inlet, which has often led to horizontal inhomogeneity of the temperature profile. This study presents a new temperature inlet profile that can yield horizontal homogeneity for neutral and near-neutral ABL conditions when used in combination with the Standard Gradient Diffusion Hypothesis (SGDH) and a temperature wall function. The horizontal homogeneity by this profile is verified by 2D Reynolds-Averaged Navier-Stokes (RANS) CFD simulations performed with the standard k-ε turbulence model and the SGDH. The approach in this paper can be extended to other types of wall functions and other RANS closure schemes for Reynolds stresses and turbulent heat fluxes.

An adapted steady RANS RSM wall-function for building external convection

Computational Fluid Dynamics (CFD) can improve usual estimates of building external convective heat transfer coefficients (hc,w) by accounting for the geometry of constructions, the aerodynamic field around them, the nature of convection and providing high resolution data. However, the limitations of usual mass flow descriptions and near wall treatments make the accurate prediction of hc,w challenging. Hence, this paper evaluates the ability of steady RANS Reynolds Stress (RSM) and k–ε realizable models to predict hc,w in case of isolated cubical obstacles. The accuracy of usual CFD methods and turbulence models, as well as fine grid near wall models and usual temperature wall functions (TWFs) are examined by comparison with experimental and detailed numerical data.When used with a low Reynolds number model (LRNM), both turbulence models accurately predict hc,w on the front and rear faces of the obstacle. However, they show different behaviors on the other faces and highlight issues related to the dynamic behavior of real flows. Moreover, hc,w predictions obtained using standard TWFs substantially deviate from the validated LRNM results. Therefore, a customized TWF suited for use with the RSM and forced convection problems is proposed by extending studies of Defraeye et al. (An adjusted temperature wall function for turbulent forced convective heat transfer for bluff bodies in the atmospheric boundary layer; Building and Environment, 2011, 46, 2130–2141). Customized TWFs substantially improve WF-based hc,w predictions with respect to LRNM results while keeping their cost effectiveness, and provides satisfactory results even for high z∗.

An adjustment to the standard temperature wall function for CFD modeling of indoor convective heat transfer

Computational fluid dynamics (CFD) has become a popular tool for investigating indoor convective heat transfer. Two methods are used for dealing with the convective heat transfer of walls in CFD. One is to apply wall functions, and the other is to implement near-wall modeling by generating sufficiently fine mesh in the boundary layer. The former method is very simple; however, it may not be applicable to indoor environments. The latter method is generally more accurate but requires a significant number of grid mesh to capture the viscous boundary sublayer. This investigation proposes to tune the wall Prandtl number to modify the standard temperature wall function for applicability to indoor convective heat transfer modeling. The adjustment attempts to obtain convective heat transfer coefficients of walls that match those provided by the correlation formulas. Because the variation of the convective heat transfer coefficients with the wall Prandtl number is nonlinear, it is necessary to repeat the CFD simulations by following the developed procedure. The proposed method has been applied to model both heat transfer and flow motion in a mixing ventilation mode and an under-floor displacement ventilation mode, respectively. The results reveal that the adjusted temperature wall function is able to solve accurately indoor convective heat transfer with a moderate grid number. The standard temperature wall function with the default wall Prandtl number yields an unacceptable temperature distribution; hence, it is not appropriate for indoor convective heat transfer modeling.

CFD simulation of heat transfer at surfaces of bluff bodies in turbulent boundary layers: Evaluation of a forced-convective temperature wall function for mixed convection

Accurate predictions of convective heat transfer are essential in building-engineering and environmental studies on urban heat islands, building energy performance, (natural) building and inter-building ventilation and building-envelope durability and conservation. In computational fluid dynamics (CFD) studies of these applications, wall functions are mostly used to model the boundary-layer region. Recently, an adjusted wall function for temperature (CWF) has been proposed (Defraeye et al., 2011a). This CWF was intended for forced-convective heat transfer at surfaces of bluff bodies, such as buildings in the atmospheric boundary layer (ABL). This CWF provides increased (wall-function) accuracy for convective heat transfer predictions and can be easily implemented in existing CFD codes. As ABL flow around buildings is often in the mixed-convective regime, the CWF performance is evaluated for situations with mixed convection in this paper. The CWF accuracy for mixed convection (∼16% for the convective heat transfer coefficient, CHTC) is also much better than standard wall functions (∼47% for the CHTC), but is Richardson-number dependent. The CWF approach can therefore significantly improve the accuracy of forced- or mixed-convective heat transfer in large-scale building-engineering or environmental studies, which are bound to rely on wall functions, but where accurate convective heat transfer predictions are required.

Effects of Wall Heating on Flow Characteristics in a Street Canyon

We develop a large-eddy simulation (LES) model based on a meteorological numerical model for a real scale street-canyon flow with rough building facets heated by a given temperature. The model is applied to a canyon with the aspect ratio of unity for two idealized heating scenarios: (1) the roof and the entire upstream wall are heated, named as ‘assisting cases’, and (2) the roof and the entire downstream wall are heated, named as ‘opposing cases’. These facets were heated up to 15 K above the air temperature. A wall function for temperature is proposed for a rough facet with an assumption that the thermal roughness length, z0T, is much smaller than the aerodynamic roughness length, z0. It is demonstrated that the sensible heat flux and canyon-air temperature are significantly influenced by the near-facet process that is parametrized by z0T as the primary factor; other processes such as in-canyon mixing and roof-level exchange are secondary. This new finding strongly suggests that it is vital to choose an appropriate value of z0T in a numerical simulation of street-canyon flows with the facet-air exchange processes of heat or any scalar. The finding also raises an awareness of the demand for carefully designed laboratory or field experiments of quantifying z0T values for various urban surfaces. For the opposing cases, an unsteady penetrating narrow updraft zone appears occasionally along the heated wall and this feature is consistent field observations. The unique result indicates the superior capability of LES. The results of this study can be used to guide the parametrization of turbulent processes inside the urban canopy layer.

An adaptive temperature wall function for mixed convective flows at exterior surfaces of buildings in street canyons

For computational fluid dynamics (CFD) simulations of large urban areas the air flow near surfaces is normally modelled using Wall Functions (WFs). This study aims at improving the accuracy of WFs, in terms of heat transfer predictions. Turbulent boundary layers at heated building surfaces in a street canyon were analysed with low-Reynolds number modelling (LRNM). Buoyancy was accounted for, due to its importance in street canyons e.g. by solar radiation. Two extreme types of normalized temperature profiles could be identified in the thermal boundary layer dependent on the Richardson (Ri) number. One extreme at low Ri number could be attributed to forced convective flow, which is adequately described by existing standard wall functions (SWFs), and the second extreme at Ri>1 to mixed convective flows, where WFs adapted for non-equilibrium flows (NEWFs) are appropriate. Based on these two extremes, an adaptive temperature wall function (AWF) was derived that varies between the two existing WFs dependent on the local Ri. This AWF can account for the co-occurrence of forced and mixed convective flow regimes at a single surface. CFD simulations of street canyon configurations with SWF showed errors in the wall heat fluxes up to 60%, compared to the LRNM results, and up to 30% for NEWFs. With the proposed AWF, these errors were reduced to less than 10% for the majority of the cases studied over the whole range of Ri numbers. We conclude that the proposed AWF allows for more accurate convective heat transfer analysis in urban CFD studies.

An adjusted temperature wall function for turbulent forced convective heat transfer for bluff bodies in the atmospheric boundary layer

Accurate convective heat transfer predictions are required in building engineering and environmental studies on urban heat islands, building energy performance, building-envelope durability or conservation and (natural) ventilation of buildings. When applying computational fluid dynamics (CFD) for these computationally-expensive studies at high-Reynolds numbers, wall functions are mostly used to model the boundary-layer region. In this study, an adjustment to the standard temperature wall function is proposed for forced convective heat transfer at surfaces of typical wall-mounted bluff bodies in turbulent boundary layers, such as the atmospheric boundary layer, at moderate to high Reynolds numbers. The methodology to determine this customised temperature wall function (CWF) from validated numerical data of CFD simulations using low-Reynolds number modelling (LRNM) is explained, where a logarithmic- law behaviour is found. The performance of this CWF is evaluated for several bluff-body configurations. Standard wall functions (SWFs) yield deviations of about 40% for the convective heat transfer coefficient, compared to LRNM. With the CWF however, these deviations are reduced to about 10% or lower. The CWF therefore combines increased (wall-function) accuracy for convective heat transfer predictions with the typical advantage of wall functions compared to LRNM, being a lower grid resolution in the near-wall region, which increases computational economy and facilitates grid generation. Furthermore, this CWF can be easily implemented in existing CFD codes, and is implemented in the commercial CFD code Fluent in this study.

A temperature wall function for turbulent mixed convection from vertical, parallel plate channels

Despite tremendous increase in computing power and an attendant increase in direct numerical simulations (DNS) of turbulent flows, near wall treatment continues to be the mainstay of most commercial packages as well as in house codes, for wall bounded turbulent flows. Even so efficient near wall treatments of truly “mixed convection flows” are not many in the open literature. This paper looks at a possible approach to the treatment of a typical mixed convection problem from vertical, parallel plate channels. The procedure employed is an asymptotic blending of natural and forced convection wall functions, which themselves are derived based on an asymptotic analysis of flow in the near wall region. Testing of the wall function was done for both aiding and opposing flows with DNS data available in literature.

Determination of temperature wall functions for high Rayleigh number flows using asymptotics: A systematic approach

This paper presents a systematic approach to determine temperature wall functions for high Rayleigh number flows using asymptotics. An asymptotic analysis of the flow and heat transfer in the near wall region forms the basis for the development of the wall functions. Appropriate normalization of the variables followed by asymptotic matching of the temperature gradients of the inner and outer layers in the overlap region leads to a logarithmic temperature profile as a wall function that has undetermined constants. A key classification that has been made in the present study is the introduction of (1) The direct problem and (2) The inverse problem. The former means that temperature profiles, either from experiments or Direct Numerical Simulations (DNS), are available and the wall function problem finally reduces to one of determining certain constants in a general wall function formula. More radical and of more interest, is the inverse problem. The idea behind this it is that when a temperature profile can be recast into a Nusselt–Rayleigh correlation, it should be perfectly possible for one to start from a Nusselt–Rayleigh correlation and end up with a wall function for temperature. This approach again will have undetermined constants that can be calibrated from either experimental or DNS data. The main advantage of using the inverse problem is the dispensation of the need to measure temperatures accurately within the boundary layer. For both the direct and inverse problems, a graded treatment to determine the constants is presented. The treatment at its highest level will result in a parameter estimation problem that can be posed as an optimization problem. The optimization problem is then solved by state of the art techniques like Levenberg–Marquardt algorithm and Genetic algorithms (GA) and the solutions are compared. While for the direct problem, the approach is illustrated for the infinite channel problem (a simple flow), for the inverse problem, the approach is elucidated for the Rayleigh–Bénard problem (a complex flow). Finally, a blending procedure to arrive at a universal temperature profile that is valid in the viscous sublayer, buffer and the overlap layers is suggested. The key ideas of (1) using optimization techniques for determining the constants in the wall function and (2) obtaining wall functions from the Nusselt numbers by the inverse approach are expected to be useful for a wide class of problems involving natural convection.

Asymptotic analysis of the near-wall region of turbulent natural convection flows

High-Grashof-number turbulent natural convection in the vicinity of vertical walls with heat transfer is analysed asymptotically. The near-wall boundary layer has a viscosity-influenced inner layer and a fully turbulent outer layer, similar to the structure of forced convection boundary layers. Scaling laws and wall functions are found by asymptotic matching of the temperature gradients in the overlap layer. The temperature wall function then is a simple logarithmic function of wall distance whereas the velocity profile in the overlap layer is a more complex correlation. Constants in these wall functions are deduced from high-quality data for large Grashof numbers. Experimental as well as numerical profiles as a whole are very well reproduced by the combination of wall functions and viscous sublayer profiles. Therefore these new asymptotic profiles can be used in CFD codes to avoid very fine grids close to the wall, when Grashof numbers are high.

Effect of fuel and engine operational characteristics on the heat loss from combustion chamber surfaces of SI engines

Understanding of engine heat transfer is important because of its influence on engine efficiency, exhaust emissions and component thermal stresses. In this paper, the effect of various parameters such as compression ratio, equivalence ratio, spark timing, engine speed, inlet mixture temperature and swirl ratio as well as fuel type on the heat transfer through the chamber walls of a spark ignition (SI) engine is studied. For this purpose, a proper tool is developed which uses a KIVA multidimensional combustion modeling program and a finite-element heat conduction (FEHC) code iteratively. Also, an improved temperature wall function is used for the KIVA program. It was found that this iterative scheme and the new wall function can improve the predictions considerably. A parametric study shows that this methodology is efficient in predicting the engine heat transfer and the effects of changes in the fuel type and engine operational parameters on the engine thermal behavior.

Thermal Effects on the Airflow in a Street Canyon – Nantes'99 Experimental Results and Model Simulations

The thermal effects on the airflow within a street canyon, which are produced by the variation of direct solar heating of the street sides and ground, are examined in this article. The investigation is based on the experimental results of the Nantes'99 campaign and numerical simulations performed with the Computational Fluid Dynamics (CFD) code CHENSI using the standard k-e model. The Nantes'99 experimental campaign was performed in a North-to-South oriented central street canyon of Nantes, France. It was observed that a thin thermal layer develops locally within a few centimetres from the heated wall. It is anticipated that, the convective flow close to the windward wall, which was visualised during the experiment, carries air masses from the street level upwards, where normally cleaner air is transported. Consequently, thermal effects may be important for the air quality in the street.Based on the temperature and wind flow measurements, the flow and temperature fields were simulated first in two dimensions with the CFD code CHENSI. It was found that CHENSI overestimates the thermal effects on the canyon airflow showing the main re-circulation simulated in the isothermal case to change into two counter-rotating vortices after the inclusion of the heating of the windward wall. A reason for this overestimation is possibly the temperature wall function implemented for such thin thermal boundary layers in conjunction with the limitations in grid resolution.

A temperature wall function formulation for variable-density turbulent flows with application to engine convective heat transfer modeling

A temperature wall function was derived for variable-density turbulent flows that are commonly found in internal combustion engines. Thermodynamic variations of gas density and the increase of the turbulent Prandtl number in the boundary layer are included in the formulation. Multidimensional computations were made of a pancake-chamber gasoline engine and a heavy-duty diesel engine under firing conditions. Satisfactory agreement between the predicted and measured heat fluxes was obtained. It was found that gas compressibility affected engine heat transfer prediction significantly while the effects of unsteadiness and heat release due to combustion were insignificant for the cases considered.