Instantaneous Heat Flux Simulation of a Motored Reciprocating Engine: Unsteady Thermal Boundary Layer With Variable Turbulent Thermal Conductivity

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
Abdalla Agrira ◽  
David R. Buttsworth ◽  
Mior A. Said
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Heat Flux ◽  
Prandtl Number ◽  
Thermal Boundary Layer ◽  
Combustion Engine ◽  
Turbulent Viscosity ◽  
Spark Ignition Engine ◽  
Turbulent Prandtl Number

Due to the inherently unsteady environment of reciprocating engines, unsteady thermal boundary layer modeling may improve the reliability of simulations of internal combustion engine heat transfer. Simulation of the unsteady thermal boundary layer was achieved in the present work based on an effective variable thermal conductivity from different turbulent Prandtl number and turbulent viscosity models. Experiments were also performed on a motored, single-cylinder spark-ignition engine. The unsteady energy equation approach furnishes a significant improvement in the simulation of the heat flux data relative to results from a representative instantaneous heat transfer correlation. The heat flux simulated using the unsteady model with one particular turbulent Prandtl number model agreed with measured heat flux in the wide open and fully closed throttle cases, with an error in peak values of about 6% and 35%, respectively.

Heat Transfer in the Accelerated Fully Rough Turbulent Boundary Layer

1981 ◽  
Vol 103 (1) ◽  
pp. 153-158 ◽  
Author(s):  
H. W. Coleman ◽  
R. J. Moffat ◽  
W. M. Kays
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Turbulent Boundary Layer ◽  
Prandtl Number ◽  
Pressure Gradient ◽  
Turbulent Heat Flux ◽  
Test Surface ◽  
Turbulent Heat ◽  
Turbulent Prandtl Number

Heat transfer behavior of a fully rough turbulent boundary layer subjected to favorable pressure gradients was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Stanton numbers and profiles of mean temperature, turbulent Prandtl number, and turbulent heat flux are reported. Three equilibrium acceleration cases (one with blowing) and one non-equilibrium acceleration case were studied. For each acceleration case of this study, Stanton number increased over zero pressure gradient values at the same position or enthalpy thickness. Turbulent Prandtl number was found to be approximately constant at 0.7–0.8 across the layer, and profiles of the non-dimensional turbulent heat flux showed close agreement with those previously reported for both smooth and rough wall zero pressure gradient layers.

Simulation of Instantaneous Heat Transfer in Spark Ignition Internal Combustion Engines: Unsteady Thermal Boundary Layer Modelling

2009 ◽  
Author(s):  
David R. Buttsworth ◽  
Abdalla Agrira ◽  
Ray Malpress ◽  
Talal Yusaf
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Internal Combustion Engine ◽  
Thermal Boundary Layer ◽  
Internal Combustion Engines ◽  
Combustion Engine ◽  
Internal Combustion ◽  
Restrictive Assumption ◽  
Low Dimensional ◽  
Energy Equations

Simulation of internal combustion engine heat transfer using low-dimensional thermodynamic modelling often relies on quasi-steady heat transfer correlations. However, unsteady thermal boundary layer modelling could make a useful contribution because of the inherent unsteadiness of the internal combustion engine environment. Previous formulations of the unsteady energy equations for internal combustion engine thermal boundary layer modelling appear to imply that it is necessary to adopt the restrictive assumption that isentropic processes occur in the gas external to the thermal boundary layer. Such restrictions are not required and we have investigated if unsteady modelling can improve the simulation of crank-resolved heat transfer. A modest degree of success is reported for the present modelling which relies on a constant effective turbulent thermal conductivity. Improvement in the unsteady thermal boundary layer simulations is expected in future when the temporal and spatial variation in effective turbulent conductivity is correctly modelled.

Calculation of a Turbulent Boundary Layer Downstream of a Step Change in Surface Temperature

1979 ◽  
Vol 101 (1) ◽  
pp. 144-150 ◽  
Author(s):  
L. W. B. Browne ◽  
R. A. Antonia
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Prandtl Number ◽  
Surface Temperature ◽  
Reynolds Shear Stress ◽  
Turbulent Viscosity ◽  
Step Change ◽  
Mean Temperature ◽  
Thermal Layer ◽  
Good Agreement

Mean temperature and heat flux distributions in a thermal layer that develops within a momentum boundary layer subjected to a step change in surface temperature are calculated using two different methods. The method of Bradshaw and Unsworth, which uses the method of Bradshaw, Ferriss and Atwell to determine the mean velocity and Reynolds shear stress distributions and then assumes a constant turbulent Prandtl number for the heat flux calculation, yields heat flux distributions that are significantly different than the available experimental results at small distances from the step. Good agreement between calculations and experimental values is achieved when the distance x from the step is about 20 δ0, where δ0 is the boundary layer thickness at the step. To obtain good agreement with measurements of heat flux and mean temperature near the step, estimated distributions of turbulent viscosity and effective Prandtl number have been derived using an iterative updating procedure and the calculation method of Patankar and Spalding. These distributions are compared with those available in the literature. Calculated heat flux distributions show that the internal thermal layer is only likely to reach self-preserving conditions when x exceeds 40 δ0.

Heat transfer in a turbulent channel flow with square bars or circular rods on one wall

2015 ◽  
Vol 776 ◽  
pp. 512-530 ◽  
Author(s):  
S. Leonardi ◽  
P. Orlandi ◽  
L. Djenidi ◽  
R. A. Antonia
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Prandtl Number ◽  
Channel Flow ◽  
Turbulent Channel Flow ◽  
Turbulent Heat ◽  
Turbulent Prandtl Number ◽  
Smooth Wall ◽  
Roughness Elements ◽  
Smooth Channel

Direct numerical simulations (DNS) are carried out to study the passive heat transport in a turbulent channel flow with either square bars or circular rods on one wall. Several values of the pitch (${\it\lambda}$) to height ($k$) ratio and two Reynolds numbers are considered. The roughness increases the heat transfer by inducing ejections at the leading edge of the roughness elements. The amounts of heat transfer and mixing depend on the separation between the roughness elements, an increase in heat transfer accompanying an increase in drag. The ratio of non-dimensional heat flux to the non-dimensional wall shear stress is higher for circular rods than square bars irrespectively of the pitch to height ratio. The turbulent heat flux varies within the cavities and is larger near the roughness elements. Both momentum and thermal eddy diffusivities increase relative to the smooth wall. For square cavities (${\it\lambda}/k=2$) the turbulent Prandtl number is smaller than for a smooth channel near the wall. As ${\it\lambda}/k$ increases, the turbulent Prandtl number increases up to a maximum of 2.5 at the crests plane of the square bars (${\it\lambda}/k=7.5$). With increasing distance from the wall, the differences with respect to the smooth wall vanish and at three roughness heights above the crests plane, the turbulent Prandtl number is essentially the same for smooth and rough walls.

Numerical Investigation on Heat Transfer of Supercritical Water With a Variable Turbulent Prandtl Number Model

2020 ◽  
Vol 6 (3) ◽  
Author(s):  
Xiangfei Kong ◽  
Dongfeng Sun ◽  
Lingtong Gou ◽  
Siqi Wang ◽  
Nan Yang ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Prandtl Number ◽  
Supercritical Fluids ◽  
Supercritical Water ◽  
Viscosity Ratio ◽  
Turbulent Viscosity ◽  
Turbulence Models ◽  
Turbulent Prandtl Number ◽  
Vertical Tubes

Abstract Turbulent Prandtl number (Prt) has a great impact on the performance of turbulence models in predicting heat transfer of supercritical fluids. Unrealistic treatment of Prt may lead to large deviations of the prediction results from experimental data under supercritical conditions. In this study, the effect of Prt on heat transfer of supercritical water was extensively studied by using shear stress transport (SST) k–ω turbulence model, and the results suggested that using the existing Prt models would lead to failures in predicting the heat transfer characteristics of supercritical water under deteriorated heat transfer (dht) conditions. A new variable Prt model was proposed with the Prt varied with pressure, turbulent viscosity ratio, and molecular Prandtl number. The new model was validated by comparing the numerical results with the corresponding experimental data, and it was found that the new variable Prt model exhibited better performance on reproducing the dht of supercritical water in vertical tubes than those of the existing Prt models.

Closed-Form Analytical Solutions for Laminar Natural Convection on Horizontal Plates

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Abhijit Guha ◽  
Subho Samanta
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Natural Convection ◽  
Prandtl Number ◽  
Boundary Layers ◽  
Wall Temperature ◽  
Temperature Profiles ◽  
Integral Analysis ◽  
Laminar Natural Convection

A boundary layer based integral analysis has been performed to investigate laminar natural convection heat transfer characteristics for fluids with arbitrary Prandtl number over a semi-infinite horizontal plate subjected either to a variable wall temperature or variable heat flux. The wall temperature is assumed to vary in the form T¯w(x¯)-T¯∞=ax¯n whereas the heat flux is assumed to vary according to qw(x¯)=bx¯m. Analytical closed-form solutions for local and average Nusselt number valid for arbitrary values of Prandtl number and nonuniform heating conditions are mathematically derived here. The effects of various values of Prandtl number and the index n or m on the heat transfer coefficients are presented. The results of the integral analysis compare well with that of previously published similarity theory, numerical computations and experiments. A study is presented on how the choice for velocity and temperature profiles affects the results of the integral theory. The theory has been generalized for arbitrary orders of the polynomials representing the velocity and temperature profiles. The subtle role of Prandtl number in determining the relative thicknesses of the velocity and temperature boundary layers for natural convection is elucidated and contrasted with that in forced convection. It is found that, in natural convection, the two boundary layers are of comparable thickness if Pr ≤ 1 or Pr ≈ 1. It is only when the Prandtl number is large (Pr > 1) that the velocity boundary layer is thicker than the thermal boundary layer.

On the sensitivity of heat transfer in the stagnation-point boundary layer to free-stream vorticity

1963 ◽  
Vol 16 (4) ◽  
pp. 497-520 ◽  
Author(s):  
S. P. Sutera ◽  
P. F. Maeder ◽  
J. Kestin
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Stagnation Point ◽  
Thermal Boundary Layer ◽  
Free Stream ◽  
Stokes Equations ◽  
Point Boundary ◽  
Oncoming Flow ◽  
Flat Plates

Experiments have given evidence of strong sensitivity of the stagnation-point heat transfer on cylinders to small changes in the intensity of free-stream turbulence. A similar effect on local heat-transfer rates to flat plates has been measured, but only when a favourable pressure gradient is present. In this work it is theorized that vorticity amplification by stretching is a possible, and perhaps the dominant, underlying mechanism responsible for this sensitivity. A mathematical model is presented for a steady, basically plane stagnation flow into which is steadily transported disturbed unidirectional vorticity having the only orientation susceptible to stretching. The resulting velocity and temperature fields in the stagnation-point boundary layer are analysed assuming the fluid to be incompressible and to have constant properties. By means of iterative procedures and electronic analogue computation an approximate solution to the full Navier-Stokes equations is achieved which indicates that amplification by stretching of vorticity of sufficiently large scale can occur. Such vorticity, present in the oncoming flow with a small intensity, can appear near the boundary layer with an amplified intensity and induce substantial three-dimensional effects therein. It is found that the thermal boundary layer is much more sensitive to the induced effects than the velocity boundary layer. Computations indicate that a certain amount of distributed vorticity in the oncoming flow causes the shear stress at the wall to increase by 5%, while the heat transfer there is augmented by 26% in a fluid with a Prandtl number of 0.74. Preliminary computations reveal that the sensitivity of the thermal boundary layer increases with Prandtl number.

An integral approach to the calculation of skin friction and heat transfer in the laminar flow of a high-Prandtl-number power-law non-Newtonian fluid past a wedge

1991 ◽  
Vol 69 (2) ◽  
pp. 83-89 ◽  
Author(s):  
G. Ramamurty ◽  
K. Narasimha Rao ◽  
K. N. Seetharamu
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Skin Friction ◽  
Layer Thickness ◽  
Power Law ◽  
Boundary Layer Thickness ◽  
Thermal Boundary Layer ◽  
Integral Approach ◽  
High Prandtl Number

An integral approach to the theoretical analysis for the skin friction of a non-Newtonian, power-law-fluid flow over a wedge is presented, when the inertia terms in the boundary-layer equations are small but need consideration. The method adopted for the solution of the equations considers an integrated average value of the inertia terms in the momentum equation. The values of the velocities and the boundary-layer thickness obtained from the hydrodynamic analysis are used for the calculation of the thermal-boundary-layer thickness. A linear velocity profile is assumed for the flow field within the thermal boundary layer as the fluids chosen for the analysis are high-Prandtl-number fluids. The results of the skin friction and the rates of the heat transfer are tabulated for a number of values of the flow behaviour index, n, varying from 0.05 to 5.0. This analysis is applicable to viscous polymer solutions having high Prandtl numbers.

Effects of Radiation and Variable Thermal Conductivity on the MHD Flow of a Viscoelastic Fluid and Heat Transfer Over a Stretching Porous Sheet

2008 ◽  
Author(s):  
P. Anuradha ◽  
S. Krishnambal
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Viscoelastic Fluid ◽  
Variable Thermal Conductivity ◽  
Integration Scheme ◽  
Viscoelastic Parameter ◽  
Porous Sheet ◽  
Effects Of Radiation

A numerical study on the effects of radiation and variable thermal conductivity on the flow and heat transfer in the boundary layer of a viscoelastic fluid (Walters’ liquid B’ model) over a stretching porous sheet in the presence of a magnetic field is studied. The momentum differential equation is solved exactly. Two cases of sheet surface conditions are considered — (i) PST case involving prescribed surface temperature and (ii) PHF case involving prescribed heat flux at the surface. The energy equation is solved with the application of the shooting technique using the fourth order Runge-Kutta integration scheme. Numerical results are obtained for various values of non-dimensional parameters — which include among others, the Prandtl number (P), the Eckert number (E) and the Radiation number (N). The significant conclusions are: (1) the momentum boundary layer can be minimized by considering the sheet to be influenced by a continuous suction of the fluid through the porous boundary and by choosing large values for the viscoelastic parameter and the magnetic parameter (2) an ideal combination for faster cooling of the thermal boundary layer would be to consider the suction velocity of the fluid along with a large value for the Prandtl number combined with small values for Radiation and Eckert numbers.

scholarly journals Heat transfer for two types of viscoelastic fluid over an exponentially stretching sheet with variable thermal conductivity and radiation in porous medium

2014 ◽  
Vol 18 (4) ◽  
pp. 1079-1093 ◽  
Author(s):  
V. Singh ◽  
Shweta Agarwal
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Porous Medium ◽  
Prandtl Number ◽  
Wall Temperature ◽  
Stretching Sheet ◽  
Variable Thermal Conductivity ◽  
Flow And Heat Transfer ◽  
Exponentially Stretching

An Analysis has been carried out to study the boundary layer flow and heat transfer characteristics of second order fluid and second grade fluid with variable thermal conductivity and radiation over an exponentially stretching sheet in porous medium. The basic boundary layer equations governing the flow and heat transfer in prescribed surface temperature (PST) and prescribed heat flux (PHF) cases are in the form of partial differential equations. These equations are converted to non-linear ordinary differential equations using similarity transformations. Numerical solutions of the resulting boundary value problem are solved by using the fourth order Runge-Kutta method with shooting technique for various values of the physical parameters. The effect of variable thermal conductivity, porosity, Prandtl number, radiation parameter and viscoelastic parameters on velocity and temperature profiles (in PST and PHF cases) are analyzed and discussed through graphs. Numerical values of wall temperature gradient in PST case and wall temperature in PHF case are obtained and tabulated for various values of the governing parameters. In this study Prandtl number also treated as variable inside the boundary layer because it depends on thermal conductivity. The results are also verified by using finite difference method.

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