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Modelisation of convective heat transfer in the CUBI experiment R.Wagemakers,P.Bécret,P.Vyvey,W.Bosschaerts,F.D.Lapierre,M. Acheroy Dept. MECA, Dept CISS, Royal Military Academy, Avenue de la Renaissance 30, 1000 Brussels Abstract - The reduction of the IR-signature of modern warships requires the development of signature simulation software. These software codes take focus mainly on the modelling of the emissivity of the surfaces, but don’t consider into detail the convective heat transfer. In this paper the commercial CFD code FLUENT is used to model convection based on experimental results of the CUBI. A short overview for the case set up is given, and the results are compared with the software code OSMOSIS. A first assessment is made to difference of the results. of convective heat transfer. The aim of this paper is twofold; To accurately model the effect of convective heat transfer and secondly to show how the detailed consideration of convective heat transfer in a thermal model can impact the validation of the software code OSMOSIS. Introduction One of the aspects in the integrating of stealth technology into modern warship design is the reduction of its IR signature. In order to conceive such reductions, it is required to have by means of a software a way to simulate and predict the signature of these ships accurately, to calculate the respective surface temperatures of the modelled ship hull. A software OSMOSIS, developed at the Royal Military Academy calculates these surface temperatures and the outputs them to further compute the actual IR program. The development of such a software code for the modelling of surface temperatures on an object requires the validation of these predicted surface temperatures. A benchmark object, CUBI  was designed as an L-shaped structure (fig1), consisting of a 4mm thin steel shell body around an insulating layer of polyurethane. Different research laboratories have installed a CUBI and have made continuous measurements of the surface temperatures by use of thermocouples, their location shown in fig(2). To create a common sharing pool for these measurements and the thermal models, the CUBI forum was created, of which the Royal Military Academy is an active member. Fig2: Location of thermocouples General overview To predict the actual convective heat transfer at the CUBI object, the flow field is calculated by means of the commercial software package FLUENT. A numerical setup is implemented which models the CUBI and its near surroundings. The CUBI itself is divided in twelve surface entities, corresponding to the respective locations of the thermocouples, as used in the experimental setup (fig2). The steel casing of the CUBI is set up as a thin shell model, allowing for calculation of the conductive heat transfer in each surface itself and between adjacent surfaces. Any conduction through the polyurethane insulation layer into the inner air mass of the hollow CUBI object is considered negligible, the boundary between them is considered adiabatic. The flow itself was calculated transient, updating the input data and calculated values at each time step, with time step taken as 60 seconds. The chosen time interval proved sufficiently small to follow the experimental curve adequately but at the same time is a compromise in limiting the computational cost to calculate the time scale of the provided data, being 24 hours. Partial simulations done with a smaller time step proved to add no significant added improvement to the results. Since the experimental meteorological data provided an update of the measurements each five minute, the used time step of one minute assumes a linear interpolation between two subsequent experimental data set points to update the boundary conditions. Each time step, an update is provided for the incoming solar and diffuse irradiation for each respective surface of the CUBI. Fig1: CUBI setup, Israel These measurements have since then been used to validate existing thermal codes such as F-TOM and RadTherm/IR However, none of these models consider in detail the modelling The meteorological data consisted of the ambient temperature, wind speed and direction, relative humidity as well as ambient air pressure. A home written code reads the data from both the meteorological and incoming solar radiation input files, makes the interpolations and writes them into an adapted scheme file to be used as a script for the simulation setup (fig3). The incoming heat flux and emissive radiation are governed by a user defined function (UDF), and added to the energy equation of each cell face. Meteorological data Experimental data Flow equations The numerical solution is based upon a finite volume approach, where for each cell of the computational domain the governing equations are solved by the Navier-Stokes equations based on the conservation of mass, momentum and energy. For the sake of brevity, the full equations will not be given here, and can be found explained in a more elaborated description in  A second order upwind scheme is used to derive the respective variables per each cell. To model the turbulence of the flow, the standard k-ε model as provided by FLUENT was used, which adds two equations to predict the turbulence kinetic energy k and its dissipation rate ε. The use of the more advanced full LES turbulence model was omitted as its computational cost is too high to calculate each separate point. At each new time step, the script file reinitialises the flow by using the flow field values of the previous time step. It stores the temperature values of the surfaces, and performs an FMG-initialisation, a multilevel grid calculation provided by FLUENT. The script then calculates the next time step iteration. Conversion to SCHEME script Radiative model Emmisivity convection UDF Heat transfer equations CUBI mesh Fluent calculations Fig3:general overview calculation scheme Mesh description The CUBI object and its surroundings are modelled in an otype domain (Fig4), with a structured hexagonal mesh. The CUBI is scaled at real size, the surrounding o-domain extends up to 4 meter around it. The total height of the domain dimensioned at 3 meter. The mesh is initially meshed at a grid size of 10 cm, and then subsequently refined locally around the solid surfaces of the setup to have a sufficiently high spatial resolution to calculate the flow field at said surfaces. This approach allows for the computation of the convective heat transfer and the boundary layer, whilst at the same time still limiting the computational calculation cost, as the flow calculation is performed anew at each time step. The o-type domain allows the wind direction to be changed as desired without the need of redefining the domain at each new time step. The CUBI object itself is meshed as a collection of twelve surfaces, already mentioned. The thin shell model gives each two-dimensionally surface entity a mathematical thickness of 4mm, corresponding with the real experiment. For each of these surface cell facet n, at time t, the energy conservation equation can be written as: Cd Tn n n n Eabs (Tn , t ) M out (Tn , t ) M cond (Tn , t ) (1) t with ρ, C, d respectively the density, thermal capacity and thickness of the cell. The right hand terms of (1) are the incoming irradiance n Eabs (W/m²) and the outgoing fluxes n n M out (W/m²), M cond (W/m²). The incoming irradiance can be split up further as : n n n n Eabs (Tn , t ) Esol (Tn , t ) Esky (Tn , t ) Emr (Tn , t ) (2) being the sum of respectively the incoming irradiance by the sun, the sky, and reflections. Since in this first stage only the top surface of the CUBI is considered, no irradiation due to reflection of the surrounding desert sand or the CUBI itself is taken into account, and the term n Emr (Tn , t ) is omitted. Both incoming solar and sky irradiance were input directly into the script file, after calculation from the experimental data as described by . The outgoing flux Fig4: o-type mesh, contour plot of wind velocity n M out (Tn , t ) is the sum of the emissivity of the surface facet and the convective heat transfer, giving: n n n M out (Tn , t ) M rad (Tn , t ) M conv (Tn , t ) (3) The radiance n M rad (Tn , t ) is calculated using a constant emissivity factor ε, independent of wavelength λ. The used sky temperature is calculated as described in OSMOSIS, . The convective heat transfer for cell facet n is defined as: n M conv (Tn , t ) hn (Tn , t )(Tn,t Tamb,t ) (4) With κ the Von Karman constant and E an empirical constant, taken as 0.418 and 9.793 respectively. The obtained velocity profile is then further used in the energy calculations. For the temperature profile, FLUENT uses a similar procedure as with the velocity profile, and makes a distinction for the near-wall region in two regions; a sublayer governed solely by conduction(8), and a turbulent layer (9) where the turbulent behaviour takes over the pure conduction. 1/ 2 T * = Pr y* +0.5 Pr C 4k1/ 2U pq p whereas hn (Tn , t ) , the convective heat transfer coefficient is n M conv (Tn , t ) is governed (8) dependant on the local flow parameters. The conductive heat transfer entirely by the thin shell model and takes into account the conduction between the adjacent surface facets and to the inner insulation mass. As mentioned above, the interface between the insulation and inner air mass is considered adiabatic. 1/ 2 T * =Prt 1 ln( Ey* ) P 0.5 q 1C 4 k 1/ 2U p (9) p Pr is the molecular Prandtl number, Prt the turbulent Prandtl number. With P dependent on the local molecular and turbulent Prandtl number or as a modified equation when the surface roughness is taken into account. Prt and yt* are computed at the Convective heat transfer coefficient h The convective heat transfer is calculated by the heat transfer coefficient hn (Tn , t ) , a function of the fluid parameters and intersection of the linear and logarithmic profiles. From the resulting near wall temperature T* the convective heat flux q can then be calculated, and subsequently the resulting heat transfer coefficient the characteristics of the flow field with respect to the cell face. Traditionally it is written characterized by the Nusselt and Prandtl number, Nu and Pr, respectively. A wide range of correlations exists, making distinction between laminar, turbulent, natural and forced convection as well as the geometry of the concerned surface, but are largely limited to the restrictions of the experimental setups they are derived from. In this paper, two different convection models are used. A simple Nu-correlation in the form of a polynomial function as employed by OSMOSIS software model, and the indigenous convection model used by FLUENT itself. The polynomial function as used by OSMOSIS is further described in . Fluent calculates the convection in a more detailed method, resolving the flow field right up to the modeled wall surfaces of the CUBI model. It does so by imposing a near wall velocity and temperature profile and based upon the adimensional wall unit y* hn ,t (Tn ,t Tamb ) q (10) The above used formulas are part of the standard wall functions, as used by FLUENT to calculate near-wall flow behavior, and they are illustrated here solely for the purpose of showing the various dependencies involved in the calculation of the convective heat transfer. However, a more profound description on the exact method and calculation procedure can be found in . The use of this approach means the spatial resolution of the grid has to be carefully examined as these laws are valid only for a specified rang of 30 < y* <300, with an advised y* as close to 30 as possible. Boundary condition inlet From equations (8),(9) it can be shown that h heavily depends on the imposed values of k and ε, and careful consideration has to be given to an accurate initial guess of their values, especially at the incoming inlet boundaries of the domain. The computational domain was deliberately kept relatively small compared to the CUBI object to limit the computational costs, but it does not allow the incoming flow to have developed fully when it reaches the CUBI object. Instead, a separated 2D domain was used to calculate a fully developed flow, for each of the given cases. The wind direction did not needed to be incorporated in the separate domain, all profiles were calculated on the same temperature. The profiles of the turbulent kinetic energy and its dissipation rate were stored for each velocity and used by the script file to impose them y* Where 1/ C 4 k 1/ 2 y p p (5) k1 2 p the turbulent kinetic energy in point p, yp the distance to the wall, and μ the kinematic viscosity. The near wall velocity in a point p is defined as: U * 1 ln( Ey* ) (6) U* 1/ U PC 4 k 1/ 2 p w / (7) directly on as the incoming boundary condition for the main domain. The factor P, as mentioned in equation  is dependent of the roughness height and will be assessed for the influence it has on the final turbulence. The effect of various roughness heights was assessed, the profiles tended to converge asymptotically from a roughness height of 3 cm. An arbitrary height of 3 cm was then chosen for the desert terrain surrounding the CUBI. Increasing the roughness height further would conflict with the mesh as the near-ground actual grid size becomes smaller than the roughness height. 333 331 329 327 T (K) 325 323 321 319 317 0 1200 2400 3600 4800 6000 7200 8400 9600 t (s) Results For the first results, the measured temperature values of the top surface on the CUBI were compared with the temperatures calculated by FLUENT. However, since the scope of the paper is meant to provide a usable output correction factor for the OSMOSIS convective model, the results will mainly focus on the behavior of the h coefficient itself, and where the FLUENT calculations and OSMOSIS polynomial differ. For the input data itself, an input file was created using the experimental data measured from 14.00h, 20/06/2005 until 13.00h, 21/06/2005. When the h coefficient calculated by FLUENT is compared, in function of wind speed, to the value of the OSMOSIS polynomial, FLUENT seems to systematically predict a dramatically higher value at higher wind speeds (fig5). 50 45 40 35 h (W/m²) T exp h-OSMOSIS h-Fluent Fig6: Comparison of experimental data with calculated data When looking at the relative difference between the results from the OSMOSIS polynomial function and h calculated by Fluent in function of the wind direction (Fig5), it is seen there is a rough linear connection. When the wind blows perpendicular on the CUBI surface, Fluent and OSMOSIS are in good agreement. However, when the angles change to ~45° the difference amounts up to 40%, giving credence to the explanation that, under this angle the geometry of the CUBI itself adds significantly to the turbulence of the surrounding flow, raising h. 1.5 1.4 h-Fluent/h-Osmosis 1.3 1.2 30 25 20 15 10 5 0 1 2 h-FLUENT 1.1 1 0.9 315 320 325 330 335 340 345 350 355 360 Wind direction (360°=N) 3 4 v (m/s) 5 h-OSMOSIS 6 7 8 9 Polynoom (h-FLUENT) Fig7: Rel. difference FLUENT/OSMOSIS as function of wind direction Fig5: Comparison h-value FLUENT and OSMOSIS The h-values can be adequately fitted with a third-order polynomial function, given by y = -0.011v³ + 0.1538v² + 5.0199v + 4.5344, with an r²-coefficient of 0.9792 However, when these values are used to calculate the top surface temperature, a good fit is seen with the experimental data, slightly better than the values predicted when using the OSMOSIS polynomial function (Fig4). Conclusions and future considerations Several cases were simulated to assess the influence of each input parameter and the assumptions made. Afterwards, this will serve as criteria to choose which models to use and minimize calculation time, while still retaining the highest possible accuracy. It is noted that some of the assumptions will prove to be critical in calculating h, while others have a less drastic influence. To provide a usable output factor for the OSMOSIS model, the results will mainly focus on the behavior of the h coefficient itself instead of the impact on the calculated results. The main conclusion here is that the polynomial as used by OSMOSIS can not take into account the orientation of the wind impingent on the surface. The actual form of the CUBI object will influence the local flow field and subsequent convection as the corners and nooks of the CUBI divert the wind flow, accelerating or stagnating it locally. The intermediate results have shown so far that it is possible to predict the convection on the top surface of the CUBI object. The main problem encountered was the significant computing time and the set up of a correct set of boundary conditions to the problem. The use of a simple polynomial function will provide an adequately accurate result, but might not always be capable to correctly take in account the effects of the geometry of the modeled object itself. So while it is possible to calculate the surface temperatures with a CFD-code, it has proven to be a very tedious and time-consuming process, but it can be used to provide useful correction factors to the OSMOSIS model should the polynomial approach not prove accurate enough. Further work will aim to determine these correction factors, making the distinction between the influence of the higher wind speed and the influence of the wind flow orientation, with respect to the geometry of the involved surfaces. To this end, a miniaturized CUBI object, a flat plat, will be equipped and installed at the RMA to further validate the results, in a controlled environment and with the possibility to be mounted under different angles. References  CUBI Forum Web Site: http://www.iard.org.il/cubi.  F.D. Lapierre, R. Dumont, A. Borghgraef, J-P Marcel, and M. Acheroy, “OSMOSIS: An Open-Source Software for Modelling of Ship Infrared Signature”, in Proceedings of the 3rd International IR Target, Background Modelling & Simulation (ITBMS) Workshop, 25-29 June 2007, Toulouse, France.  A. Malaplate, P. Grossman, and F. Schwenger, “CUBI - A Test Body for Thermal Object Model Validation”, in proceedings of the SPIE Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XVIII, volume 6543, April 2007, Orlando, FL, USA.  A. Reinov, Y. Bushlin, A. Lessin, D. Clement, and M. Kremer, “CUBI: Comparison of Thermal Radiation Modeling with a Natural Desert Experiment”, in Proceedings of the 2nd International IR Target, Background Modelling & Simulation (ITBMS) Workshop, 26-29 June 2006, Ettlingen, Germany.  Fluent Web Site: http://www.fluent.com.  Fluent User Guide: https://www.fluentusers.com  F. D. Lapierre, “OSMOSIS (open-source software for the modeling of ship infrared signatures), http://www.osmosisproject.org.
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