Ahmad Fawaz

Yuchao Hua

Steven Le Corre

Yilin Fan

Lingai Luo

Convergent-divergent design of fins for

Convergent-divergent design of fins for simultaneous thermohydraulic improvement assisted by dual-flow topology optimization Ahmad FAWAZ (1) , Yuchao HUA (1*) , Steven LE CORRE (1) , Yilin FAN (1) & Lingai LUO (1*) (*) Lingai LUO (Lingai.Luo@univ-nantes.fr), Yuchao HUA (yuchao.hua@univ-nantes.fr)

(1) Nantes Université, CNRS, Laboratoire de thermique et énergie de Nantes, LTeN, UMR6607, F-44000 Nantes, France o The critical importance of heat exchangers (HXs) on energy systems has been widely recognized.

o Enhancing their thermal performance will inherently lead to a commensurate elevation in pressure losses.

o Topology optimization (TO) is a mathematical method used to optimize the material distribution of a given design domain for the purpose of boosting the performance under several constraints.

o Among the researchers who conducted the TO, a significant majority of 92% applied the TO technique on single-flow HXs, while a minor proportion of 8% implemented it on dual-flow HXs.

Objective:

Applying the density-based TO on a simplified 2D counter flow plate heat exchanger to increase its thermo-hydraulic performance.

Boundary Conditions in TO:

Method

  's principal: The density-based TO is conducted to optimize solid/fluid distribution of the PHE for the purpose of improving its thermo-hydraulic performance. The optimization objective is set the maximizing of the exchanged heat transfer while the pressure drop is diminished by testing different designs acquired under various Reynolds number. « VOS LOGOS » 1&2. The design domain is parametrized using densities (or porosities) that represents the ratio between solid and fluid which are initially set to 0.5. Then they are correlated with the thermo-hydraulic properties of solid & fluids. 3. Dimensionless equations for conjugate heat transfer physics 4 &5. The discrete adjoint analysis is utilized to compute the objective function sensitivities. Then, a gradientbased optimizer (GCMMA) is used to iteratively update the densities distribution. 6. To avoid the checkerboard effect in the acquired topology, the densities are filtered using the Helmholtz filter. The densities are then projected by the hyperbolic tangent projection method for the aim of removing the intermediate densities created by the filter. :Fawaz et al. "Topology optimization of heat exchangers: A review." Energy (2022). * Re: Reynolds number, Pr: Prandtl number, C k :Thermal conductivity ratio This work is financially supported by Région Pays de la Loire within the NExT2Talents program TOP-OPTIM project (998UMR6607 EOTP NEXINTERTALENTHUA).

  Design variables, R: Filter radius,𝜷:Projection slope,𝜸 𝜷 : Projection point o A density-based TO is applied on a bi-flow HX to optimize its thermo-hydraulic performance. o The heat transfer rate of the optimized HX is magnified compared to the conventional one with an intensification rate up to 22 %. o The PEC (Performance evaluation criteria) is used as a criteria to compare the thermo-hydraulic performance. The results show the superiority of the optimized HX with an enhancement up to 16%. On-going work: o Experimental validation of the numerical results by testing different HXs and prove the advantage of the proposed design over the conventional one. o Perform size optimization on the Convergent-divergent distribution to test the effect essential parameters on the thermo-hydraulic performance of the HX. o Integration of the machine learning techniques with the TO algorithm to increase its efficiency. et al., "Application of rough surfaces to heat exchanger design, IJHMT, 1972.


V Wilquet

R Drummond

A Mahieux

S Robert

A C Vandaele

J.-L Bertaux

Climatology of the Venus upper haze as measured by SOIR onboard Venus Express

.

Here we investigate the possibility to use the SOIR channel alone, to obtain information on the aerosols present in the mesosphere of Venus. This offers a larger data set, although less informative in terms of microphysical properties. The temporal and geographical variations of the vertical profiles of the aerosol extinction were investigated for a particular spectral window around 3.0 µm; this was registered in many solar occultations (~170 SO) over a period of almost 4 years, from September 2006 till June 2010.

Introduction

Aerosols have been studied extensively because their optical properties impact the radiative balance through absorption and scattering of solar radiation and because of their crucial role in heterogeneous chemistry. Important information on aerosol extinction can be obtained from satellite remote measurements. However the retrieval of extinction coefficients is known to be difficult due to the lack of spectral signatures of aerosols. We recently demonstrated the potential of the SPICAV/SOIR suite of instruments onboard the Venus Express spacecraft to characterize the aerosols in the mesosphere of Venus [START_REF] Wilquet | Preliminary characterization of the upper haze by SPICAV/SOIR solar occultation in UV to mid-IR onboard Venus Express[END_REF].

SOIR is an echelle grating spectrometer onboard the Venus Express (VEX) spacecraft [START_REF] Nevejans | Compact high-resolution space-borne echelle grating spectrometer with AOTF based on order sorting for the infrared domain from 2.2 to 4.3 micrometer[END_REF]. It is designed to measure the atmospheric transmission in the IR (2.2-4.3 µm) using the SO method. The continuum of absorption is primarily shaped by the extinction caused by the aerosol particles known to be present in the upper haze (between ~70 and 90 km) of Venus' atmosphere.

Theory

The continuum is obtained by fitting the baseline of a spectrum, using the ASIMAT retrieval code [START_REF] Mahieux | Venus atmospheric densities and temperature profiles retrieved from SOIR solar occultations on board Venus Express[END_REF], the baseline being the observed transmittance (T) from which absorption signatures have been removed. The aerosol optical depth (τ) and the local extinction coefficient (β) were retrieved (see equations 1 and 2) from the series of transmittances averaged in each selected spectral window. The onion-peeling method [START_REF] Vandaele | Composition of the Venus mesosphere measured by Solar Occultation at Infrared on board Venus Express[END_REF] is used to determine the extinction (β i ) in each atmospheric layer supposed to be homogenous.

,

N i i e x t N i ext N dz z dz τ β λ β - = - ⋅ = ∑ (2)

Results

The general trend of the vertical profiles of aerosol extinctions is a decrease of the extinction with increasing altitude, except when aerosol layers are observed. Within such layers, the dependence of β on wavelength was shown to be high [START_REF] Wilquet | Preliminary characterization of the upper haze by SPICAV/SOIR solar occultation in UV to mid-IR onboard Venus Express[END_REF]. In addition, in some SO for which the extinction profile is smooth for each spectral window, a wavelength dependence of β was observed that could also be used to derive information on the size of the aerosol particles (Fig. 1).

We also took advantage of the fairly good geotemporal coverage to analyze the latitudinal and temporal variations of the extinction vertical profiles obtained within one spectral window. The extinction clearly shows a latitudinal dependence with the local extinction at a particular altitude decreasing towards the poles (Fig. 2). In order to eliminate latitudinal variations, the timedependence of the extinction profiles was analyzed for two groups of SO occurring at similar latitudes, i.e. one group of SO at high northern latitudes and one group of SO around the equator (Fig. 3). The vertical profiles were averaged for each period of time. Despite the fact that seasons are almost absent on Venus, the extinction due to aerosol particles in the upper haze is clearly not constant over time and this variation over time is not the same at all latitudes.

EPSC Abstracts

Summary and Conclusions

We can conclude that the SOIR channel is well suited to study the vertical distribution of the aerosols in the atmosphere of Venus. The present data set shows temporal and latitudinal variability of the aerosol loading. The profiles also demonstrate a wavelength dependence of the extinction which is being exploited for the microphysical characterization of the particles.

Figure 1 .

 1 Figure 1. The wavelength dependence of β. The vertical profiles for 2 SO are plotted. β was derived from T obtained at 3.4 (blue), at 3.0 (pink) and at 2.4 µm (green). The horizontal bars are the error on β.

Figure 2 .

 2 Figure 2. Variation of β with the latitude. An interpolation of β along the altitude axis is plotted on the left panel and on the right panel, a polynomial fit of 2nd order through each altitude. The data set covers a period of ~500 days and comprises 83 SO.

Figure 3 .

 3 Figure 3. Temporal variation of β. The left panel covers a period of ~1050 days (34 SO at latitudes between -25° and +25°). β is averaged over 5 periods of 210 days. The right panel covers 4 periods of 100 days (with a gap w/o data) for 84 SO at latitudes between +70° and +90°.

Acknowledgements

The research program was supported by the Belgian Federal Science Policy Office and the European Space Agency (ESA-PRODEX program contracts C 90268, 90113, and 17645).