### A Pluto.jl notebook ### # v0.19.32 using Markdown using InteractiveUtils # This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error). macro bind(def, element) quote local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end local el = $(esc(element)) global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el) el end end # ╔═╡ 9f3b47f6-b3b3-4591-a766-7a7061582fbc begin import DelimitedFiles: readdlm using Interpolations import PlutoUI using Roots using CairoMakie end # ╔═╡ d44469e0-8fd1-11ee-36ef-ef325e0f02bc md""" # Semelhança por coeficiente de arrasto """ # ╔═╡ e5071393-1e67-477b-8c31-c01d8a2c0dca md""" ## Especificando o problema Fazer um ensaio em túnel de vento mantendo semelhança dinâmica ($Re_m = Re_p$) é, quase sempre, muito difícil. Em se tratando de problemas envolvendo a atmosfera isso é quase impossível. Em geral, a influência do número de Reynolds diminui a medida que aumenta. Mas se o Re do edifício é grande, o Re de uma janela é consideravelmente menor. Neste tipo de sistuação onde uma gama de escalas dimensionais existem no modelo, pode ser importante distorcer a escala de simulação dos menores elementos. Este notebook tenta calcular esta distorção para o caso onde os elementos são cilindros. """ # ╔═╡ b428ca3e-fdf3-4c15-a503-1c4667757d04 md""" ## Equacionamento do problema Seja um protótipo com um elemento cilíndrico de diâmetro $D_p$ e velocidade de referência $U_p$. Neste caso, a força de arrasto de um cilindro com comprimento $L_p$ é dado por: $C_{D,p} = C_D(Re_p) = \frac{F_p}{D_p L_p \Delta P_p}$ onde $\Delta P_p = \frac{1}{2}\rho_p U_p^2$ idealmente, para o modelo em escala reduzida $\lambda_L = L_m / L_p$ teríamos uma relação semelhante: $C_{D,m} = C_D(Re_m) = \frac{F_m}{D_m L_m \Delta P_m}$ Mas infelizmente em geral, $C_D(Re_m) \ne C_D(Re_p)$ O que vamos fazer é distorcer a escala dimensional do diâmetro, de modo que nesta escala distoricida, temos $D'_m = \gamma D_m\qquad Re'_m = \gamma Re_m$ Com isso, temos $C_D(Re'_m) = \frac{F_m}{D'_m L_m \Delta P_m} = \frac{F_m}{\gamma D_m L_m \Delta P_m} = C_D(\gamma Re_m)$ Para calcular $\gamma$, fazemos $\frac{F_m}{D_m L_m \Delta P_m} = \gamma C_D(\gamma\cdot Re_m) = C_D(Re_p)$ Ou seja, temos que resolver a equação $\gamma C_D(\gamma\cdot Re_m) = C_D(Re_p)$ """ # ╔═╡ eb00dd66-5299-4775-b901-e9a77d3bcfc1 md""" ## Dados do protótipo: | Parâmetro | Valor | Unidade | | --------- | ----- | ------- | | Velocidade | $(@bind Up PlutoUI.NumberField(0.1:0.1:100, default=10.0)) | m/s | | Diâmetro | $(@bind Dp PlutoUI.NumberField(0.01:0.01:100, default=1.0)) | m | ## Dados do modelo: | Parâmetro | Valor | Unidade | | --------- | ----- | ------- | | Escala dimensional | 1:$(@bind fL PlutoUI.NumberField(0.1:0.1:1000, default=100.0)) | | | Velocidade | $(@bind Um PlutoUI.NumberField(0.1:0.1:100, default=10.0)) | m/s | """ # ╔═╡ 1bbbc17e-7e82-4a05-8081-ce47769b6c31 md""" ## Parâmetros calculados """ # ╔═╡ 4af541f9-9e3f-4245-8a97-e87ec75a5545 function solve_distortion(cdfun, Rep, Rem) Cdp = cdfun(Rep) find_zero(γ->γ*cdfun(Rem*γ) - Cdp, 0.5) end # ╔═╡ 9d5b82f1-d666-492f-9662-e64bc7f2ab74 24/8 # ╔═╡ 92740a26-d1e5-48ef-b42e-5ee25268f9d3 cdfun = # ╔═╡ 05b13795-4747-406e-9b25-2783453f857a const tabcd = [ #0.0001 24/0.0001 #0.0005 24/0.0005 #0.001 24/0.001 #0.005 24/0.005 #0.01 24/0.01 #0.05 24/0.05 #0.1 24/0.1 #1.0 24/1.0 2.0 24/2.0 3.0 24/3 4 24/4 5 24/5 6 24/6 7.68950786478 2.98739495798 8.86106599596 2.84243697479 10.6299578596 2.60924369748 13.2824202762 2.36974789916 15.620206718 2.21218487395 22.9708480471 1.92857142857 29.9274350926 1.83403361345 45.8828838765 1.67647058824 67.5470304641 1.55042016807 112.382670934 1.41806722689 158.872182251 1.32983193277 259.022462585 1.21638655462 467.673105425 1.10924369748 794.306107941 1.00840336134 1464.07693887 0.939075630252 3051.01920077 0.920168067227 4589.07499662 0.951680672269 7645.96741325 1.02731092437 11502.3639608 1.08403361345 16953.6728536 1.13445378151 23506.1244184 1.19117647059 39948.982155 1.18487394958 86728.3953288 1.18487394958 147396.10221 1.17857142857 212782.459993 1.17226890756 226085.099978 1.09033613445 235308.181149 0.970588235294 276783.149324 0.844537815126 318925.942787 0.686974789916 382706.381872 0.497899159664 488454.783382 0.378151260504 611070.306398 0.31512605042 780521.48278 0.308823529412 1017638.98276 0.321428571429 1274349.7177 0.403361344538 1662058.85353 0.466386554622 2124498.77001 0.567226890756 2553740.85378 0.63025210084 3069577.14326 0.686974789916 3615569.87408 0.762605042017 5115610.99932 0.800420168067 9057646.44087 0.819327731092 ] # ╔═╡ ef17cd88-01b4-4139-92f7-4bbd652f4f95 cdfun = linear_interpolation(tabcd[:,1], tabcd[:,2]) # ╔═╡ 3f3a7496-ab76-4662-bf9c-de122350b1d5 begin const ν = 1.5e-5 lamL = 1/fL Dm = Dp * lamL Rep = Up * Dp / ν Rem = Um * Dm / ν γ = solve_distortion(cdfun, Rep, Rem) Dm1 = Dm * γ end # ╔═╡ f3638eb6-aae8-4bf4-9c4b-32059e857eaf let fig=Figure() cdp = cdfun(Rep) cdm = cdfun(Rem) Rem1 = Rem*γ cdm1 = cdfun(Rem1) ax = Axis(fig[1,1], xlabel=L"Re", ylabel=L"C_D", xscale=log10) ylims!(ax, 0, 4) lines!(ax, tabcd[:,1], tabcd[:,2]) scatter!(ax, [Rep], [cdp], color=:blue, markersize=10, label="D = $(Dp) m") scatter!(ax, [Rem], [cdm], color=:green, markersize=10, label="D = $(round(Dm*1000,digits=2)) mm") scatter!(ax, [Rem1], [cdm1], color=:red, markersize=15, label="D = $(round(Dm1*1000,digits=2)) mm") axislegend(ax) fig end # ╔═╡ b92ae879-847c-4613-8919-9ac42aa90d65 md""" | Parâmetro | Valor | Unidade | | --------- | ----- | ------- | | $Re_p$ | | $(round(Rep, digits=2)) | | | $Re_m$ | | $(round(Rem, digits=2)) | | | $\gamma$ | $(round(γ, digits=3)) | | | $D_m$ | $(round(Dm*1000, digits=2)) | mm | | $D'_m$ | $(round(Dm1*1000, digits=2)) | mm | """ # ╔═╡ 89cace70-ee06-47f3-9fb0-189b1b6bf31f cdfun(1000000) # ╔═╡ de3bac78-8321-474c-8cd0-edd850ff53fc tabcd # ╔═╡ 00000000-0000-0000-0000-000000000001 PLUTO_PROJECT_TOML_CONTENTS = """ [deps] CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab" Interpolations = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59" PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" Roots = "f2b01f46-fcfa-551c-844a-d8ac1e96c665" [compat] CairoMakie = "~0.11.0" DelimitedFiles = "~1.9.1" Interpolations = "~0.14.7" PlutoUI = "~0.7.54" Roots = "~2.0.22" """ # ╔═╡ 00000000-0000-0000-0000-000000000002 PLUTO_MANIFEST_TOML_CONTENTS = """ # This file is 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git-tree-sha1 = "b4bfde5d5b652e22b9c790ad00af08b6d042b97d" uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b" version = "1.15.0+0" [[deps.Xorg_xtrans_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl"] git-tree-sha1 = "e92a1a012a10506618f10b7047e478403a046c77" uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10" version = "1.5.0+0" [[deps.Zlib_jll]] deps = ["Libdl"] uuid = "83775a58-1f1d-513f-b197-d71354ab007a" version = "1.2.13+0" [[deps.isoband_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "51b5eeb3f98367157a7a12a1fb0aa5328946c03c" uuid = "9a68df92-36a6-505f-a73e-abb412b6bfb4" version = "0.2.3+0" [[deps.libaom_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4" uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b" version = "3.4.0+0" [[deps.libass_jll]] deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47" uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0" version = "0.15.1+0" [[deps.libblastrampoline_jll]] deps = ["Artifacts", "Libdl"] uuid = "8e850b90-86db-534c-a0d3-1478176c7d93" version = "5.8.0+0" [[deps.libfdk_aac_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55" uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280" version = "2.0.2+0" [[deps.libpng_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"] git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c" uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f" version = "1.6.38+0" [[deps.libsixel_jll]] deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "libpng_jll"] git-tree-sha1 = "d4f63314c8aa1e48cd22aa0c17ed76cd1ae48c3c" uuid = "075b6546-f08a-558a-be8f-8157d0f608a5" version = "1.10.3+0" [[deps.libvorbis_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"] git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c" uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a" version = "1.3.7+1" [[deps.nghttp2_jll]] deps = ["Artifacts", "Libdl"] uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d" version = "1.52.0+1" [[deps.p7zip_jll]] deps = ["Artifacts", "Libdl"] uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0" version = "17.4.0+0" [[deps.x264_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2" uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a" version = "2021.5.5+0" [[deps.x265_jll]] deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"] git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9" uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76" version = "3.5.0+0" """ # ╔═╡ Cell order: # ╟─d44469e0-8fd1-11ee-36ef-ef325e0f02bc # ╟─e5071393-1e67-477b-8c31-c01d8a2c0dca # ╟─b428ca3e-fdf3-4c15-a503-1c4667757d04 # ╟─eb00dd66-5299-4775-b901-e9a77d3bcfc1 # ╟─1bbbc17e-7e82-4a05-8081-ce47769b6c31 # ╟─f3638eb6-aae8-4bf4-9c4b-32059e857eaf # ╟─b92ae879-847c-4613-8919-9ac42aa90d65 # ╠═4af541f9-9e3f-4245-8a97-e87ec75a5545 # ╠═3f3a7496-ab76-4662-bf9c-de122350b1d5 # ╠═9f3b47f6-b3b3-4591-a766-7a7061582fbc # ╠═ef17cd88-01b4-4139-92f7-4bbd652f4f95 # ╠═89cace70-ee06-47f3-9fb0-189b1b6bf31f # ╠═9d5b82f1-d666-492f-9662-e64bc7f2ab74 # ╠═de3bac78-8321-474c-8cd0-edd850ff53fc # ╠═92740a26-d1e5-48ef-b42e-5ee25268f9d3 # ╠═05b13795-4747-406e-9b25-2783453f857a # ╟─00000000-0000-0000-0000-000000000001 # ╟─00000000-0000-0000-0000-000000000002