Gradient-Based Estimation of Air Flow and Geometry Configurations in a Building Using Fluid Dynamic Adjoint Equations

Transcription

1 Purdue University Purdue e-pubs International High Performance Buildings Conference School of Mechanical Engineering 2016 Gradient-Based Estimation of Air Flow and Geometry Configurations in a Building Using Fluid Dynamic Adjoint Equations Runxin He Department of Electrical and Systems Engineering, Washington University in Saint Louis, United States of America, runxinhe@ .wustl.edu Humberto Gonzalez Department of Electrical and Systems Engineering, Washington University in Saint Louis, United States of America, hgonzale@wustl.edu Follow this and additional works at: He, Runxin and Gonzalez, Humberto, "Gradient-Based Estimation of Air Flow and Geometry Configurations in a Building Using Fluid Dynamic Adjoint Equations" (2016). International High Performance Buildings Conference. Paper This document has been made available through Purdue e-pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for additional information. Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at Herrick/Events/orderlit.html

2

3 R R R > [, ] R (, ) (() (, )) () (, ) = (, ), [, ] R R = (, ) (, ) = (),. () (() ) () () () () = (),, () =,

4 R = R () () () () = = (),, () (),. () = ( ( ) ) < () = > () = {, } = = I I () = I () = {, } R {, } R (, ) = ( ) ( ) I (), (, ) = ( ) ( ) I (), = R {, } [, ]. [, ] = R, R (, ) = = ( (, ;, ),), {,..., }, = (,),, > (, ;, ),() [, ],, =,()

5 { } = (,,,,, { } = ) = (, ), (() ) [,], [,], ( ),,, (, ),, = () () L () = (,, ), [,] =, = =, ( () (, ),()) (, ) (() (, )) () (, ) =, () = (, ), (, ) (, ) () () () () () () () () =,, () =, (, ) = (, ) = [, ] (, ) = (, ) (, ) (, ) (, ) (,, ) (,, ) D, =,, D, =,, D, =,, D = = ( D, D, ).

6 D D (, ) = = D R, R, D,, {,..., }, > = = = =, N (, ) (,, )., (, ) = { } = = { } =.. { } =. = = = = = =. =... /. / =. =. =. =. =. =.

7 d 3 h s 2 h 4 d 4 s 3 h 3 d 2 d 1 s 1 h (B) (G) 0.2 (B) (G) =,, R, P() P( ) P() = ( ), =, (, ;,, ) [, ] {, }, (, ;,, ),, E [ (, ;,, ) ] =, (, ; E [, ], ) (, ) E [, (, ;,, )] = {,}, (, ; E [, ], ) P(),, [, ]. {, } {(,,, ), (,,, ), (,,, ), (,,, ), (,,, ), (,,, )} (, ) = = ˆ ˆ = ˆ ˆ

8 d 3 s 2 h 4 d 4 s 3 h 3 d 2 h 2 s 1 d 1 h d 3 s 2 h 4 d 4 s 3 h 3 d 2 h 2 s 1 d 1 h d 3 s 2 h 4 d 4 s 3 h 3 d 2 h 2 s 1 d 1 h Maximum memory usage (GB) Banks and Bihari s method Gradient-based method 0.0 (B) (G) 0.00 (B) (G) 0.75 (B) (G) Number of doors nd

9 {, } =. (,, ) (,, ), [,] =, [,] =, [,], ( ) [,], [,], (, ) =., =, =, [,], ( ) ( ),, =,, =, =, ( ), (, ), (, ) [,] [,] (, ), (, ), [,], [,] =,, [,],, ( ),, =,, [,],, (,, ),,,

10 (, ) ( ) ( ) =, =, =, (, ) = [, ] (, ) = () () = (, ) (, ) =, [,],, ( ) ( ) [,],,, [,],, (, ), { } = (, ) (, ) =,, [,],,

11 buildingsdatabook.eren.doe.gov/docs/databooks/_bedb.pdf -better-policy-compilation-green-building-policy-adoptions-united-states-