When calc formulas producing empty strings are evaluated in the default
mode, an empty cell is produced. When evaluated in duration mode (U, T,
or t) a zero duration is produced. I feel the behavior should be
consistent with the number formats, producing a empty value instead of a zero.

Test case:

| case         |   result |
|--------------+----------|
| default mode |          |
| default + E  |          |
| U + E        |    00:00 |
| T + E        | 00:00:00 |
| t + E        |     0.00 |
#+TBLFM: @2$2=string("")::@3$2=string("");E::@4$2=string("");EU::@5$2=string("");ET::@6$2=string("");Et


Analysis: the problem (if it is a problem) is here:
https://code.orgmode.org/bzg/org-mode/src/master/lisp/org-table.el#L2616
The value produced for durations always comes from a call to
string-to-number, which returns 0 for empty strings.
org-table-time-seconds-to-string turns that into a zero duration
string in the requested format. An explicit test for an empty value here
fixes the issue.



Emacs  : GNU Emacs 27.1.50 (build 1, x86_64-pc-linux-gnu, GTK+ Version 2.24.32, cairo version 1.16.0)
 of 2020-09-01
Package: Org mode version 9.4.6 (9.4.6-12-gdcc3a8-elpa @ /home/jet/.config/emacs/elpa/org-20210816/)

current state:
==============
(setq
 org-duration-format 'h:mm
 org-src-mode-hook '(org-src-babel-configure-edit-buffer org-src-mode-configure-edit-buffer)
 org-latex-listings t
 org-link-shell-confirm-function 'yes-or-no-p
 org-metadown-hook '(org-babel-pop-to-session-maybe)
 org-clock-out-hook '(org-clock-remove-empty-clock-drawer)
 org-html-format-inlinetask-function 'org-html-format-inlinetask-default-function
 org-ascii-format-inlinetask-function 'org-ascii-format-inlinetask-default
 org-export-creator-string "Emacs 27.1.50 (Org mode 9.4.5)"
 org-mode-hook '((closure
                  (org--rds reftex-docstruct-symbol org-with-time org-defdecode org-def
                   org-read-date-inactive org-ans2 org-ans1 org-columns-current-fmt-compiled
                   org-end-time-was-given org-time-was-given org-blocked-by-checkboxes org-state
                   org-agenda-headline-snapshot-before-repeat org-struct-menu org-last-state
                   org-id-track-globally texmathp-why remember-data-file iswitchb-temp-buflist
                   align-mode-rules-list org-id-overriding-file-name
                   org-indent-indentation-per-level ffap-url-regexp org-inlinetask-min-level t)
                  nil (add-hook 'change-major-mode-hook 'org-show-all 'append 'local))
                 (closure (*this* org-babel-confirm-evaluate-answer-no t) nil
                  (add-hook 'change-major-mode-hook 'org-babel-show-result-all 'append 'local))
                 (closure (org-table-tab-recognizes-table\.el t) nil
                  (setq imenu-create-index-function 'org-imenu-get-tree))
                 #[0 "\301\211 \207" [imenu-create-index-function org-imenu-get-tree] 2]
                 org-bullets-mode org-tempo-setup (lambda nil (electric-indent-local-mode -1))
                 #[0 "\300\301\302\303\304$\207"
                   [add-hook change-major-mode-hook org-show-all append local] 5]
                 #[0 "\300\301\302\303\304$\207"
                   [add-hook change-major-mode-hook org-babel-show-result-all append local] 5]
                 org-babel-result-hide-spec org-babel-hide-all-hashes)
 org-archive-hook '(org-attach-archive-delete-maybe)
 org-confirm-elisp-link-function 'yes-or-no-p
 org-agenda-before-write-hook '(org-agenda-add-entry-text)
 org-metaup-hook '(org-babel-load-in-session-maybe)
 org-bibtex-headline-format-function #[257 "\300 \236A\207" [:title] 3 "\n\n(fn ENTRY)"]
 org-latex-format-drawer-function #[514 "\207" [] 3 "\n\n(fn _ CONTENTS)"]
 org-babel-pre-tangle-hook '(save-buffer)
 org-tab-first-hook '(org-babel-hide-result-toggle-maybe org-babel-header-arg-expand)
 org-babel-load-languages '((emacs-lisp . t) (dot . t) (ditaa . t))
 org-export-backends '(ascii html icalendar latex md confluence re-reveal)
 org-html-creator-string "<a href=\"https://www.gnu.org/software/emacs/\">Emacs</a> 27.1.50 (<a href=\"https://orgmode.org\">Org</a> mode 9.4.5)"
 org-ascii-format-drawer-function #[771 " \207" [] 4 "\n\n(fn NAME CONTENTS WIDTH)"]
 org-agenda-loop-over-headlines-in-active-region nil
 org-occur-hook '(org-first-headline-recenter)
 org-ditaa-jar-path "/usr/share/ditaa/ditaa.jar"
 org-structure-template-alist '(("n" . "notes") ("a" . "export ascii") ("c" . "center")
                                ("C" . "comment") ("e" . "example") ("E" . "export")
                                ("h" . "export html") ("l" . "export latex") ("q" . "quote")
                                ("s" . "src") ("v" . "verse"))
 org-cycle-hook '(org-cycle-hide-archived-subtrees org-cycle-hide-drawers
                  org-cycle-show-empty-lines org-optimize-window-after-visibility-change)
 org-speed-command-hook '(org-speed-command-activate org-babel-speed-command-activate)
 org-export-before-parsing-hook '(org-attach-expand-links)
 org-confirm-shell-link-function 'yes-or-no-p
 org-link-parameters '(("attachment" :follow org-attach-follow :complete org-attach-complete-link)
                       ("id" :follow org-id-open) ("treemacs" :store treemacs-store-org-link)
                       ("eww" :follow org-eww-open :store org-eww-store-link)
                       ("rmail" :follow org-rmail-open :store org-rmail-store-link)
                       ("mhe" :follow org-mhe-open :store org-mhe-store-link)
                       ("irc" :follow org-irc-visit :store org-irc-store-link :export
                        org-irc-export)
                       ("info" :follow org-info-open :export org-info-export :store
                        org-info-store-link)
                       ("gnus" :follow org-gnus-open :store org-gnus-store-link)
                       ("docview" :follow org-docview-open :export org-docview-export :store
                        org-docview-store-link)
                       ("bibtex" :follow org-bibtex-open :store org-bibtex-store-link)
                       ("bbdb" :follow org-bbdb-open :export org-bbdb-export :complete
                        org-bbdb-complete-link :store org-bbdb-store-link)
                       ("w3m" :store org-w3m-store-link) ("file+sys") ("file+emacs")
                       ("shell" :follow org-link--open-shell)
                       ("news" :follow
                        (closure
                         ((scheme . "news") (--dolist-tail--) org-id-link-to-org-use-id
                          clean-buffer-list-kill-buffer-names t)
                         (url arg) (browse-url (concat scheme ":" url) arg))
                        )
                       ("mailto" :follow
                        (closure
                         ((scheme . "mailto") (--dolist-tail--) org-id-link-to-org-use-id
                          clean-buffer-list-kill-buffer-names t)
                         (url arg) (browse-url (concat scheme ":" url) arg))
                        )
                       ("https" :follow
                        (closure
                         ((scheme . "https") (--dolist-tail--) org-id-link-to-org-use-id
                          clean-buffer-list-kill-buffer-names t)
                         (url arg) (browse-url (concat scheme ":" url) arg))
                        )
                       ("http" :follow
                        (closure
                         ((scheme . "http") (--dolist-tail--) org-id-link-to-org-use-id
                          clean-buffer-list-kill-buffer-names t)
                         (url arg) (browse-url (concat scheme ":" url) arg))
                        )
                       ("ftp" :follow
                        (closure
                         ((scheme . "ftp") (--dolist-tail--) org-id-link-to-org-use-id
                          clean-buffer-list-kill-buffer-names t)
                         (url arg) (browse-url (concat scheme ":" url) arg))
                        )
                       ("help" :follow org-link--open-help)
                       ("file" :complete org-link-complete-file)
                       ("elisp" :follow org-link--open-elisp) ("doi" :follow org-link--open-doi))
 org-latex-format-headline-function 'org-latex-format-headline-default-function
 org-export-allow-bind-keywords t
 org-re-reveal-root "https://cdn.jsdelivr.net/npm/reveal.js@3.6.0"
 org-link-elisp-confirm-function 'yes-or-no-p
 org-latex-format-inlinetask-function 'org-latex-format-inlinetask-default-function
 org-tab-before-tab-emulation-hook '(org-tempo-complete-tag)
 org-html-format-drawer-function #[514 "\207" [] 3 "\n\n(fn NAME CONTENTS)"]
 org-latex-packages-alist '(("" "moresize" t) ("" "fancyvrb" t) ("" "inconsolata" t) ("" "tikz" t)
                            ("" "color" t) ("" "listings" t))
 org-latex-classes '(("beamer"
                      "\\documentclass[11pt,aspectratio=169]{beamer}\n                  \\usenavigationsymbolstemplate{} % no navigation bar\n                  \\beamertemplateballitem         % items have little balls"
                      ("\\section{%s}" . "\\section*{%s}")
                      ("\\subsection{%s}" . "\\subsection*{%s}")
                      ("\\subsubsection{%s}" . "\\subsubsection*{%s}"))
                     ("article" "\\documentclass[11pt]{article}"
                      ("\\section{%s}" . "\\section*{%s}")
                      ("\\subsection{%s}" . "\\subsection*{%s}")
                      ("\\subsubsection{%s}" . "\\subsubsection*{%s}")
                      ("\\paragraph{%s}" . "\\paragraph*{%s}")
                      ("\\subparagraph{%s}" . "\\subparagraph*{%s}"))
                     ("report" "\\documentclass[11pt]{report}" ("\\part{%s}" . "\\part*{%s}")
                      ("\\chapter{%s}" . "\\chapter*{%s}") ("\\section{%s}" . "\\section*{%s}")
                      ("\\subsection{%s}" . "\\subsection*{%s}")
                      ("\\subsubsection{%s}" . "\\subsubsection*{%s}"))
                     ("book" "\\documentclass[11pt]{book}" ("\\part{%s}" . "\\part*{%s}")
                      ("\\chapter{%s}" . "\\chapter*{%s}") ("\\section{%s}" . "\\section*{%s}")
                      ("\\subsection{%s}" . "\\subsection*{%s}")
                      ("\\subsubsection{%s}" . "\\subsubsection*{%s}"))
                     )
 org-html-format-headline-function 'org-html-format-headline-default-function
 org-ditaa-eps-jar-path "/home/jet/.config/emacs/elpa/contrib/scripts/DitaaEps.jar"
 org-confirm-babel-evaluate nil
 org-latex-listings-options '(("basicstyle" "\\footnotesize\\ttfamily")
                              ("showstringspaces" "false") ("breaklines" "true"))
 org-re-reveal-title-slide "<h2>%t</h2><h2>%a</h2><h2>%d</h2>"
 )